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Study of 47Ti with the 45Sc(3He, p)47Ti and 45Sc(3He, pγ)47Ti reactions
~
Nuclear Physics A199 (1973) 593--623; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
STUDY OF 47Ti WITH THE 4SSc(3He, p)47Ti AND 4SSc(3He, p~)47Ti REACTIONS L. MEYER-SCHt)TZMEISTER, J. W. SMITH t, G. HARDIE t~ and H. SIEFKEN
Argonne National Laboratory, Argonne, Illinois 60439 ~ and K. T. KNOPFLE, M. ROGGE and C. MAYER-BORICKE
Institut fiir Kernphysik der Kernforschungsanlage Jiilich, Jiilich, Germany Received 7 August 1972 (Revised 10 October 1972)
Abstract: The 45Sc(3He, p)47Ti reaction has been studied at E(3He) = 17 MeV by magnetic analysis with the Argonne split-pole spectrograph. The energy resolution was about 25 keV (FWHM). The excitation energies of 22 levels at excitations up to 7.5 MeV were determined, and the angular distributions associated with them were measured and analyzed in terms of twonucleon transfer DWBA calculations. Angular distributions indicating orbital angular-momentum transfer Lnp = 0 were observed for two states: the analog state at 7.346 MeV and the 3.223 MeV state which is assumed to be the antianalog. The decay of the 47Ti levels was studied by measuring the p-y coincidences in the '~SSc(3He, py) reaction at E(SHe) = 12 and 17 MeV, and level and decay schemes were established on the basis of the results. In the discussion of the properties of the ¢~Ti states, the results of the present work are compared with those obtained in one-nucleon transfer reactions, and all the data are compared with the results of calculations based on two different models for 47Ti. Comparing the reaction data with theory allows us to single out eleven 47Ti states that have simple configurations and are reasonably well described by theory. However, in examining the y-decay data to obtain a more stringent test of the current models, we found the models incapable of accounting for the y-decay of some of these simple states. In particular, the 1.548 MeV state, which seemed to have a large (fl.)6(p~) component, is not well described by the Coriolis-coupling model.
1. Introduction In recent years there have been many studies, both theoretical and experimental, of the 47Ti nucleus. Two different theoretical approaches have been taken. One, by McCullen et al. 1), is a shell-model calculation based on an f~ nucleon configuration. The other, by Malik and Scholz 2), introduces Coriolis forces in the calculation of an f~ nucleon coupled to the collective motions of a deformed core. Both calculations are able to account for the anomalous } - ground state and the low-lying } - first excited state, but they predict different energies and spin sequences for the higher excited states. * Present address: Physics Department, Ohio State University, Columbus, Ohio. ** Also at Physics Department, Western Michigan University, Kalamazoo, Michigan. ** Present address: Physics Department, Greenville College, Greenville, Illinois. **~ Work performed under the auspices of the US Atomic Energy Commission. 593
594
L. MEYER-SCI-IOTZMEISTER et
aL
Experimentally, a number of stripping and pick-up reactions have been studied. These studies indicated large spectroscopic factors for a few levels and, consequently, it is likely that these levels can be described reasonably well theoretically by using a rather simple nucleon configuration. We have extended these studies in 47Ti by investigating the two-nucleon transfer reaction 45Sc(3He, p)47Ti and measuring the angular distributions of the outgoing protons for many 47Ti levels. For the captured n-p pair, most of these angular distributions show orbital angular-momentum transfers Lnp = 0 and thus indicate that both nucleons populate the same shell, predominantly the lf~ shell. TheLnp = 0 transitions peak strongly at 0 ° to the incoming beam. Many of them have a sufficient yield to allow a p-? coincidence experiment. By applying this method to the reaction 45Sc(3He, p?)47Ti, we have studied the ?-decay of some 47Ti levels. The proton detector was placed at 0 ° to favor the L.p = 0 transitions. The strong Lnp = 0 transitions seem to populate a number of states with rather simple nucleon configurations, and since electro-magnetic transitions involve only one-nucleon operators, it may be expected that sometimes the final state reached in the ?-decay will also have a rather simple nucleon configuration. In such cases, the comparison between the measured ?-branching ratios and theoretical results should be of particular interest. Many nuclear properties of the 47Ti levels have been calculated by use of the model of McCullen, Bayman and Zamick 1) (the MBZ model) as well as the Coriolis-coupiing model 2). Theoretical and experimental results of some one- and two-nucleon transfer reactions and of the ?-decay of a few 47Ti levels will be compared. The discussion will include not only our own work on the (aHe, p) and (3He, pT) reactions described in this paper but also the results of earlier investigations.
2. Magnetic spectrograph measurements 2.1. ENERGY LEVELS IN 47Ti The 45Sc(3He, p)47Ti reaction was studied with the Argonne split-pole magnetic spectrograph 3, 4). A 17 MeV 3He ÷+ beam from the Argonne F N tandem Van de Graaff accelerator bombarded a target made t by rolling 45Sc metallic foil to a thickness of 140/tg/cm 2. The protons were detected by Kodak NTB emulsions, 50 ~tm thick, covered with acetate foils to stop particles produced in other reactions. After exposure and photographic developments, the emulsions were scanned by an automatic nuclear-emulsion scanner 5). The resulting proton spectra have in general an energy resolution of 26 keV (FWHM), largely due to energy losses in the target. An additional measurement, made at an angle of 9 ° with a rolled 45Sc target only 80/~g/cm 2 thick, yielded an energy resolution which is good enough to indicate two closely spaced levels (nos. 10 and 11 of fig. 1 at an excitation energy of about 3.2 MeV) that were not resolved in an earlier measurement 6). t We thank Mr. F. J. Karasek, Materials Science Division, Argonne National Laboratory, for preparing the target.
STUDY OF 47Ti
595
Since the ground state of 47Ti is only weakly excited, the energy of the well-populated level at 2.835 MeV is chosen as reference; the energy of all other states in 47Ti are measured relative to it. This particular level is not only a prominent feature of the particle spectrum but also is the starting point of a ?-cascade containing three prominent ?-rays with energies of 2.678, 1.284 and 1.391 MeV (fig. 8 and subsect. 3.2.2). The insert in fig. 8 indicates that these three 7-rays are due to transitions from this level to the first excited state, which measurements with lithium-drifted germanium detectors ~) have shown to lie at 159+__3 keV. This value, combined with the energies of the three ?-rays and their associated uncertainties, yields an excitation energy Ex = 2835_ 10 keV for this prominent level. t~
/
C~ I--
¢n 8 0 0 E E uo 04
d n," W t3.
600
D
O3 3¢;
< n~ 4 0 0
z o I-o
"~ 2 0 0
m
2 11 t 20 ,, -LIt I j
,,
,,
I
u. 0
I
nuJ rn
m z
0
I 4.2
T
-~-
5.4
,
1 -1- q r 6.6 7.8 Q VALUE ( M e V )
l 9.0
'
I 10.2
II . 4
Fig. 1. Proton spectrum of the 4SSc(aHe, p)47Ti reaction measured with the split-pole magnetic spectrograph at an angle of 9 ° to the incoming 17 MeV beam. The target was a rolled 4SSc foil 80/~g/cm2 thick. The energies of the proton groups labeled by numbers are given in table 1, column 2. Below E x = 4 MeV the proton spectrum is simple and only a few levels are strongly excited, while at higher energies the spectrum becomes complex and is dominated by a level at 7.370 MeV which is the analog of the 47Sc ground state with J " = ~ - and T = ~. In fig. 1, the numbered levels of 4VTi are those that either are of interest here or are sufficiently well populated at all angles to stand out from the background. The excitation energies Ex of the numbered levels in fig. 1 are listed in three columns of table 1. The values in column 2 are averages of measurements at a number of angles, though the spread of values was generally less than _ 5 keV over the range of angles. The ?-decay energies (column 7) are those with measured the Ge(Li) counter (sect. 3). Most of these energies agree with those in column 2 within the error of the measure-
2.613
2.835 3.219 3.246 3.817 3.919 4.252 4.705 4.755 5.372 5.458 6.530 6.864 7.370 7.504
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
0+2 0+2 0+2 0 0+2
2 0+2 0+2
0+2 0 0+2
0+2
2 2 2 ?
(2) 0+2
L,p r) I) z) g) r) f) f)
42 4-4 ~) 20 4-2 ~) 9 4-1 e) 3.04-5 e) 6.04-1.0 f) 14 4-2 g) 27 4-3 s) 26 + 3 g) 24 4-4 ~) 32 4-3 g) 26 4-7 ~) 44 4-8 ") 324 4-20 g) 41 4-8 g)
13.84-1.1 s)
2.04-0.5 6.44-0.5 0.74-0.3 1.4±0.5 9.1 4-1.0 4.94-0.6 6.24-0.5 3.44-5
(d(r/dO) ..... (.,ub/sr)
Magnetic spectrograph a)
0.11 0.05 0.02 0.01 0.02 0.04 0.06 0.08 0.08 0.08 0.06 0.09 1.00 0.12
0.04
0.01 0.02 0.01 0.01 0.03 0.02 0.03 0.01
~ Y, ,,= 1
6
0.16 0.06 0.04 0.02 0.06 0.06 0.09 0.13 0.14 0.16 0.09 0.12 1.00 0.20
0.05
0.02 0.03 0.01 0.02 0.08 0.04 0.06 0.02
Y. Y~ sin 0, ,,= 1
7.3464-0.006 7.4804-0.010
2.8354-0.004 3.223
2.6144-0.004
0.157±0.004 1.2494-0.004 1.441 4-0.004 1.5484-0.002 1.7944-0.002 2.1604-0.002
E~ (MeV)
v-decay b)
1
3
1 1 1 1 3
3
0.82
0.9
2.4 0.7 0.06 0.32 1.3
5.1
/,1 ( 2 J f + l ) S g
(d, p studies ¢)
3
0.76
0.54G-)
3
3
0.17({--) 0.29(]-) 0.25(~-)
~ 0.2 h)
3.18
Cz5¢
3
1 h)
3
1,
(3He, or) studies a)
7.37
3.913
3.276
2.615 2.835
0.159 1.247 1.442 1.549 1.793 2.161 2.545
o
E~ (Mev)
~-
~-; T =
½-, 8 -
½-
~(~-)
.~~-, ~~-, ~~½~-, ~.~-
jn
Ref. 9) Summary ")
") The quantities ~Y, and ;EY, sin 0,, where the Y, are the yields at 0, = 5 °, 10 °, 15 °, 20 °, 30 ° and 40 °, are used as a measure of the integrated cross sections of the (3He, p) reactions. b) These y-ray energies were measured with the Ge(Li) detector. ~) Ref. 19). a) Ref. 6). ~/ Most likely spin assignment in view of both the earlier and the present studies. r) Value at about 20 ° (lab). ~) Value at 7 ° (lab). ") Ref. 9).
0.012 0.150 1.245 1.455 1.545 1.788 2.162 2.530
E~ (MeV)
0 1 2 3 4 5 6 7
no.
Level
TABLE 1
Comparisons among the present magnetic-spectrograph results, the present v-decay results, the (d, p) studies of R a p a p o r t et al. 19) and the (3He, ct) studies of Rao et al. 6)
-I N
r~ ,<
STUDY OF *TTi
597
ments. In only a few cases is the difference larger than a few keV. For example, the ground state is 12 keV too high relative to the prominent 2.835 MeV level (whose energy was obtained in the y-ray measurement and taken as reference energy). On the other hand, the first excited state is too low; its magnetic-spectrograph value is only 150 keV instead of the well-established 159 keV [ref. 7)]. Finally the high excitation energies (those near 7.4 MeV) obtained with the y-detector are about 25 keV smaller than those measured with the magnetic spectrograph, as they were also in a previous experiment s). The values o f E x from other work (column 12), from a Nuclear Data Sheets compilation 9) based mainly on measurements on one-nucleon transfer reactions, are given only for levels that are not difficult to relate to those seen in our (3He, p) study. Throughout this paper, the energy values obtained from the ~-ray measurements (table 1, column 7) were used whenever available. 2.2. A N G U L A R DISTRIBUTIONS
Angular distributions of the protons from the 4 5Sc(3He ' p),TTi reaction have been measured at nine angles in the range 0lab = 7 °-35°. We concentrated on these very forward angles both because these are the most important ones in determining the orbital angular-momentum transfer and because, for this rather low-yield reaction, only the forward cross sections are large enough that a sufficient number of proton tracks in the nuclear emulsions could be obtained in a reasonable exposure time. At some angles, the proton groups of interest were masked by impurities and no cross section could be obtained. The angular distributions of all proton groups except those belonging to the 1.249 and 1.411 MeV levels in table 1 are shown in figs. 2-4. These two angular distributions are rather fiat and somewhat uncertain because of the low proton yield, as indicated in column 4 of table 1. Many of the other angular distributions display characteristic patterns more strongly. The forward-peaked ones are presented in fig. 2, those with a maximum yield at about 20 ° in fig. 3 and the remaining ones in fig. 4. Angular distributions of five levels at excitation energies 0.0, 0.157, 2.160, 2.835 and 3.223 MeV (the latter as an unresolved pair) have been studied before by Rao et al. 6) in the same reaction. Although these authors used a beam energy of 13 MeV, their angular distributions differ little from those we measured with a beam energy of 17 MeV, in agreement with the assumption of direct-interaction mechanisms. In nearly all cases, their cross sections reported at a specific angle are slightly higher than ours at the same angle, but the two sets of data agree with each other within the experimental error. DWBA calculations (subsect. 2.3) indicate that the cross sections in the angular range studied are expected to increase by about 10-15 ~ when the beam energy is raised from 13 to 17 MeV. Consequently, according to DWBA calculations, our cross-section values are somewhat lower than those reported by Rao et al. 6). 2.3. ANALYSIS OF THE A N G U L A R DISTRIBUTIONS
The orbital angular-momentum transfer of the n-p pair in the 45Sc(3He, p)*7Ti
598
L. MEYER-SCI-IOTZMEISTER et aL
r e a c t i o n is d e t e r m i n e d by c o m p a r i n g the m e a s u r e d a n g u l a r d i s t r i b u t i o n s with those c a l c u l a t e d in the d i s t o r t e d - w a v e B o r n a p p r o x i m a t i o n by use o f the code T W O P A R [ref. 1 o)]t. T h e initial optical p o t e n t i a l s were those o f R a o et aL 6). T h e y were slightly c h a n g e d to give a g o o d fit to the m e a s u r e d a n g u l a r d i s t r i b u t i o n f o r the a n a l o g state at 7.346 MeV. T h e p a r a m e t e r s finally used for all calculations are listed in table 2. T h e p o t e n t i a l well o f the transferred nucleon p a i r was a d j u s t e d by the T W O P A R c o d e to I0.0~----
7
i --
-i~-~lO0.Ol--
,ooL- " ~.
F
-4
oooLX ?
-
\
..._
-E,=7 ~46 M,v
\ ! .
,0.05
. . . .
o*
Do* co*
-
#
I E xE3=3.223MeV .223MI " ...
o*
io*
20"
30 °
30*
~c.rN.
Fig. 2. Angular distributions of protons from the 4SSc(aHe, p)47Ti reaction with a strong contribution of orbital angular-momentum transfer L.p = 0, as identified by forward peaking of the distribution. The energy of the 3He beam was 17 MeV. Circles indicate the measured results; the solid lines were obtained by DWBA calculations for L.p = 0 with the code TWOPAR j o) and the optical potentials of table 2. give the right b i n d i n g energy EB for each o f the nucleons, a n d we have chosen this to be EB = ½(IS.pl-Ex), where S,p represents the n-p p a i r s e p a r a t i o n energy o f - 17.011 M e V for the A T = 0 t r a n s i t i o n s a n d - 19.236 M e V f o r A T = 1, a n d E X is the excitation energy o f the states in the 47Ti nucleus. A l t h o u g h the e x t r a c t i o n o f We are grateful to B. F. Bayman for making this code available to us.
,o.o~--~-~
I.O~-
"~
5.0z -
~ ,,.o ~("
,.79,
,
,
~
°
5.0-
b
1o
5.00+1~1 i~÷~' ,1, t '~ =o"
zo °
3o °
8c.m. Fig. 3. Same as fig. 2 except that L.p = 2.
I0.0~
I
I I : Ex=Z.530 MeV--
I0.0~ ~ 3.246
I0.01
5.oiI ~t
-
6
5.oI
I
I
--
Ex=4.755
MeV-
5.372
t ~-
-
-
I0. :-
I.
3
I
5"ii
3.817
5.458
4.705
6.530
(~~
I.
5o~~o / ,~,1,o
,o
4.~5j+
50-
I •
I0
i
I
I
I0 °
20*
I
50"
to °
I 20*
I
-
30*
OC. m. Fig. 4. S a m e as fig. 2 except t h a t L.p is u n d e t e r m i n e d a n d no D W B A calculations were m a d e
L. M E Y E R - S C H O T Z M E I S T E R et al.
600
TABLE 2 The optical potentials and parameters used in the D W B A calculations Unbound particle p aHe
V (MeV)
av (fm)
rv (fm)
53.6
0.61
1.217
160.0
0.734
1.13
W (MeV)
aw (fm)
0 16.21
r~v (fm)
Ws (MeV)
as (fm)
rs (fm~
0.61
1.217
17. l
0.31
1.26
1.13
0.734
0
0.753
1.604
The potential for these u n b o u n d particles is Vtot
=
Vfv (r) --i I/Vfw (r) -k4ias Wsfs'(r),
--
where fx : {1-}-exp [(r--r~A~})/ax]} - t , a n d f ' indicates the derivative. The bound neutron and proton move in a potential with the parameters av = 0.65 fm, rv = 1.2 fro. The real potential well is adjusted by the program until it gives the binding energy Ea = ½ []S,p[--Ex ], where Ex is the excitation energy o f the final nucleus and S,p is the separation energy o f the n-p pair. For the T = 1 transfer we used S ° p : --19.236 MeV and for the T : 0 transfer S,p = --17.011 M e V . The potential contains a spin-orbit term.
spectroscopic factors in the (3He, p) reaction is doubtful, the orbital angular momenta L,p transferred by the n-p pair can be obtained since the shape of the angular distribution depends almost entirely on L.p. This is shown in fig. 5, in which calculated lo) angular distributions are plotted for a n-p pair transfer into the 3.919 MeV level with total angular momentum J = 3 and orbital angular momentum L,p = 2. Curve (a) is the result of placing both nucleons in the lf~ shell; curve (b) is for the transfer of one of the nucleons to the lf~ shell and the other to the 2p~ shell. Both angular distributions have the same shape, but the cross sections are larger when the 2p shell is populated. To form the low-lying states in 47Ti, the n-p pair will be preferentially absorbed in the 2p and If shells and one therefore expects some angular distributions that show I
'
"~ 2 0 -
l
×
l X
X
o
i
'
I
'
I
'
X
X
X
X
~
o
X
X
~, 1 0 - -
'
X
x
X
b X
7,
5 0
0
0
0
0
z
0 0
o
ti
0 O o
i
o*
I
I0"
,
t
20*
,
i
30*
,
t 40 °
t
I
50*
o t
60*
70*
0e. rn. Fig. 5. D W B A calculations [code T W O P A R 1o) and optical potentials o f table 2] for the 4SSc(aHe, p)47Ti reaction populating the 3.919 MeV 47Ti level. The n-p pair transfers 3 units o f total angular m o m e n t u m to the target nucleus; the orbital angular-momentum transfer is L,~ = 2. Curve (a): both nucleons are transferred into the lf~ shell. Curve (b): One nucleon is placed in the lf~_ shell, the other in the 2p~ shell.
STUDY OF 't7Ti
601
the characteristic pattern of Lop = 0 and 2 transfer reactions. The distributions for which Lap = 0 is predominant are plotted in fig. 2. The two measured curves for the isobaric analog at 7.346 MeV and the state at 3.223 MeV are well fitted by the calculation with the optical parameters listed in table 2, AT = l, Sap = - 19.236 MeV, and the assumption of a pure Lap - 0 contribution. These calculated angular distributons (solid lines) are normalized to the data. All other angular distributions in fig. 2 were calculated on the assumptions that AT = 0 and that the separation energy Snp is the deuteron value So = - 17.01 MeV. This smaller value of Snp makes the calculated curves slightly steeper. In contrast to the good fit for the distributions for the states at 7.346 and 3.223 MeV, the measured angular distributions for the states at 0.157, 2.614, 2.835, 6.864 and 7.480 MeV all show the same large deviation from the calculated Lap = 0 curve: the first theoretical minimum is filled in for each. We take this deviation as an indication of an L,p = 2 contribution. In earlier studies 11), the pure Lap -- 0 angular distribution is connected with the transfer of an n-p pair in its singlet state to populate the isobaric analog state and the corresponding antianalog state with T -- T<. The states showing Lop = 0 + 2 contributions in the (aHe, p) reaction, however, may be formed by the n-p pair in its triplet state. Consequently, the pure Lnp = 0 angular distribution found for the 3.223 MeV state leads to the belief that this state is formed by an n-p transfer with S = 0, T = 1 and hence has the assignment J~ = 7 - , T = ~. The patterns of the five angular distributions shown in fig. 3 are compatible with the assumption of L,p = 2 transitions, for which them aximum yield is at about 20 °. All are well fitted by the angular distributions (solid lines) calculated with pure Lap = 2 transfers and S,o = -17.011 MeV. In the (da/dt2)c.m" column of table l, the strengths of these five transitions are indicated by the yields at 20 ° where the cross section is maximum.
3. Particle-? coincidence measurements 3.1. EXPERIMENTAL PROCEDURES The 45Sc(aHe, p?)47Ti reaction was studied at Heidelberg with the 12 MeV 3He beam of the EN tandem Van de Graaff of the Max-Planck Institute (MPI) and at Argonne (ANL) with the 17 MeV 3He beam of the FN tandem Van de Graaff. The experimental arrangements used in both cases had been described earlier s, 12--14), SO only a few essential details are given. In this description, the M P I values are given first and the A N L values follow in parentheses. The M P I target consisted of a 1 mg/cm 2 45Sc layer evaporated on a 290 mg/cm 2 Au foil, while the A N L target was a rolled 0.9 mg/cm 2 4SSc foil backed by an Au foil 150 mg/cm 2 thick. The Au foil stopped the incident 3He beam but allowed the high~ energy protons and deuterons from the (3He, p) and (3He, d) reactions with Q = 11.508 and 4.857 MeV, respectively, to reach the particle detectors with little energy loss. As seen in fig. 6, however, the energy resolution of the particle spectrum deteriorated, the width increasing to several hundred keV. The particle detector, thick
602
L. M E Y E R - S C I - [ O T Z M E I S T E R e t aL
16
14
(D hi t.) Z l.d iS)
t IC"
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s
8 -!
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6
==>=
~:
• ]E Z
4 0 "7" F-
2 0
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I 400 600 800 PROTON ENERGY (channel number) Fig. 6. P r o t o n s p e c t r u m o f the 45Sc(aI-Ie, p)47Ti reaction in coincidence with all ),-rays. T h e labels on the peaks indicate s o m e 4?Ti levels p o p u l a t e d in this reaction a n d also s o m e 46Ti levels excited by the 45Sc(aHe, d)46Ti reaction. A n arrow indicates the t h r e s h o l d o f the 4~Sc(aHe, np)46Ti reaction. I
I
I
I
I
20
= 2 . 4 5 7 MeV
I0 e~
u)
bJ
o
z
bJ
o
0ow
z bJ
"
° Z
-
30 0
--
,~
=
_
/~X
E7 "
-2.678
7.187Mev
MeV-
-
I0 o ¢'> It.
M. 020 0c
0
0¢
m
ET,= 1 . 5 4 8
--,.¢x dot
',J
Z
xl 6O0
~_
MeV
EX=7"480MeV Z
I
I
650
700
750
I 800
850
PROTON ENERGY (ehonnel number) Fig. 7. Portions of the 4~Sc(3He, p ) 4 ; T i proton spectra measured in coincidence with the indicated ),-rays. These are typical o f the decay o f a n u m b e r o f the '~?Ti states s h o w n in fig. 12. T h e observed ),-energies E l, = 7.480, 7.187, 2.678, 2.457 a n d 1.548 M e V originate f r o m the '~?Ti states at 7.480, 7.346. 2.835, 2.614 and 1.548 MeV, respectively. In order to o b t a i n better statistics, the doubleescape peaks at 6.458 a n d 6.167 M e V were used for the ),-rays o f energies 7.480 a n d 7.187 MeV, respectively. Since the coincidence c o u n t i n g rate is very small, 17 p r o t o n channels were s u m m e d a n d the resulting coincidence rate was assigned to the middle c h a n n e l n u m b e r . This p r o c e d u r e was repeated at 4-channel intervals.
STUDY OF *YTi
603
enough to stop all proton groups, was located at 0 ° to the incoming beam and subtended an angle of +28 ° at MPI (+__10° at ANL). A lithium-drifted germanium counter with an active volume of 38.5 cm 3 (30 cm 3) was located at 90 ° (80 ° ) to the incoming beam. The ?-ray detector subtended an angle of + 19°(+ 17°) and the efficiency as a function of the energy has been measured in earlier experiments s, 22). The width (FWHM) of the ?-ray lines, which is mainly due to the high counting rates, was 6 keV at Er = 2 MeV and 12 keV at 6 MeV for the detectors used. Details of the electronic measuring system and the data-taking procedures are described elsewhere s, 12 - 1,). The cross section of the *SSc(3He, p?)*7Ti reaction is rather small for particle-? coincidence experiments. Unfortunately one cannot compensate for this by using larger beam currents since the particles and ?-rays from the high-yield reactions *SSc(3He, d?)46Ti and *SSc(3He, np?)46Ti limit the counting rate in the detectors. The spectrum of particles in coincidence with all ?-rays, which is the one of present interest, is shown in fig. 6. The peaks at large particle energies are due to the "5Sc (3He, p?)47Ti reaction and are well separated from the deuterons produced in the 45Sc(3He, d?)*6Ti reaction. One of the pronounced peaks is from the 7.346 MeV analog state in *YTi, and the others are from excited states in *6Ti; the first two (at 0.889 and 2.009 MeV) are marked. The 2.835 MeV levels in *YTi is barely seen in the spectrum. All these peaks are on a smooth background which rises steeply with decreasing particle energy. To a great extent this is due to the *SSc(3He, np?)46Ti reaction. The threshold for the population of the ground state in *6Ti by the (3He, np) reaction is indicated in fig. 6 by the arrow labeled (3He, np). A particle spectrum of more interest for the present investigations is obtained by selecting the protons in coincidence with those ?-rays that proceed from states in *7Ti and that appear to be undisturbed by ?-rays of neighboring states. Parts of five such proton spectra are displayed in fig. 7. The three spectra at the right are for protons in coincidence with ?-rays of energy Er = 2.457 MeV (top curve), 2.678 MeV (middle), and 1.548 MeV (bottom), while the two at the left are for protons in coincidence with the 7.187 and 7-.480 MeV ?-rays (with double-escape peaks, the most prominent ones in the ?-spectrum, at Er = 6.167 and 6.458 MeV, respectively). Since the y-rays with which these plots are associated proceed from the states at 7.480, 7.346, 2.835, 2.614 and 1.548 MeV (as seen in fig. 12), these states are indicated by peaks in the coincidence spectrum. Similar spectra of protons in coincidence with other observed ?-rays were used to unravel the ?-decay scheme of the *7Ti levels. Unfortunately we were able to extract ?-decay schemes for only a few *YTi levels because of difficulties in the data analysis: (i) The cross sections of the (3He, p) reaction populating the *YTi levels (table 1) are small. (ii) Although the reactions in the present experiment predominantly populate only a few levels, the level density in *YTi is high: more than 100 levels with Ex < 6 MeV are observed. This high level density led to ambiguities in fitting some of the ?-rays into the level scheme. (iii) In many cases
604
L. MEYER-SCHI~TZMEISTER et aL
the )'-decay is complex. Gamma branches of about 10-20 ~ of the total )'-strength might have been overlooked. (iv) Levels that decay by high-energy )'-rays also result in a relatively large background for the low-energy )'-rays. Hence, as seen in fig. 9 of subsect. 3.2.4. (the)'-ray spectrum of the analog state), the signal-to-noise ratio is small for low-energy )'-rays. 3.2. RESULTS The energy of the )'-ray proceeding from the first excited state could not be measured directly since it was below the lowenergy cut-offat about E~ = 300 keV. Instead, this energy was found as the difference 1.548-1.391 = 0.157_+0.003 MeV between the energies of the two ),-rays proceeding from the 1.548 MeV level. This result is in good agreement with the measured value given in ref. 7). Both the 1.249 and 1.441 MeV levels are supposed to be high-spin states (J~ = ~and ~ - - ) [ref. 1s)]; they are hardly populated by the (3He, p) reaction. Consequently the )'-decay could not be seen in coincidence with the protons populating these levels. However, one would expect that these levels, being so close to the ground state, would be excited by the )'-decay of many high-energy levels. In particular, since our forwardangle measurement of the 4SSc(aHe, p)aTTi reaction favors states with spin J~ = ~--, 7- and ~-, one expects high-spin states at the lower energies to be populated by their decay. Indeed, two prominent )'-rays at relatively low energy (E~ = 1.092_+0.002 and 1.284_+0.002 MeV) consistently appear in coincidence with protons from reactions populating high energy levels. They are assumed to arise from the transitions from the 1.249 and 1.441 MeV levels, respectively, to the first excited state at 0.157 MeV. In agreement with ref. 6) but in contrast to the reported observation 16) of the )'-decay of the 1.249 MeV level, the ground-state transition was not indicated from either level. 3.2.2. The 1.548, 1.794 and 2.160 M e V levels. These three levels are only moderately excited with an L,p = 2 transfer in the (3He, p) reaction, especially in the present arrangement in which the proton detector is placed at forward angles. However, the counting efficiency is relatively high for the low-energy y-rays from these levels, and the spectra have low background. Consequently we have been able to study their )'-decay. The spin assignments of these levels (table 1) are either J~ -- ½- or ½-. Their 7decay had been studied in several earlier experiments: (i) They were populated in the radioactive decay 17) of 47V, whose ground state has spin J~ = ~r-- (ii) The 1.548 and 1.794 MeV levels with J~ = ½- or ~-- were excited is) by E1 )'-decay from the ½+ states in 47Ti from the thermal-neutron capture reaction 46Ti(n, 7)- (iii) The 1.548 MeV level was studied 6) by use of the (p, p')') reaction on 47Ti. Our measurements confirm the earlier conclusion that the 1.548 MeV state decays by the emission of two )'-rays: the ground-state transition with an energy of 1548_+ 2 keV and the 1391 -+2 keV transition to the first excited state. The 1.794 MeV level )'-decays in two branches: a ground-state decay (E~ = 17944- 2 3.2.1. The 0.157, 1.249 and 1.441 M e V levels.
STUDY OF 47Ti
17,18) and
k e Y ) in agreement with refs.
605
the transition ~s) to the 1.548 M e V state.
Since the latter is below the cut-off energy in our y-spectrum, we observe only the subsequent y-ray f r o m the 1.548 M e V level. The 2.160 M e V level decays predominantly to the ground state, although we could detect a y-ray leading to the first excited state. The latter transition was already indicated as a possibility in ref. ~ 7). 3.2.3. The 2.614, 2.835, 3.223 and 7.480 MeV levels. These levels have not been studied before. A l t h o u g h they are m u c h m o r e strongly populated than the 1.548, 130 511
4.
3
5Sc ( He,p ~')"'T
(7/2-)
~[
3223
(5/2-
~ wa ao!; ,,,,,; - e,-.' ~,N . . . . * L
261z.
7/2" 3/2"
'
,1/2-9/2LLI Z Z ,,~ T O
9/2-11/2"
1092
!
t'~
2835
~;f
Ii
l~ I/~1,
i
!
i
, ~]
15'6
1.~i 12z.9
65 5/2 "
128~
LLI be}
I'
0
1391 i
Z
, t 5z.81 ,, i
O C)
200
60~?
{1974)
2~57
2678 i
1000
lz.O0
1800
GAMMA ENERGY (CHANNEL NUMBER)
Fig. 8. Spectrum ofF-rays in coincidence with the proton groups populating the 2.614, 2.835 and 3.223 MeV levels of "7Ti in the reaction 4sSc(SHe, p)4VTi. A typical },-peak width is about 10 channels at the base and about 6 channels at half maximum. The lines whose energies (keV) are indicated in parentheses are not prominent in this spectrum; those at 1.548 and 1.974 MeV have been definitely identified from our other }'-ray measurements, but the 2.835 MeV line is weak even in the best of the other spectra. The dashed lines represent either weak transitions or (in a few cases) those that could not be uniquely fitted into the level scheme. 1.794 and 2.160 M e V levels discussed in subsect. 3.2.2, their decay schemes are difficult to extract. In addition to difficulties due to possible complexity o f their decays and ambiguities in fitting the 7-rays into the level scheme (as mentioned in subsect. 3.1), m o s t o f these states are not populated by pure L,p = 0 transfer but have appreciable L,p = 2 contributions. Consequently the y-rays are not necessarily emitted isotropically and hence those in cascade need not be o f equal intensity. These intensities are therefore not a useful clue in the level-fitting procedure. In fig. 8 is the spectrum o f y-rays in coincidence with protons populating the 2.614,
606
L. MEYER-SCHIDTZMEISTER et al.
2.835 and 3.223 MeV levels, whose 7-decay should therefore be seen. Indeed the 7-rays whose energies are indicated are observed among others, although only two of them (2.457 and 2.678 MeV) are easily fitted into the 7-decay of the 2.835 and 2.614 MeV levels. They indicate strong transitions of both these states to the first excited state. The 1.287, 1.394 and 1.548 MeV 7-rays also are members of cascades from these two levels, and some possible combinations are shown in the insert of fig. 8. The 3.223 MeV level is about as strongly populated in the present experiment as is the 2.614 MeV level (as seen in fig. 1), yet no strong 7-rays belonging to this state are identified. In particular, we observe no strong 7-transition to the ground state or first excited state. However, a weak 7-ray populating the second excited state seems 7:%C I 511
[I i
~-~ '~ f
"
197~
I~
i
,
:
,
,
:
t ,
~
i I'~:8'-
]
, '
1.5
3
47
(He,p~') T,
5c
.
,~s 7,2-
!.
•
~
7480
~"
73/.6
,q
I
7/2-
~lii ; I,,
i
'i~:bi
"
]
i
r
=
3/2~v2-
:
~,~-
31%,n.
261~
12/.9
0
r
j
I
,,,o
¢ 0
I00C GAMMA
2000 ENERGY(CHANNEL
3000
NUMBER}
Fig. 9. Spectrum ofT-rays in coincidence with the proton group from the 45Sc(31-[e, p)47Ti reaction populating the analog state at 7.346 MeV. The three-pronged brackets for the high-energy7-rays indicate the photopeak and the single- and double-escape peaks. The 7-decay of the 7.480 MeV level is also seen. The parentheses and dashed lines have the same significance as in fig. 8. to be present. Consequently we assume that the 7-decay is complex, having many branches of about equal intensities. The 7.480 MeV level 7-decays predominantly to the ground state, in contrast to what is found for all other cases in which the 7-decay of a level populated by L,p = 0 or L,p = 0 + 2 transfer could be observed. 3.2.4. The isobaric analog state at 7.346 M e V . The 7-decay of this state is displayed in fig. 9. The two strong 7-rays leading to the 0.157 and 3.223 MeV levels have relative intensities of 2 and 3, respectively. Although no direct ground-state transition is indicated, the upper limit for the intensity of this transition is fairly high ( < 20 % of that of the 7.189 MeV ),-ray). Two additional strong 7-rays are observed at E = 1.284 and 1.092 MeV. Their
STUDY OF 47Ti
607
energies are the same as those attributed to the decay of the 2.835 MeV level (fig. 8), although we showed that neither this state nor the state at 2.613 MeV is directly excited in the ~-decay of the analog (i.e., the transition probabilities are smaller than 15 and 5%, respectively). In addition, the 1.092 and 1.284 MeV 7-rays are prominent in the spectra taken in coincidence with proton groups leading to excitations in the range E~ = 5-7.5 MeV. These lines could arise in two possible ways: (i)They could originate from the 1.441 and 1.249 MeV states which are not directly populated in the (3He, p) reaction (transition probability < 10 %) but must be populated through ;~-cascades via states at higher energy. (ii) They might well be emitted sequentially, as is indicated in the insert of fig. 9. This possibility requires no further assumptions to explain the experimental fact that these two lines have about equal intensities. The sum of the intensities of the two ~-rays is about the same as the combined strength of the transitions from the isobaric analog state to the 3.223 and 0.157 MeV states. 4.
Discussion
4.1. COMPARISON BETWEEN THE RESULTS OF (3He, p) EXPERIMENTS AND THOSE OF ONE-NUCLEON TRANSFER REACTIONS The 45Sc(3He, p)47Ti reaction populates many low-energy states in 47Ti by transferring the n-p pair into the lf~ and 2p~ shells of the target nucleus. If the pair goes into only one of the shells, the shape of the angular distributions is expected to reflect some contribution of Lnp -- 0 transfer; but if the two nucleons populate different shells, n o Lnp = 0 contributions are possible. Twelve angular distributions have shapes characteristic of orbital angular-momentum transfers Lnp = 0 o r Lnp ---- 0 + 2 and thus one might expect for states at low excitation energies a large ( 1 ~ ) 7 component in the nucleon configuration. This identification is indeed confirmed for a number of states by the one-nucleon transfer reactions - both the 46Ti(d, p)47Ti reaction 19-22) t and the 48Ti(3He, ~)47Ti reaction studied by Rao et al. 6). In these reactions the target nucleus has either a (lf~) 6 or a (lfk) 8 nucleon configuration. The transfer of one nucleon into or out of the lf~ shell leads to 7 - states in 47Ti with (lf~) 7 nucleon configurations. This process is reflected in an angular distribution whose shape is characteristic of an orbital angular-momentum transfer l, = 3. In table 1 the results of these reactions are compared with those of the (3He, p) reaction. We would like to point out that DWBA calculations indicate a larger (3He, p) reaction cross section for the transfer of a nucleon into the 2p~ shell than into the lf_~ shell (see table 3). Consequently even small admixtures of other nuclear components like (lf÷)5(2p~) 2 into a predominant (lf~) 7 nucleon configuration might influence the (3He, p) cross section appreciably 23). Of the twelve states populated by Lnp = 0 or L , , = 0 + 2 transfer in the (3He, p) reaction, the only ones seen in the one-nucleon transfer reactions are the five lowest ones (the states at 0.157, 2.614, 2.835, 3.223 and 3.246 MeV, of which the last two were * We are grateful to W. Haeberli for making some of the results of the 45Sc(d,p)*TTi polarization measurements by W. Haeberli and K. C. Kocher available to us prior to publication.
608
L. M E Y E R - S C H I ~ T Z M E I S T E R
et al.
not resolved in earlier work) and the analog at 7.346 MeV. That they are populated with In = 3 in the latter reactions, as expected, confirms the strong (lf~) 7 characters ot these states. The six states (those at 4.252, 4.705, 5.458, 6.530, 6.864 and 7.480 MeV) are not seen in either of the one-nucleon transfer reactions. It might well be that some of these states are in effect particle states with strong (lf~)~(2p) 2 components in the nucleon configuration. One also expects that one of them will be a state with spin 2~- , T = ½ formed by adding an n-p pair with spin 1 ÷, T = 0 to the 45Sc target with spin 7- T ~ (as explained in subsect. 4.2.4(c) below). Of special interest is the 7.346 MeV analog of the J~ = 7 - , T = ~ ground state of 47Sc. Since its formation should be restricted by isospin selection rules, we expect to find that (i) this state is not populated in the (d, p) reaction, (ii) it is populated freely in the (3He, 0t) reaction, (iii) it is excited in the (3He, p) reaction only if the n-p pair is absorbed in its singlet mode with S = 0, T = 1, and (iv) its excitation via the (3He, p) reaction is connected with an angular distribution of Lnp = 0 [ref. 11)]. TABLE 3 Calculated relative cross sections for a n u m b e r o f different n u c l e o n configurations Configuration
(1 f~_)2
Lnp 0 2 4
(2pgr) z
(lf~_) 2
AJnv = 1 1.0 0.12
(i f~_)2p~_ ZIJap = 3
7.8 0.31
0.27 0.02
1.4 0.04
I n the calculations the code T W O P A R so) a n d the optical potentials o f table 2 were used. T h e cross sections integrated f r o m 0 ° to 60 ° are given, the value for the (lf.~) z cross section has been arbitrarily set equal to 1.0. T h e isospin transfer equals ATnp = 0 a n d the total a n g u l a r m o m e n t u m transfer equals 3 J . p = 1 or 3.
Indeed all four of these predictions are borne out in the experimental results shown in table 1. We observe the same four restrictions for the 3.223 MeV state. For this reason we are tempted to conclude that the 3.223 MeV state has the same spin and spatial nucleon configuration as the analog state but that is has T = T<. That is, it appears to be the antianalog. Since in this case the antianalog is produced by transferring the n-p pair from the (3He, p) reaction into the f÷ nuclear shell already partiallypopulated, the cross section O'AAs is expected to be much less than the cross section a~As connected with the formation of the analog at 7.346 MeV. That is indeed true. The ratio 0"AAS/0"IAs is about 2-~, in rather good agreement with the theoretically estimated value* t W e w o u l d like to t h a n k D. K u r a t h for providing us with the theoretical value. T h e calculation is based o n the following a s s u m p t i o n s : (i) T h e 45Sc target nucleus has seniority 1 a n d is well described by a ~fk n u c l e o n configuration. (ii) T h e n-p pair is transferred in its singlet state with S = 0, T = I. (iii) T h e ratio was n o t corrected for the effect o f the different excitation energies o f the analog a n d antianalog. This latter a p p r o x i m a t i o n s h o u l d have little effect since the Q-value o f the reaction is high.
STUDY OF '*TTi
609
of about 1 : 14. We would like to point out that Hansen and Nathan 24) have recently summarized the available experimental cross sections of (SHe, p) reactions on doubly even target nuclei leading to the 0 + analog and the corresponding antianalog states. In all these examples, the experimentally observed ratio aAAs/tr~As was smaller, often substantially, than the theoretical values given. This is also true in the present case but the discrepancy is relatively small and might well be due to the rough theoretical estimates. In this context it might be questionable if the 3.223 MeV state indeed can be identified with the antianalog. For this reason we have started to study the 45Sc(:~, d)*TTi reaction which should easily populate all states excited by the (3He, p) reaction with Lnp = 0 and Lnp = 0 + 2 transfers except the analog and the antianalog. Preliminary results 2s) of these measurements indicate that indeed the 3.223 MeV state is the ~- antianalog. The angular distributions for the (3He, p) reaction to the states at 1.548, 1.794, 2.168 and 3.919 MeV are characteristic of pure Lnp = 2 transfer. As pointed out earlier in this section, this might indicate a (lf~)62p nucleon configuration for the final states. Such a configuration with spin J = 3- or ½- should easily be excited by the (d, p) reaction with In = 1 but not by the (SHe, a) reaction. This in fact true, as seen in table 1, although the ~z- state at 1.548 MeV which shows most of the In = 1 strength in the (d, p) reaction is also populated by the (3He, ~) reaction, but only weakly. This fact probably indicates some impurity in the assumed nucleon configuration in either the final or the target nucleus or both. Although the ground state of 47Ti has an (f~)7 nucleon configuration 1, 2), it has an anomalous spin of ~- and is not expected to be populated by either the (d, p) or the (SHe, , ) reaction. Indeed it is only weakly excited. Since the same is expected to b~ true for the (SHe, p) reaction, its angular distribution will be discussed in subsect. 4.2.4(b). The states at 1.249 and 1.441 MeV also are only weakly excited in the (d, p) reactions 19) and are not reported in the (3He, ~) work 6). However, they are well populated by the s 0V(p, a)47Ti reaction 15), and this fact led to the assumption that the 1.249 and 1.441 MeV states are high-spin states (J~ -- { - and 1@-) that theory predicts 1, 2) in this energy region. Moreover, as discussed in subsect. 4.2.4(c), both of these states are only weakly populated in the (3He, p) reaction. The states at 1.823 and 2.371 MeV are excited by In = 2 and l~ = 0 transfer in the (3He, a) reaction; they are assumed to be ld~ and 2s½ hole states 6). Hence they should not be populated by the (SHe, p) reaction, and indeed they are hardly seen in it. They are not listed in table 1. 4.2. COMPARISON BETWEEN THEORETICAL PREDICTIONS AND EXPERIMENTAL RESULTS ON PARTICLE REACTIONS LEADING TO *TTi TWO theoretical approaches will be considered in the comparison with the experimental data. One by McCullen et al. 1) is based on shell-model calculations using only f~ nucleon configurations and thus excludes levels with nucleon excitation into higher shells. The other, by Malik and Scholz 2), is the Coriolis-coupling model which
610
L. MEYER-SCH{)TZMEISTER
et al.
includes configurations in which nucleons are excited to the p-shell as well. Both models have been used to calculate n o t only energy-level schemes and spectroscopic factors for some pick-up and stripping reactions but also electromagnetic transition probabilities. The c o m p a r i s o n between these theoretical results and the available experimental data thus constitutes a test o f the models. 3"~r
(MeV) l l
7/2---
Jf
(MeV)
--7.480
I~--7.346 ----6.884
712--- I~,S __ 6.64 //
----6.530 /,/
----5.45e -----5.372
5/2~'-//
- - ' ~
//
----4.252
7/24__---3.90
9/2i/ 5r2~ - -
3/2-, I / 2 - - - -
~3.919
~3.87
- - 3.09
7/2,~ /2.78 3/2~--~=~===.--- 2.71 9/2~/ ~2.70
712~" .
/4.755 4.705
- - 5.52
jlr
(MIV)
~,/2~--
--4.54.
5/~ . . . . .
5/24 - -
4.34
--';.02
~3.817 ./-3.246 ~3.223
7/2-~(5/2-)--
- - 2.835 .~2.614
7/2-----
I/2 i --3.72 I/2~----.~. I--3.51 9/2-~_ __.J 3.26 7/z ~ / 3.14 5/2 --!
512~-~
'
5/2~
~
/
~ .02
2.75
/2.52
--2.45
9/2~'-~1.80 i/2~'/__"~i .71
~/2~
~,,~1.60
1I / 2 / /
~
3/2~'--
- - 1.01
5/2~
--0.30
7/2~'--
--0.160
M B Z
1/2--3/2--~
- --I.794 --1.548 ~IA41
H/2-,9/~'~ 1.43
7/2----5/2---
--0.157 --0 EXPT.
I/2f--~__~-I
.69
7 / 2 ~ - " ~ _ _ ~ I. 56 3/2i/ ~].51 9/2~--
- - 1.02
7/2~". . . . . 5/2~---
t~-0.183 -- 0
MALIK
a SCHOLZ
Fig. 10. Experimental and theoretical level schemes of 47Ti. The experimental results include those of both the present investigations and refs. 17-22). The theoretical results are those of refs. 26-28). 4.2.1. Energy-level scheme. In the 47Ti level schemes shown in fig. 10, the energies measured in this experiment and their spin assignments - b o t h the established ones and (in parentheses) those suggested f r o m the present and earlier work 9,17-22) _ are c o m p a r e d with the calculated energies and spins f r o m refs. 26-28) t. Both models t We are grateful to B. F. Bayrnan and J. D. McCullen for providing us with the calculations
based on the MBZ model. The calculations based on the model of Malik and Scholz were provided by J. R. Comfort.
STUDY OF 47Ti
611
[refs. 1, 2)] are able to place both the ½- and ~- states close to the ground state along with the ~ - - and ~- as required by the experimental data. However, the level energies and the spin sequences are different. Of course, excitation energies and spin assignments do not reveal much information about the nucleon configuration associated with the states. Much more information will be obtained by comparing calculated and measured spectroscopic factors for nucleon-transfer reactions populating the states in question. 4.2.2. Spectroscopic factors for the 46Ti(d,p)47Ti reaction. Table 4 shows the experimental results reported in refs. 19 - 22) and the theoretical values from refs. 26.28 ). Since the calculations of ref. 26) are restricted to the lf~ nucleon configuration, they apply only to 1, = 3 transfers; but those of ref. 2a) include excitations into the lf~,~ and 2p~p, shells and hence predict spectroscopic factors for In --- 3 and In = 1 transfers. In both calculations the In = 3 strength of the lf~ shell is concentrated in the lowest -~- state, in good agreement with the experimental results. In fact, the measured 19,22) spectroscopic factor for the state at 0.157 MeV is (2Jr+ 1)5a ~ 5 although a value of 4 exhausts the shell-model sum rule 29). For this reason one might be tempted to assume that the states at 2.614 and 2.835 MeV, also populated by In = 3 transfer, have spin ~ - with a nucleon in the f~ shell. The calculations of ref. 2a) indeed predict such a state with a relatively large spectroscopic factor at an energy of about 2.5 MeV (as seen in table 4). However, recent experiments 20, 22) indicate that at least the 2.614 MeV state has J~ = ~-. The spin of the 2.835 MeV state is uncertain and might well be ~-. This result is somewhat unsatisfactory both because it implies that the experimental spectroscopic factors for the f~r shell are grossly overestimated (at least 50 % greater than the sum-rule limit) and because it is strange that so little strength for 1n = 3 transitions into the f~ shell is observed for excitation energies up to more than 5 MeV. The agreement between experimental and theoretical results is quite good for the In = 1 transitions leading into the p~ shell. More than half of the measured strength is concentrated on the ½- state at 1.548 MeV, while the rest is most likely for transitions to states with higher excitation energies. Many such states are populated by In = 1 transfers, but no spin assignments can be made at present. Theoretically, as seen in table 4, one finds that nearly half of the l --- 1 strength for transitions populating ½- states is concentrated on one state (the one at 1.84 MeV, which is the second ~ - state and is distinguished hereafter as ½2), and the rest is distributed anaong transitions to states at higher excitation energies. Reasonable agreement between theory and experiment is also observed for the l = 1 strength for the population of ½- states. About a third of that strength is experimentally associated with a low-energy state at 1.794 MeV, while theoretically about a fifth of the total strength is to a state at 1.69 MeV. 4.2.3. Spectroscopic factors for the 4aTi(3He, ~)4 7Ti reaction. In table 5 the measured spectroscopic factors reported in ref. 6) are compared with the ones calculated by use of the f~ shell model 1). The agreement between experiment and theory for the
612
L. MEYER-SCH1]TZMEISTER et al.
- levels is g o o d . M o s t o f the s t r e n g t h is c o n c e n t r a t e d in the t r a n s i t i o n to t h e l o w e s t 7-
state at 0.157 M e V , a n d the s t r e n g t h f o r p o p u l a t i n g t h e 3.223 M e V state is in
r e a s o n a b l e a g r e e m e n t w i t h t h e p r e d i c t i o n s m a d e f o r t h e c a l c u l a t e d level at 2.78 M e V . TABLE 4 Spectroscopic factors (2Jr+ 1)6P for the 46Ti(d, p)47Ti reaction Measured refs. 19-21)
Calculated ref. 22)
Ex jrr (2J~+1)5¢ l,, J~r(ZJt-~l)SP (MeV) 0.0 ~0.157 ~-1.548 ~1.799 (½-) 2.160 2.530 2.614 2.789 2.835 3.545 3.676 3.919 ½-, ~4.637 4.924 5.013 5.580 5.810 5.810
5.1 2.36 0.71 0.06 0.32 1.32 0.25 0.89 0.20 0.48 0.82 0.21 0.1 0.13 0.32 0.31 0.33
3 I I
~-
4.64
1 1
3
~--
1.46
ref. 26)
ref. 28) jTr ( 2 J t q - l ) J 1,
E~
(MeV) 0 0.183 1.51 1.56 1.69
~~~-~½1.84 ~-2.46 ~2.52 ~2.75 ~-3.02 ~3.14 7z3.51 t3.72 ½4.020 ~4.34 ~4.54 :a-
0.009 3.20 0.06 0.67 0.41 1.75 0.05 2.0 0.11 2 x 1 0 -5 0.14 0.02 6 x 1 0 -7 0.12 1.40 1.4
Ex (MeV)
3 3 I 3 1
jz, (2jt_~l)Sa
l,
0.157 2.45 2.78
~½5-
3.94 0.04 0.016
3 3 3
3.90
~-
0.000
3
l
3 3 3 1 3 1 1 1 3 1
TABLE 5 Spectroscopic factor C25 a for the 4STi(3He, ~)47Ti reaction Measured a)
Calculated b)
Ex (MeV)
j~r
0.157
?z~-~--
3.18 0.17 0.29
3
,~½(.~-) ~-
0.25 0.43 0.54 0.19 0.76
3
2.614 2.835 3.223 3.558 7.346*
C26a
1
E~
jn
C2~ '
l
(MeV)
* Isobaric analog state.
~) Ref. 6).
3
3 3 3
0.16
'~1 -
4.77
3
2.45
']z-
0.14
3
2.78
~3-
0.55
3
6.64*
~-
0.40
3
~) Refs. t.6).
A t h i g h e x c i t a t i o n e n e r g y , the full s t r e n g t h f o r the t r a n s i t i o n to the a n a l o g state ( w h i c h is o b s e r v e d at 7.346 M e V t h o u g h the c a l c u l a t i o n s w o u l d p l a c e it at 6.64 M e V ) is p i e d i c t e d to be 0.4; t h e m e a s u r e d v a l u e is 0.76. T h e l a t t e r is m o s t likely a n o v e r -
STUDY OF 47Ti
613
estimate due to the difficulties in the extraction of spectroscopic factors, an explanation that is also indicated by the results obtained in the studies of the 4STi(p, d)47Ti reaction 30). The spectroscopic factors measured in this latter work are all somewhat lower than those of ref. 6); in particular, that for populating the analog state is 0.34, which is close to the theoretical limit of 0.4. In conclusion, the comparison between the measured and calculated transition strengths in the (d, p) and (3He, ~) reactions populating 47Ti levels leads to a more appropriate coordination of measured and calculated states than is obtained by comparing the measured and calculated level schemes shown in fig. 10. For example, the first calculated ½- level at 1.51 MeV surely does not represent the measured ~r- state at 1.548 MeV, but the calculated ½2 state at 1.84 MeV does (table 4). TABLE 6 Possible coordination between experimental and theoretical 47Ti levels as established by use of
spectroscopic factors for one-nucleon transfer reactions [refs. 6.19-22.26.2S)l Exp. Ez (MeV) 0.0 0.157 1.249 1.441 1.548 1.794 2.614 2.835 3.223 3.919 7.346*
jzr
~½~-, a~~ t - , ~.~½6(~--) 6½-, { 6-
MBZ Ex (MeV)
Jrrn
0.30 0.16 1.80
~-1½t~t-
2.45
62-
2.78
~3-
6.64
6- *
Malik and Scholz Ex (MeV) J% 0.0 0.183 1.02 1.83 1.84 1.69 1.56 2.52 2.46; 3.14 (4.54)
~l ½1~1~132½, 62~263;*({5-)
* Isobaric analog state.
As a result of this comparison between measurements and calculations, we have ten states that are reasonably well described by theory, as shown in table 6. For four of these states (those at 2.614, 2.835, 3.223 and 3.919 MeV), the coordination is uncertain - mostly because of their relatively small spectroscopic factors in the (d, p) and (3He, 00 reactions. 4.2.4. The two-nucleon (3He, p) transfer reaction. The cross sections and the angular distributions for the 45Sc(3He, p)47Ti reaction leading to a number of states in 47Ti were calculated in ref. 26) (MBZ). The results for a few ~-, ½-, 3 - and ~ states and the isobaric analog are shown in table 7. Since more than one total angular momentum Jnp of a transferred n-p pair can lead to a given final state, these calculations involve a summation over all Jnp terms. The strengths of the different J,p contri, butions are given for the reactions to a number of 47Ti levels. When the n-p pair is transferred in its singlet mode ( S = 0, T = 1), the orbital angular-momentum transfer is Lnp = Jnp; and since the only prominent states in our spectra are those populated
614
L. MEYER-SCHOTZMEISTER et aL
in the (3He, p) reaction without parity change, the Jnp values are even. However, for an n-p pair transferred in its triplet mode ( S = 1, T = 0) J,p is odd and the orbital angular-momentum transfer has the two values Lnp = J , p + 1. The angular distributions that follow from the J.p values of table 7 are calculated with the code TWOPAR ~0) by use of the optical potentials of table 2. A few of these angular distributions are shown in fig. 11 and their shapes and strengths will be compared with the experimental results. Most of these distributions are for reactions to states that were found to be well described by the MBZ model in subsects. 4.2.2 and 4.2.3. (a) The analog state. Several total angular-momentum transfers J,p contribute to the formation of most of the 47Ti states listed in table 7; no single J,p term predominates. An obvious exception is the analog state whose calculated excitation energy (MBZ) is 6.64 MeV. It is formed primarily o f J . p = 0 transfer so Lnp --- 0. Since the measured angular distribution of the analog state was well represented by a pure L,p = 0 transfer, as discussed in subsect. 2.3 and seen in fig. 2, the calculated angular distribution derived from table 7 is expected to fit the measured one well. In fact, it gives a slightly better fit since the weak contribution of higher J,p terms (table 7) will decrease the deep minimum at about 33 ° and bring the calculated and measured values even closer together. This is seen in fig. 1 la, in which the calculated curve is plotted as a solid line labeled by the measured excitation energy of 7.346 MeV, while the measured angular distribution is indicated by open circles. (b) The states with spin assignment ~- or ~-. In subsects. 4.2.1.-4.2.3, it was shown that the ground state and the first excited state are well described by the MBZ model, and that consequently the (3He, p) calculations might be able to predict the measured angular distributions of both states. This is indeed true for the ground state. Of all the ~- states indicated in table 7, only the ground state has an angular distribution that has a broad maximum at an angle of about 25 ° and fits the measured distribution within the experimental error. This is shown in fig. I ld, where the calculations are represented by a solid line and the measurements by crosses. However, the calculated angular distribution of the first excited state (the ~" state at E x = 0.16 MeV) deviates markedly from the measured one. The ~ - and ~2 states at the MBZ energies 0.16 and 2.45 MeV show nearly fiat distributions because high J.p terms play an important role. The calculated distribution for the ~- state is shown as a solid line in fig. 1 lc; the measured angular distribution of the 0.157 MeV state is indicated by open circles. In contrast to the calculated angular distributions, it seems to show a strong L,p = 0 contribution. In fact, all known ~ - levels show measured angular distributions with strong L,p = 0 contributions (as seen in table 1). This discrepancy between the m~asured and calculated angular distributions is seen for the ½~" and ~ states, for example. However, the theoretical curve in fig. 1 lb shows a strong L,p = 0 contribution to the k~ state at Ex(MBZ) = 2.78 MeV, which may correspond to the measured level at 3.223 MeV. But even for this state, the measured and calculated angular distributions disagree markedly. In fact, with the exception of the analog, 11o calculated angular distribution for a 7-z state shows a pure L.p = 0 transfer similar
STUDY OF *TTi
615
to that measured for this 3.223 MeV state. Note that pure Lap = 0 transfers are calculated not only for the ~- analog state but also for the {~ and {~ states (as seen in table 7). However, these two states cannot be associated with the 3.223 MeV state whose rather strong population in the (3He, ~) reaction makes the { - and { - spin assignments most unlikely for this state. (c) The ~- states. The states at 1.249 and 1.441 MeV are considered to be the first states with spin as high as J = { - or ~ - . They have small cross sections, and consequently their measured angular distributions are uncertain. In fig. 1le, the mea'
400i
1
'
I
'
I
'
:_
7.348 MeV (7/2-, I A S I
-
2
4C
o
2C
2
IC
'
I
'
I
' j
0 • 57Me
7
j.
I)
I--
IOC ~' 6C =
I
4
o
20(
'
O.:.~_..
d g.s. ( 5/2t-1
2L-
~
T
T
~
_
E e 3
4
~
2
0.
3.223 MeV(7/2£)
.J.
o*
f~ 1.441MeV
2~-~.[
0.E
0.4
1.2
T
O.
,
f,
I
io*
zo*
,
°"4I-,~1 ~,
,
30*
40*
o*
io*
I,
20*
I , -
30*
40*
Oe.m.
Fig. 11. Comparison of calculated and measured angular distributions for the 45Sc(3He,p)*TTi reactions leading to a few selected *TTilevels. Circles and crosses represent the data, solid and dashed lines the calculations. The experimentally established levels are marked by their excitation energies; their theoretical identifications are in parentheses. In angular distribution (e), the crosses are the values for the 1.441 MeV state, the circles are those for the 1.249 MeV state.
sured angular distributions for the 1.441 and 1.249 MeV levels are given by crosses and open circles, respectively, and the calculated ones for the 1.80 and 2.17 MeV levels (the first two { - states from the MBZ calculation) are plotted as the solid and the dashed line, respectively. Although the uncertainty in the measurements is too great for a good comparison, it is obvious that neither the experimental nor the calculated angular distribution shows a strong Lap = 0 contribution. Neither in theory nor in fact, therefore, does the lowest { - state include an appreciable component corresponding to the nucleon configuration of the target nucleus into which an n-p
616
L. MEYER-SCHOTZMEISTER et aL
pair in its S = I, T = 0 state has been transferred with Lnp = 0. In the MBZ calculation, the state formed by transfer of this latter n-p pair is the 2~; level at a calculated energy of 3.87 MeV, as indicated in table 7 by its angular distribution with strong Lnp = 0 contributions. Since such a state is not expected to be populated by onenucleon transfer reactions, it is most likely one of the six states observed at higher excitation energy. As mentioned in subsect. 4.1, these states are indeed not populated by a one-nucleon transfer reaction and their angular distributions in the (3He, p) reaction show strong Lnp = 0 contributions. (d) Transition strengths in the (3He, p) reaction. As a measure of the transition strengths in the (3He, p) reaction populating different 47Ti states, we have formed the sums ~ Y . and ~ Y . sin 0., where Y. is the yield at the angles 0. = 5 °, 10 °, 15°, 20 °, 30 ° and 40 ° and the sum is over these six angles. These sums for the calculated 2 6) and for the measured results are listed in table 7. The measured results are also shown in table 1. The values are normalized to the analog state, whose value was set to 1.00. The peculiar set of angles was chosen in order to de-emphasize the larger angles, at which the yields Y. often are small and the associated errors are large. The experimental Y. values were obtained from a smooth curve drawn through the measured points of the angular distribution. Although the use of ~ Y . sin 0n or ~ Y . to compare transition strengths is rather arbitrary, some firm conclusions can be drawn from thevalues in table 7. The measured transition strength to the analog state is very much larger than that for any other state, but the calculated strength for the analog is comparable to those of the others. For a few states that are reasonably well described by the MBZ model (especially the J = ~ - ground state, the 7 - state at 0.157 MeV and the ~2 - state either at 1.249 or 1.441 MeV), the experimental strength is at most a few percent of that for the analog; but their calculated strengths are comparable to (though smaller than) that of the analog state. In conclusion, we find that the MBZ calculations of the (3He, p) reactions are able to reproduce the angular distributions for some states that are reasonably well described by the theory. However, the calculated transition strengths show much less variation than the experimental ones do. In particular, the theory does not predict either the strong enhancement of the transfer leading to the analog state or the weak transitions to the ~ - ground state and to the ~ - state at 1.249 or 1.441 MeV. This failure to indicate the strong enhancement of the transfer leading to the analog state, is a fact which agrees well with the observations 31) in the (t, p) reactions of f~ nuclei. Here also the measured cross sections of the ground-state transitions (orbital angular momentum transfer L . . = 0) are larger (by a factor of six) than the ones calculated by the MBZ theory. 4.3. GAMMA-DECAYS OF STATES IN 47Ti The comparison between the calculated and measured v-decays tests the validity of the theoretical models even more stringently than does the comparison between the
~-
~-
]27,-3 -
-,]-4-
2.17 3.87 0.16 2.45 2.78 3.90 6.64* 0.30 1.60 3.09 5.52 1.01 2.16 2.71
1.80
0.0380 0.2823 0.0021 0.0067 0.0778 0.0213 0 0.0019 0.0930 0.1021 0.1126
0.0470 0 0.0336 0.1344 0.0211 0.043 0.0337 0.0742 0.3334 0.0360 0.0011 0.108 0.0594 0.2676
0.0139
2
0.0944 0 0.1555 0.00783 0.0330 0.0422 0 0.1847 0.0232 0.0481 0.0015 0.1412 0.039 0.0160
0.0363
3
0.0160 0.0364 0.3479 0.4243 0.0007 0.0008 0 0.0482 0.0007 0.0242 0.0022 0.3136 0.0781 0.0627
0.0449
5
0.0460 0.0157 0.3885 0.0000 0.0157 0.0002 0.0001 0.1271 0.1108 0.0029 0.0004
0.1576
6
7
0.1312 0.0247 0.0732 0.0523 0.0019 0.0030 0
0.1139
b) Tentative correlation.
0.0065 0.0009 0.2289 0.1331 0.0305 0.0018 0.0667 0.0755 0.0273 0.0767 0.0001 0.1505 0.6075 0.0444
0.3148
4
Calculated strength contributed by J,p t e r m
0.0048
1
a) T w o alternative values,
0.0155 0.0224 0.0196 0.0003 0.4889
F~ (MBZ) Jop = 0 (MeV)
* Isobaric analog state,
t
~t
] ~•
•.~
T
~2-
½-
TABLE 7
Yn
1.44
1.00
0.45 0.67 0.44 0.30 0.41 0.19 0.19
1.00
0.26 0.49 0.36 0.29 0.22 0.10 0.11
1.15 0.87 0.48
1.30
0.66 0.53 0.41
0.60
0.50
7.346 0.00
0.157 2.614 b) 3.223 b)
1.249 1.441 a)
1.00 0.01
0.02 0.04 0.05
0.01 0.01 "~)
Y' Yn n=l
6
n=l
1.00 0.02
0.03 0.05 0.06
0.01 0.02 ")
Yn sin
M e a s u r e d (table 1)
~ Yn sin 0, Ex *~1 (MeV)
0.43
0.26
,=1
6
Calculated
Calculated strengths 26) contributed by total a n g u l a r - m o m e n t u m transfers J~p = 0 - 7 in 45Sc(aHe, p)47Ti reactions leading to several 47Ti levels (which are listed in order o f decreasing If )
0,,
©
,q
O~
618
L. MEYER-SCH(JTZMEISTER et aL
transition strengths in nucleon-transfer reactions. Of course, the only states one can hope to understand are those with rather simple nucleon configurations: A few such states in table 6 are singled out by their large spectroscopic factors in nucleon-transfer reactions, and the ones whose y-decay we were able to study will now be discussed. In the decay scheme shown in fig. 12, our data are at the right and the earlier results [refs. 17. ~8)] are at the left. Most of the y-rays studied so far proceed from levels with spin assignment J~ = ½- or ~:- since the observations were made by using the reaction 46Ti(n, y)gYTi, which leads through a ½+ resonance ~7), or by studying the radioactive decay x6) of 47V whose spin is ~--. Two exceptions are the high-spin states at 1.249 and 1.441 MeV, which had been investigated by the (p, p'y) reaction 6) and by heavy-ion Coulomb excitation ~6). The 47Ti states whose y-decay was studied in the present experiment but not in earlier ones include some with spins ~ - and ~-. Of these, the analog state is especially important since its y-decay is observed and its simple nucleon configuration allows the calculation of this y-decay. The results shown in fig. 12 indicate that, as had been observed for isobaric analogs in many other fp shell nuclei 32-34), the y-decay is complex. In the sd shell nuclei, however, several strong M1 transitions from the analog state to its antianalog have been observed. Ern6 et al. 35) were the first to see and recognize such a transition (in 38Ar) and have related it to the process in which an unpaired f~ nucleon recouples in isospin space to an inert (d~)" core in such a way that the isospin decreases by one unit and the antianalog state results. More recently, Kurath 36) has shown that such strong M1 transitions are unlikely in fp shell nuclei since the core consists of f~ nucleons that will participate in the y-decay. Interferences between the y-transition amplitudes of the core and those of the unpaired nucleon might cause strong population of states other than the antianalog and consequently the transition strength to the latter will be reduced. This agrees well with our results that we see the y-decay to the antianalog, but that this transition is not dominant. 4.3.1. M B Z calculations. Since the MBZ model restricts its configuration space to the f~ nuclear shell, only the ground state of 47Ti, the first excited state, and a few of the others listed in table 6 are well described by this model. As a test of the model, therefore, the most important state whose y-decay we have studied in the analog. Its y-decay and that of a few others predicted by MBZ calculation 27) are shown in fig. 13. The MBZ states and those found experimentally are coordinated according to table 6. There is little doubt that the .}~-, ½l- and 97 states represent the experimental states at 0.0, 0.157 and 1.249 or 1.441 MeV, respectively, and we assume that the ~2 and ~3 states correspond to the levels at 2.614 and 3.223 MeV. A comparison between figs. 12 and 13 shows that in agreement with the MBZ calculations, the analog has a rather complex y-decay and, in particular, shows two strong transitions (with about the right intensity ratio) leading to the states at 0.157 and 3.223 MeV; no direct transition to either the 1.249 or 1.441 MeV state is observed. However, the predicted y-rays leading to the 2.614 MeV state and the ground state have not been detected in our experiment.
S T U D Y O F 47Ti
619
The absence or low intensity of any direct ground-state transition is observed not only for the analog but also in all other ~- and ½- low-energy states (namely those at 2.614, 2.835 and 3.223 MeV) which we were able to study by the (3He, p?) reaction, Ex (keV) 7480 7346
j~
~2--
2O 5340 3925 3685 3556 32:>3 2835 2"798 2614 2556 2533 2160 17"94 1548 144 I 1249 157 0
112. 312-
! 1I
(5/2-)-7/23/2-
I/2-
3/2"
T
4) 1~ .
9/2-, 11/2-
.
-
/
7/2-~ 5
/
2
r
-
~
m
_1
4 7T i Fig. 12. G a m m a decay o f 47Ti. T h e decay indicated on the r i g h t - h a n d side represents the present results, that on the left-hand side shows the results f r o m refs. 6, 17, 18). Each vertical line represents y-transitions to t h e final state indicated by the arrow point; a n arrow that does n o t e n d on one o f the levels in the d i a g r a m represents a transition that c a n n o t be fitted uniquely into the level scheme. T h e circles m a r k the levels f r o m which the y-rays originate; the transitions indicated by filled circles are definite, those indicated by open circles are weak or uncertain. 27
(MeV} 7. 346
....
(MBZ) 7/2-, IAS
7/2; 9/21
7/2 i 0
v
5/27
Fig. 13. T h e y-decay o f a few 47Ti levels as calculated by use o f the M B Z m o d e l 27).
while the MBZ calculations display a strong direct ground-state transition for the 52 state. The only direct ground-state transition which we were able to observe belongs to a state at the high excitation energy Ex = 7.480 MeV.
620
L. MEYER-SCHtJTZMEISTER et al.
4.3.2. Calculations with the Coriolis-coupling model. The 47Ti levels that seem to be reasonably well described by this model are shown in table 6. For most of these states, both measured and calculated ?-decay schemes are available. The calculated ones are shown in fig. 14, where the measured energies of the levels are given on the left and the theoretical spins and parities are at the right. For the 3.223 MeV level, we consider two possible states: ~3 and ~-. The isobaric analog is also included although the model does not produce analog states. In calculating the decay of this 47Ti state, the wave function used was that of the corresponding state, namely the 47Sc ground state. The strengths of the ~-ray transitions to the different 47Ti levels were then calculated, and the decay scheme of this nucleus was derived by using the measured level energies. (MeV) 7.346 .
3.223--
Ref. 28 .
.
.
.
.
'
7/2~ 4
5/z? Fig. 14. The ~,-decay of some 47Ti levels as calculated by applying the Coriolis-coupling model =8).
For the initial calculations, the parameters of ref. 2) were used. Most of the results were very similar to those displayed in fig. 14, which were calculated with the set of parameters used in the final calculations. The exception was the ~-decay of the ½2 state at 1.548 MeV, for which a very different decay scheme was predicted by the initial calculations. They called for a predominant M 1 transition to the ground state. However, the fact that the measured intensities of the ~-rays to the first excited state and to the ground state are about equal indicates strong electric-quadrupole contributions. Since the calculated ~}2 state and the measured state at 1.548 MeV are very strongly populated in the (d, p) reaction with 1, = 1 transfer, no mistake in the coordination between experiment and theory (table 4) seems possible. The discrepancy in the ~,decay must then indicate that this level is not well described by the Coriolis-coupling model with the parameters of ref. 2). Comfort 28) was kind enough to repeat the calculation with different parameters. In fact, the changes in these parameters were slight and in agreement with his earlier studies ~ ) , and they produced hardly any variation in the spectroscopic factors of any of the levels under consideration. Even the decay schemes and the branching ratios shown in fig. 14 were not appreciably
STUDY OF 47Ti
621
changed for any level except the ] 2 state. Its branching ratio changed drastically while the lifetime varied over two orders of magnitude. This indicates that this level with a large p~ nuclear component is only poorly described by the Coriolis-coupling model. In contrast to this anomalous behavior of the ½2 state at 1.548 MeV, the ½7 state - whose reasonably large spectroscopic factor for the (d, p) reaction with 1. = 1 transfer indicates a P~r nuclear component - showed only small changes when the parameters were varied as described; its lifetime varies only by a factor of 2. Thus this state seems to be well described by the Coriolis-coupling model, although (as seen in figs. 12 and 14) the experimental and theoretical 7-decay schemes do not agree well. The experiment shows a strong electric quadrupole transition to the ground state, while theoretically the M1 transition to the state at 1.548 MeV dominates by far. In this case, however, the coordination of the ½~- state to the 1.794 MeV level is less certain than that of the ½2 state to the 1.548 MeV level. The Coriolis-coupling predictions of the y-decays of the ~ - and ~- levels at 2.614, 2.835 and 3.223 MeV are similar to those from the MBZ calculations in that the most pronounced transitions are those to the ground state and first excited state. However, the experiment indicates no ground-state transition except a possible weak one from the 2.835 MeV state. The strong transitions to the first excited state are in agreement with the theory. The measured and the calculated y-spectra of the analog state at 7.346 MeV agree in that both show a complicated decay with a relatively strong branch to the first excited state. However, much as in the MBZ results, the Coriolis-coupling model shows a reasonably strong transition to the ground state - strong enough that it should be observed in the experiment. Actually, however, it is not; the calculated intensity of this decay branch is at least 2-3 times the experimental upper limit. Although the calculations do not predict the experimentally observed y-decay from the analog to the 3.223 MeV state, theory and experiment agree that there is no transition (or at most a weak one) either to the ½2 state at 1.548 MeV or to the ~7 state at 1.249 MeV. 5. Conclusion
Both the MBZ and the Coriolis-coupling models are able to produce a level scheme for ~VTi that agrees reasonably well with energies and spin assignments of levels obtained experimentally. For some of these levels, both theory and experiment indicate large spectroscopic factors in one-nucleon transfer reactions, and hence a correlation between some of these theoretically and experimentally established states is possible. For the (d, p) reaction, the spectroscopic factors calculated with the MBZ model 26) are more strongly concentrated on the first ~-- state than are the experimental ones. The theoretical spectroscopic factors for the (3He, c~) reaction, however, are quite consistent with the experimental values 2, 6). The MBZ calculations for some ~- and ~ - states populated by the 45Sc(3He, p)47Ti
622
L. MEYER-SCHOTZMEISTER et al.
reaction 26) display rather flat angular distributions because of strong contributions of high orbital angular momentum L.p in the n-p pair transfer. Experimentally, however, all but one of the known 3 - and ~- levels are associated with forward-peaked angular distributions indicating strong L,p = 0 contributions. The one exception, the 3 - ground state, shows a rather flat distribution which is fitted well within the experimental error by the curve calculated from the MBZ model. An even better fit between the calculated and measured angular distribution is obtained for the analog state at 7.346 MeV, which is excited with almost pure L.p = 0 transfer. The measured relative transition strengths of the (3He, p) reactions leading to the 47Ti levels differ greatly from those calculated with the MBZ model 26) Experimentally, the analog is populated far more strongly than is any other state, at least by a factor of 5 and in many cases by a factor of about 50. However, the MBZ theory predicts that the transition strengths to most studied levels are comparable with that of the analog state. In only a few cases does the calculated strength differ by a factor 5-10. Thus the 45Sc(3He ' p)47Ti reaction is actually much more selective in populating the analog than the MBZ model predicts. This fact is already indicated by (t, p) reactions on f~_ shell nuclei. The observed L.n = 0 transitions 31) are by a factor six stronger than those calculated by the MBZ model. The (d, p) spectroscopic factors predicted by the Coriolis-coupling model - not only for levels with the nucleon configuration (fg_)" but also for those with p~,~ f~-1 o r f ~g_ f , - 1 configuration - seem to satisfactorily fit the experimental results reported in refs. 19-22). Difficulties arise, however, when the calculated y-decays of the p~_ and pa states are compared with the observed ones. For the ~ - state at 1.84 MeV, the calculated ~-decay varies strongly with small changes of the parameters chosen for the calculation, while the calculated y-strength for the ½~-, 2~z, 22,3,4-, 79 - and _1~_~ 2I states hardly vary at all in response to the same changes. This behavior indicates that the latter states might be well described by the Coriolis-coupling model in its present state but that the p~ state at 1.84 MeV is not. Similar discrepancies are observed for the first p~ state, if indeed it can be identified with the state at 1.794 MeV. Theoretically, this state is supposed to decay by a dominant M1 transition to the 51~ state at 1.84 MeV, but experimentally a strong E2 transition to the ground state is observed in addition to the y-ray leading to the 1.548 MeV state. The analog state at 7.346 MeV shows a complex y-decay and has no dominant 7branch leading to any one low energy level. The complex y-decay of the analog is predicted by both the MBZ and the Coriolis-coupling model, and both also call for two strong y-transitions that indeed are seen experimentally. However, the predicted transitions to the ground state and to some low-lying ~ - states are not seen in our experiment. We wish to thank Dr. B. F. Bayman, Dr. J. D. McCullen and Dr. J. R. Comfort not only for the calculations of some properties in the production and in the 7-decay of the 47Ti nucleus but also for many fruitful discussions. We are also indebted to
STUDY OF 47Ti
623
D r . D . K u r a t h , D r . R . D . L a w s o n a n d D r . F. B. M a l i k f o r s t i m u l a t i n g discussions. W e are v e r y g r a t e f u l to D r . W . H a e b e r l i f o r m a k i n g us a w a r e o f s o m e o f his results o n t h e r e a c t i o n 46Ti(d, p ) 4 7 T i b e f o r e final p u b l i c a t i o n . O n e o f us (G. H . ) wishes to t h a n k t h e W e s t e r n M i c h i g a n U n i v e r s i t y Office o f R e s e a r c h S e r v i c e s f o r p a r t i a l supp o r t o f this w o r k t h r o u g h a f a c u l t y r e s e a r c h grant.
References l) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36)
J. D. McCullen, B. F. Bayman and L. Zamick, Phys. Rev. 134 (1964) B515 F. B. Malik and W. Scholz, Phys. Rev. 150 (1966) 919 J. R. Erskine, Argonne National Laboratory report ANL-7641 (1969) p. 7 J. R. Erskine, Argonne National Laboratory report ANL-7728 (1970) p. 43 J. R. Erskine and R. H. Vonderohe, Nucl. Instr. 81 (1970) 221 M. N. Rao, J. Rapaport, T. A. Belote and W. E. Dorenbusch, Nucl. Phys. A151 (1970) 351 R. E. Wood, J. M. Palms and P. Venugopala Rao, Nucl. Phys. A126 (1969) 300 K. T. KnSpfle, M. Rogge, C. Mayer-B6ricke, D. S. Gemmell, L. Meyer-Schiitzmeister, H. Ohnuma and N. G. Puttaswamy, Phys. Rev. C4 (1971) 818 M. B. Lewis, compiler, Nucl. Data Sheets II4 (1970) 313 B. F. Bayman, private communication L. Meyer-Schtitzmeister and D. S. Gemmell, Phys. Rev. Lett. 27 (1971) 869 L. Meyer-Schiitzmeister, D. S. Gemmell, R. E. Holland, F. T. Kuchnir, H. Ohnuma and N. G. Puttaswamy, Phys. Rev. 187 (1969) 1210 James W. Smith, Ph.D. thesis, Indiana University, Bloomington, Indiana, June 1971 Karl-Tasso Kn6pfle, Ph.D. thesis, Heidelberg University, Heidelberg, Germany, 1971 W. F. Buhl, D. Kovar, J. R. Comfort, O. Hansen and D. J. Pullen, Nucl. Phys. A131 (1969) 99 O. F. Afonin, A. P. Grinberg, I. Kh. Lemberg and I. N. Chugunov, Sov. J. Nucl. Phys. 6 (1968) 160 B. Rosner and L. Broman, Nucl. Phys. 100 (1967) 59 J. Tenenbaum, R. Moreh, Y. Wand, B. Arad and G. Ben-David, Phys. Rev. 177 (1969) 1595 J. Rapaport, A. Sperduto and W. W. Buechner, Phys. Rev. 143 (1966) 808 G. Brown, A. Denning, A. E. MacGregor and R. N. Glover, Nucl. Phys. A165 (1971) 641 J. L. Alty, L. L. Green, G. D. Jones and J. F. Sharpey-Schafer, Nucl. Phys. A100 (1967) 191 W. Haeberli, private communication D. G. Fleming, R. A. Broglia, K. Abd.o, O. Nathan, D. J. Pullen, B. Rosner and O. Hansen, Phys. Rev. C5 (1972) 1356 O. I-[ansen and O. Nathan, Phys. Rev. Lett. 27 (1971) 1810 L. Meyer-Schtitzmeister, G. Hardie and T. Braid, to be published B. F. Bayman, private communication J. D. McCullen, private communication J. R. Comfort, private communication M. H. Macfarlane and J. B. French, Rev. Mod. Phys. 32 (1960) 567 R. Sherr, B. F. Bayman, E. Rost, M. E. Rickey and C. G. Hoot, Phys. Rev. 139 (1965) B1272 R. F. Casten, E. R. Flynn, O. Hansen and T. J. Mulligan, Phys. Rev. C4 (1971) 130 G. B. Vingiani, G. Chilosi and W. Bruynesteyn, Phys. Lett. 26B (1968) 285 J. C. Legg, D. G. Megli, D. R. Abraham, L. D. Ellsworth and S. Hechtl, Phys. Rev. 186 (1969) 1138 S. Maripuu, Nucl. Phys. A149 (1970) 593 F. C. Ern6, W. A. M. Veltman and J. A. Jr. Wintermans, Nucl. Phys. 88 (1966) 1 D. Kurath, Bull. Am. Phys. Soc. 13 (1968) 1400; Argonne National Laboratory report No. ANL-7512 (1968) p. 84
Nuclear Physics A199 (1973) 593--623; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
STUDY OF 47Ti WITH THE 4SSc(3He, p)47Ti AND 4SSc(3He, p~)47Ti REACTIONS L. MEYER-SCHt)TZMEISTER, J. W. SMITH t, G. HARDIE t~ and H. SIEFKEN
Argonne National Laboratory, Argonne, Illinois 60439 ~ and K. T. KNOPFLE, M. ROGGE and C. MAYER-BORICKE
Institut fiir Kernphysik der Kernforschungsanlage Jiilich, Jiilich, Germany Received 7 August 1972 (Revised 10 October 1972)
Abstract: The 45Sc(3He, p)47Ti reaction has been studied at E(3He) = 17 MeV by magnetic analysis with the Argonne split-pole spectrograph. The energy resolution was about 25 keV (FWHM). The excitation energies of 22 levels at excitations up to 7.5 MeV were determined, and the angular distributions associated with them were measured and analyzed in terms of twonucleon transfer DWBA calculations. Angular distributions indicating orbital angular-momentum transfer Lnp = 0 were observed for two states: the analog state at 7.346 MeV and the 3.223 MeV state which is assumed to be the antianalog. The decay of the 47Ti levels was studied by measuring the p-y coincidences in the '~SSc(3He, py) reaction at E(SHe) = 12 and 17 MeV, and level and decay schemes were established on the basis of the results. In the discussion of the properties of the ¢~Ti states, the results of the present work are compared with those obtained in one-nucleon transfer reactions, and all the data are compared with the results of calculations based on two different models for 47Ti. Comparing the reaction data with theory allows us to single out eleven 47Ti states that have simple configurations and are reasonably well described by theory. However, in examining the y-decay data to obtain a more stringent test of the current models, we found the models incapable of accounting for the y-decay of some of these simple states. In particular, the 1.548 MeV state, which seemed to have a large (fl.)6(p~) component, is not well described by the Coriolis-coupling model.
1. Introduction In recent years there have been many studies, both theoretical and experimental, of the 47Ti nucleus. Two different theoretical approaches have been taken. One, by McCullen et al. 1), is a shell-model calculation based on an f~ nucleon configuration. The other, by Malik and Scholz 2), introduces Coriolis forces in the calculation of an f~ nucleon coupled to the collective motions of a deformed core. Both calculations are able to account for the anomalous } - ground state and the low-lying } - first excited state, but they predict different energies and spin sequences for the higher excited states. * Present address: Physics Department, Ohio State University, Columbus, Ohio. ** Also at Physics Department, Western Michigan University, Kalamazoo, Michigan. ** Present address: Physics Department, Greenville College, Greenville, Illinois. **~ Work performed under the auspices of the US Atomic Energy Commission. 593
594
L. MEYER-SCI-IOTZMEISTER et
aL
Experimentally, a number of stripping and pick-up reactions have been studied. These studies indicated large spectroscopic factors for a few levels and, consequently, it is likely that these levels can be described reasonably well theoretically by using a rather simple nucleon configuration. We have extended these studies in 47Ti by investigating the two-nucleon transfer reaction 45Sc(3He, p)47Ti and measuring the angular distributions of the outgoing protons for many 47Ti levels. For the captured n-p pair, most of these angular distributions show orbital angular-momentum transfers Lnp = 0 and thus indicate that both nucleons populate the same shell, predominantly the lf~ shell. TheLnp = 0 transitions peak strongly at 0 ° to the incoming beam. Many of them have a sufficient yield to allow a p-? coincidence experiment. By applying this method to the reaction 45Sc(3He, p?)47Ti, we have studied the ?-decay of some 47Ti levels. The proton detector was placed at 0 ° to favor the L.p = 0 transitions. The strong Lnp = 0 transitions seem to populate a number of states with rather simple nucleon configurations, and since electro-magnetic transitions involve only one-nucleon operators, it may be expected that sometimes the final state reached in the ?-decay will also have a rather simple nucleon configuration. In such cases, the comparison between the measured ?-branching ratios and theoretical results should be of particular interest. Many nuclear properties of the 47Ti levels have been calculated by use of the model of McCullen, Bayman and Zamick 1) (the MBZ model) as well as the Coriolis-coupiing model 2). Theoretical and experimental results of some one- and two-nucleon transfer reactions and of the ?-decay of a few 47Ti levels will be compared. The discussion will include not only our own work on the (aHe, p) and (3He, pT) reactions described in this paper but also the results of earlier investigations.
2. Magnetic spectrograph measurements 2.1. ENERGY LEVELS IN 47Ti The 45Sc(3He, p)47Ti reaction was studied with the Argonne split-pole magnetic spectrograph 3, 4). A 17 MeV 3He ÷+ beam from the Argonne F N tandem Van de Graaff accelerator bombarded a target made t by rolling 45Sc metallic foil to a thickness of 140/tg/cm 2. The protons were detected by Kodak NTB emulsions, 50 ~tm thick, covered with acetate foils to stop particles produced in other reactions. After exposure and photographic developments, the emulsions were scanned by an automatic nuclear-emulsion scanner 5). The resulting proton spectra have in general an energy resolution of 26 keV (FWHM), largely due to energy losses in the target. An additional measurement, made at an angle of 9 ° with a rolled 45Sc target only 80/~g/cm 2 thick, yielded an energy resolution which is good enough to indicate two closely spaced levels (nos. 10 and 11 of fig. 1 at an excitation energy of about 3.2 MeV) that were not resolved in an earlier measurement 6). t We thank Mr. F. J. Karasek, Materials Science Division, Argonne National Laboratory, for preparing the target.
STUDY OF 47Ti
595
Since the ground state of 47Ti is only weakly excited, the energy of the well-populated level at 2.835 MeV is chosen as reference; the energy of all other states in 47Ti are measured relative to it. This particular level is not only a prominent feature of the particle spectrum but also is the starting point of a ?-cascade containing three prominent ?-rays with energies of 2.678, 1.284 and 1.391 MeV (fig. 8 and subsect. 3.2.2). The insert in fig. 8 indicates that these three 7-rays are due to transitions from this level to the first excited state, which measurements with lithium-drifted germanium detectors ~) have shown to lie at 159+__3 keV. This value, combined with the energies of the three ?-rays and their associated uncertainties, yields an excitation energy Ex = 2835_ 10 keV for this prominent level. t~
/
C~ I--
¢n 8 0 0 E E uo 04
d n," W t3.
600
D
O3 3¢;
< n~ 4 0 0
z o I-o
"~ 2 0 0
m
2 11 t 20 ,, -LIt I j
,,
,,
I
u. 0
I
nuJ rn
m z
0
I 4.2
T
-~-
5.4
,
1 -1- q r 6.6 7.8 Q VALUE ( M e V )
l 9.0
'
I 10.2
II . 4
Fig. 1. Proton spectrum of the 4SSc(aHe, p)47Ti reaction measured with the split-pole magnetic spectrograph at an angle of 9 ° to the incoming 17 MeV beam. The target was a rolled 4SSc foil 80/~g/cm2 thick. The energies of the proton groups labeled by numbers are given in table 1, column 2. Below E x = 4 MeV the proton spectrum is simple and only a few levels are strongly excited, while at higher energies the spectrum becomes complex and is dominated by a level at 7.370 MeV which is the analog of the 47Sc ground state with J " = ~ - and T = ~. In fig. 1, the numbered levels of 4VTi are those that either are of interest here or are sufficiently well populated at all angles to stand out from the background. The excitation energies Ex of the numbered levels in fig. 1 are listed in three columns of table 1. The values in column 2 are averages of measurements at a number of angles, though the spread of values was generally less than _ 5 keV over the range of angles. The ?-decay energies (column 7) are those with measured the Ge(Li) counter (sect. 3). Most of these energies agree with those in column 2 within the error of the measure-
2.613
2.835 3.219 3.246 3.817 3.919 4.252 4.705 4.755 5.372 5.458 6.530 6.864 7.370 7.504
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22
0+2 0+2 0+2 0 0+2
2 0+2 0+2
0+2 0 0+2
0+2
2 2 2 ?
(2) 0+2
L,p r) I) z) g) r) f) f)
42 4-4 ~) 20 4-2 ~) 9 4-1 e) 3.04-5 e) 6.04-1.0 f) 14 4-2 g) 27 4-3 s) 26 + 3 g) 24 4-4 ~) 32 4-3 g) 26 4-7 ~) 44 4-8 ") 324 4-20 g) 41 4-8 g)
13.84-1.1 s)
2.04-0.5 6.44-0.5 0.74-0.3 1.4±0.5 9.1 4-1.0 4.94-0.6 6.24-0.5 3.44-5
(d(r/dO) ..... (.,ub/sr)
Magnetic spectrograph a)
0.11 0.05 0.02 0.01 0.02 0.04 0.06 0.08 0.08 0.08 0.06 0.09 1.00 0.12
0.04
0.01 0.02 0.01 0.01 0.03 0.02 0.03 0.01
~ Y, ,,= 1
6
0.16 0.06 0.04 0.02 0.06 0.06 0.09 0.13 0.14 0.16 0.09 0.12 1.00 0.20
0.05
0.02 0.03 0.01 0.02 0.08 0.04 0.06 0.02
Y. Y~ sin 0, ,,= 1
7.3464-0.006 7.4804-0.010
2.8354-0.004 3.223
2.6144-0.004
0.157±0.004 1.2494-0.004 1.441 4-0.004 1.5484-0.002 1.7944-0.002 2.1604-0.002
E~ (MeV)
v-decay b)
1
3
1 1 1 1 3
3
0.82
0.9
2.4 0.7 0.06 0.32 1.3
5.1
/,1 ( 2 J f + l ) S g
(d, p studies ¢)
3
0.76
0.54G-)
3
3
0.17({--) 0.29(]-) 0.25(~-)
~ 0.2 h)
3.18
Cz5¢
3
1 h)
3
1,
(3He, or) studies a)
7.37
3.913
3.276
2.615 2.835
0.159 1.247 1.442 1.549 1.793 2.161 2.545
o
E~ (Mev)
~-
~-; T =
½-, 8 -
½-
~(~-)
.~~-, ~~-, ~~½~-, ~.~-
jn
Ref. 9) Summary ")
") The quantities ~Y, and ;EY, sin 0,, where the Y, are the yields at 0, = 5 °, 10 °, 15 °, 20 °, 30 ° and 40 °, are used as a measure of the integrated cross sections of the (3He, p) reactions. b) These y-ray energies were measured with the Ge(Li) detector. ~) Ref. 19). a) Ref. 6). ~/ Most likely spin assignment in view of both the earlier and the present studies. r) Value at about 20 ° (lab). ~) Value at 7 ° (lab). ") Ref. 9).
0.012 0.150 1.245 1.455 1.545 1.788 2.162 2.530
E~ (MeV)
0 1 2 3 4 5 6 7
no.
Level
TABLE 1
Comparisons among the present magnetic-spectrograph results, the present v-decay results, the (d, p) studies of R a p a p o r t et al. 19) and the (3He, ct) studies of Rao et al. 6)
-I N
r~ ,<
STUDY OF *TTi
597
ments. In only a few cases is the difference larger than a few keV. For example, the ground state is 12 keV too high relative to the prominent 2.835 MeV level (whose energy was obtained in the y-ray measurement and taken as reference energy). On the other hand, the first excited state is too low; its magnetic-spectrograph value is only 150 keV instead of the well-established 159 keV [ref. 7)]. Finally the high excitation energies (those near 7.4 MeV) obtained with the y-detector are about 25 keV smaller than those measured with the magnetic spectrograph, as they were also in a previous experiment s). The values o f E x from other work (column 12), from a Nuclear Data Sheets compilation 9) based mainly on measurements on one-nucleon transfer reactions, are given only for levels that are not difficult to relate to those seen in our (3He, p) study. Throughout this paper, the energy values obtained from the ~-ray measurements (table 1, column 7) were used whenever available. 2.2. A N G U L A R DISTRIBUTIONS
Angular distributions of the protons from the 4 5Sc(3He ' p),TTi reaction have been measured at nine angles in the range 0lab = 7 °-35°. We concentrated on these very forward angles both because these are the most important ones in determining the orbital angular-momentum transfer and because, for this rather low-yield reaction, only the forward cross sections are large enough that a sufficient number of proton tracks in the nuclear emulsions could be obtained in a reasonable exposure time. At some angles, the proton groups of interest were masked by impurities and no cross section could be obtained. The angular distributions of all proton groups except those belonging to the 1.249 and 1.411 MeV levels in table 1 are shown in figs. 2-4. These two angular distributions are rather fiat and somewhat uncertain because of the low proton yield, as indicated in column 4 of table 1. Many of the other angular distributions display characteristic patterns more strongly. The forward-peaked ones are presented in fig. 2, those with a maximum yield at about 20 ° in fig. 3 and the remaining ones in fig. 4. Angular distributions of five levels at excitation energies 0.0, 0.157, 2.160, 2.835 and 3.223 MeV (the latter as an unresolved pair) have been studied before by Rao et al. 6) in the same reaction. Although these authors used a beam energy of 13 MeV, their angular distributions differ little from those we measured with a beam energy of 17 MeV, in agreement with the assumption of direct-interaction mechanisms. In nearly all cases, their cross sections reported at a specific angle are slightly higher than ours at the same angle, but the two sets of data agree with each other within the experimental error. DWBA calculations (subsect. 2.3) indicate that the cross sections in the angular range studied are expected to increase by about 10-15 ~ when the beam energy is raised from 13 to 17 MeV. Consequently, according to DWBA calculations, our cross-section values are somewhat lower than those reported by Rao et al. 6). 2.3. ANALYSIS OF THE A N G U L A R DISTRIBUTIONS
The orbital angular-momentum transfer of the n-p pair in the 45Sc(3He, p)*7Ti
598
L. MEYER-SCI-IOTZMEISTER et aL
r e a c t i o n is d e t e r m i n e d by c o m p a r i n g the m e a s u r e d a n g u l a r d i s t r i b u t i o n s with those c a l c u l a t e d in the d i s t o r t e d - w a v e B o r n a p p r o x i m a t i o n by use o f the code T W O P A R [ref. 1 o)]t. T h e initial optical p o t e n t i a l s were those o f R a o et aL 6). T h e y were slightly c h a n g e d to give a g o o d fit to the m e a s u r e d a n g u l a r d i s t r i b u t i o n f o r the a n a l o g state at 7.346 MeV. T h e p a r a m e t e r s finally used for all calculations are listed in table 2. T h e p o t e n t i a l well o f the transferred nucleon p a i r was a d j u s t e d by the T W O P A R c o d e to I0.0~----
7
i --
-i~-~lO0.Ol--
,ooL- " ~.
F
-4
oooLX ?
-
\
..._
-E,=7 ~46 M,v
\ ! .
,0.05
. . . .
o*
Do* co*
-
#
I E xE3=3.223MeV .223MI " ...
o*
io*
20"
30 °
30*
~c.rN.
Fig. 2. Angular distributions of protons from the 4SSc(aHe, p)47Ti reaction with a strong contribution of orbital angular-momentum transfer L.p = 0, as identified by forward peaking of the distribution. The energy of the 3He beam was 17 MeV. Circles indicate the measured results; the solid lines were obtained by DWBA calculations for L.p = 0 with the code TWOPAR j o) and the optical potentials of table 2. give the right b i n d i n g energy EB for each o f the nucleons, a n d we have chosen this to be EB = ½(IS.pl-Ex), where S,p represents the n-p p a i r s e p a r a t i o n energy o f - 17.011 M e V for the A T = 0 t r a n s i t i o n s a n d - 19.236 M e V f o r A T = 1, a n d E X is the excitation energy o f the states in the 47Ti nucleus. A l t h o u g h the e x t r a c t i o n o f We are grateful to B. F. Bayman for making this code available to us.
,o.o~--~-~
I.O~-
"~
5.0z -
~ ,,.o ~("
,.79,
,
,
~
°
5.0-
b
1o
5.00+1~1 i~÷~' ,1, t '~ =o"
zo °
3o °
8c.m. Fig. 3. Same as fig. 2 except that L.p = 2.
I0.0~
I
I I : Ex=Z.530 MeV--
I0.0~ ~ 3.246
I0.01
5.oiI ~t
-
6
5.oI
I
I
--
Ex=4.755
MeV-
5.372
t ~-
-
-
I0. :-
I.
3
I
5"ii
3.817
5.458
4.705
6.530
(~~
I.
5o~~o / ,~,1,o
,o
4.~5j+
50-
I •
I0
i
I
I
I0 °
20*
I
50"
to °
I 20*
I
-
30*
OC. m. Fig. 4. S a m e as fig. 2 except t h a t L.p is u n d e t e r m i n e d a n d no D W B A calculations were m a d e
L. M E Y E R - S C H O T Z M E I S T E R et al.
600
TABLE 2 The optical potentials and parameters used in the D W B A calculations Unbound particle p aHe
V (MeV)
av (fm)
rv (fm)
53.6
0.61
1.217
160.0
0.734
1.13
W (MeV)
aw (fm)
0 16.21
r~v (fm)
Ws (MeV)
as (fm)
rs (fm~
0.61
1.217
17. l
0.31
1.26
1.13
0.734
0
0.753
1.604
The potential for these u n b o u n d particles is Vtot
=
Vfv (r) --i I/Vfw (r) -k4ias Wsfs'(r),
--
where fx : {1-}-exp [(r--r~A~})/ax]} - t , a n d f ' indicates the derivative. The bound neutron and proton move in a potential with the parameters av = 0.65 fm, rv = 1.2 fro. The real potential well is adjusted by the program until it gives the binding energy Ea = ½ []S,p[--Ex ], where Ex is the excitation energy o f the final nucleus and S,p is the separation energy o f the n-p pair. For the T = 1 transfer we used S ° p : --19.236 MeV and for the T : 0 transfer S,p = --17.011 M e V . The potential contains a spin-orbit term.
spectroscopic factors in the (3He, p) reaction is doubtful, the orbital angular momenta L,p transferred by the n-p pair can be obtained since the shape of the angular distribution depends almost entirely on L.p. This is shown in fig. 5, in which calculated lo) angular distributions are plotted for a n-p pair transfer into the 3.919 MeV level with total angular momentum J = 3 and orbital angular momentum L,p = 2. Curve (a) is the result of placing both nucleons in the lf~ shell; curve (b) is for the transfer of one of the nucleons to the lf~ shell and the other to the 2p~ shell. Both angular distributions have the same shape, but the cross sections are larger when the 2p shell is populated. To form the low-lying states in 47Ti, the n-p pair will be preferentially absorbed in the 2p and If shells and one therefore expects some angular distributions that show I
'
"~ 2 0 -
l
×
l X
X
o
i
'
I
'
I
'
X
X
X
X
~
o
X
X
~, 1 0 - -
'
X
x
X
b X
7,
5 0
0
0
0
0
z
0 0
o
ti
0 O o
i
o*
I
I0"
,
t
20*
,
i
30*
,
t 40 °
t
I
50*
o t
60*
70*
0e. rn. Fig. 5. D W B A calculations [code T W O P A R 1o) and optical potentials o f table 2] for the 4SSc(aHe, p)47Ti reaction populating the 3.919 MeV 47Ti level. The n-p pair transfers 3 units o f total angular m o m e n t u m to the target nucleus; the orbital angular-momentum transfer is L,~ = 2. Curve (a): both nucleons are transferred into the lf~ shell. Curve (b): One nucleon is placed in the lf~_ shell, the other in the 2p~ shell.
STUDY OF 't7Ti
601
the characteristic pattern of Lop = 0 and 2 transfer reactions. The distributions for which Lap = 0 is predominant are plotted in fig. 2. The two measured curves for the isobaric analog at 7.346 MeV and the state at 3.223 MeV are well fitted by the calculation with the optical parameters listed in table 2, AT = l, Sap = - 19.236 MeV, and the assumption of a pure Lap - 0 contribution. These calculated angular distributons (solid lines) are normalized to the data. All other angular distributions in fig. 2 were calculated on the assumptions that AT = 0 and that the separation energy Snp is the deuteron value So = - 17.01 MeV. This smaller value of Snp makes the calculated curves slightly steeper. In contrast to the good fit for the distributions for the states at 7.346 and 3.223 MeV, the measured angular distributions for the states at 0.157, 2.614, 2.835, 6.864 and 7.480 MeV all show the same large deviation from the calculated Lap = 0 curve: the first theoretical minimum is filled in for each. We take this deviation as an indication of an L,p = 2 contribution. In earlier studies 11), the pure Lap -- 0 angular distribution is connected with the transfer of an n-p pair in its singlet state to populate the isobaric analog state and the corresponding antianalog state with T -- T<. The states showing Lop = 0 + 2 contributions in the (aHe, p) reaction, however, may be formed by the n-p pair in its triplet state. Consequently, the pure Lnp = 0 angular distribution found for the 3.223 MeV state leads to the belief that this state is formed by an n-p transfer with S = 0, T = 1 and hence has the assignment J~ = 7 - , T = ~. The patterns of the five angular distributions shown in fig. 3 are compatible with the assumption of L,p = 2 transitions, for which them aximum yield is at about 20 °. All are well fitted by the angular distributions (solid lines) calculated with pure Lap = 2 transfers and S,o = -17.011 MeV. In the (da/dt2)c.m" column of table l, the strengths of these five transitions are indicated by the yields at 20 ° where the cross section is maximum.
3. Particle-? coincidence measurements 3.1. EXPERIMENTAL PROCEDURES The 45Sc(aHe, p?)47Ti reaction was studied at Heidelberg with the 12 MeV 3He beam of the EN tandem Van de Graaff of the Max-Planck Institute (MPI) and at Argonne (ANL) with the 17 MeV 3He beam of the FN tandem Van de Graaff. The experimental arrangements used in both cases had been described earlier s, 12--14), SO only a few essential details are given. In this description, the M P I values are given first and the A N L values follow in parentheses. The M P I target consisted of a 1 mg/cm 2 45Sc layer evaporated on a 290 mg/cm 2 Au foil, while the A N L target was a rolled 0.9 mg/cm 2 4SSc foil backed by an Au foil 150 mg/cm 2 thick. The Au foil stopped the incident 3He beam but allowed the high~ energy protons and deuterons from the (3He, p) and (3He, d) reactions with Q = 11.508 and 4.857 MeV, respectively, to reach the particle detectors with little energy loss. As seen in fig. 6, however, the energy resolution of the particle spectrum deteriorated, the width increasing to several hundred keV. The particle detector, thick
602
L. M E Y E R - S C I - [ O T Z M E I S T E R e t aL
16
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==>=
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I 400 600 800 PROTON ENERGY (channel number) Fig. 6. P r o t o n s p e c t r u m o f the 45Sc(aI-Ie, p)47Ti reaction in coincidence with all ),-rays. T h e labels on the peaks indicate s o m e 4?Ti levels p o p u l a t e d in this reaction a n d also s o m e 46Ti levels excited by the 45Sc(aHe, d)46Ti reaction. A n arrow indicates the t h r e s h o l d o f the 4~Sc(aHe, np)46Ti reaction. I
I
I
I
I
20
= 2 . 4 5 7 MeV
I0 e~
u)
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,~
=
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650
700
750
I 800
850
PROTON ENERGY (ehonnel number) Fig. 7. Portions of the 4~Sc(3He, p ) 4 ; T i proton spectra measured in coincidence with the indicated ),-rays. These are typical o f the decay o f a n u m b e r o f the '~?Ti states s h o w n in fig. 12. T h e observed ),-energies E l, = 7.480, 7.187, 2.678, 2.457 a n d 1.548 M e V originate f r o m the '~?Ti states at 7.480, 7.346. 2.835, 2.614 and 1.548 MeV, respectively. In order to o b t a i n better statistics, the doubleescape peaks at 6.458 a n d 6.167 M e V were used for the ),-rays o f energies 7.480 a n d 7.187 MeV, respectively. Since the coincidence c o u n t i n g rate is very small, 17 p r o t o n channels were s u m m e d a n d the resulting coincidence rate was assigned to the middle c h a n n e l n u m b e r . This p r o c e d u r e was repeated at 4-channel intervals.
STUDY OF *YTi
603
enough to stop all proton groups, was located at 0 ° to the incoming beam and subtended an angle of +28 ° at MPI (+__10° at ANL). A lithium-drifted germanium counter with an active volume of 38.5 cm 3 (30 cm 3) was located at 90 ° (80 ° ) to the incoming beam. The ?-ray detector subtended an angle of + 19°(+ 17°) and the efficiency as a function of the energy has been measured in earlier experiments s, 22). The width (FWHM) of the ?-ray lines, which is mainly due to the high counting rates, was 6 keV at Er = 2 MeV and 12 keV at 6 MeV for the detectors used. Details of the electronic measuring system and the data-taking procedures are described elsewhere s, 12 - 1,). The cross section of the *SSc(3He, p?)*7Ti reaction is rather small for particle-? coincidence experiments. Unfortunately one cannot compensate for this by using larger beam currents since the particles and ?-rays from the high-yield reactions *SSc(3He, d?)46Ti and *SSc(3He, np?)46Ti limit the counting rate in the detectors. The spectrum of particles in coincidence with all ?-rays, which is the one of present interest, is shown in fig. 6. The peaks at large particle energies are due to the "5Sc (3He, p?)47Ti reaction and are well separated from the deuterons produced in the 45Sc(3He, d?)*6Ti reaction. One of the pronounced peaks is from the 7.346 MeV analog state in *YTi, and the others are from excited states in *6Ti; the first two (at 0.889 and 2.009 MeV) are marked. The 2.835 MeV levels in *YTi is barely seen in the spectrum. All these peaks are on a smooth background which rises steeply with decreasing particle energy. To a great extent this is due to the *SSc(3He, np?)46Ti reaction. The threshold for the population of the ground state in *6Ti by the (3He, np) reaction is indicated in fig. 6 by the arrow labeled (3He, np). A particle spectrum of more interest for the present investigations is obtained by selecting the protons in coincidence with those ?-rays that proceed from states in *7Ti and that appear to be undisturbed by ?-rays of neighboring states. Parts of five such proton spectra are displayed in fig. 7. The three spectra at the right are for protons in coincidence with ?-rays of energy Er = 2.457 MeV (top curve), 2.678 MeV (middle), and 1.548 MeV (bottom), while the two at the left are for protons in coincidence with the 7.187 and 7-.480 MeV ?-rays (with double-escape peaks, the most prominent ones in the ?-spectrum, at Er = 6.167 and 6.458 MeV, respectively). Since the y-rays with which these plots are associated proceed from the states at 7.480, 7.346, 2.835, 2.614 and 1.548 MeV (as seen in fig. 12), these states are indicated by peaks in the coincidence spectrum. Similar spectra of protons in coincidence with other observed ?-rays were used to unravel the ?-decay scheme of the *7Ti levels. Unfortunately we were able to extract ?-decay schemes for only a few *YTi levels because of difficulties in the data analysis: (i) The cross sections of the (3He, p) reaction populating the *YTi levels (table 1) are small. (ii) Although the reactions in the present experiment predominantly populate only a few levels, the level density in *YTi is high: more than 100 levels with Ex < 6 MeV are observed. This high level density led to ambiguities in fitting some of the ?-rays into the level scheme. (iii) In many cases
604
L. MEYER-SCHI~TZMEISTER et aL
the )'-decay is complex. Gamma branches of about 10-20 ~ of the total )'-strength might have been overlooked. (iv) Levels that decay by high-energy )'-rays also result in a relatively large background for the low-energy )'-rays. Hence, as seen in fig. 9 of subsect. 3.2.4. (the)'-ray spectrum of the analog state), the signal-to-noise ratio is small for low-energy )'-rays. 3.2. RESULTS The energy of the )'-ray proceeding from the first excited state could not be measured directly since it was below the lowenergy cut-offat about E~ = 300 keV. Instead, this energy was found as the difference 1.548-1.391 = 0.157_+0.003 MeV between the energies of the two ),-rays proceeding from the 1.548 MeV level. This result is in good agreement with the measured value given in ref. 7). Both the 1.249 and 1.441 MeV levels are supposed to be high-spin states (J~ = ~and ~ - - ) [ref. 1s)]; they are hardly populated by the (3He, p) reaction. Consequently the )'-decay could not be seen in coincidence with the protons populating these levels. However, one would expect that these levels, being so close to the ground state, would be excited by the )'-decay of many high-energy levels. In particular, since our forwardangle measurement of the 4SSc(aHe, p)aTTi reaction favors states with spin J~ = ~--, 7- and ~-, one expects high-spin states at the lower energies to be populated by their decay. Indeed, two prominent )'-rays at relatively low energy (E~ = 1.092_+0.002 and 1.284_+0.002 MeV) consistently appear in coincidence with protons from reactions populating high energy levels. They are assumed to arise from the transitions from the 1.249 and 1.441 MeV levels, respectively, to the first excited state at 0.157 MeV. In agreement with ref. 6) but in contrast to the reported observation 16) of the )'-decay of the 1.249 MeV level, the ground-state transition was not indicated from either level. 3.2.2. The 1.548, 1.794 and 2.160 M e V levels. These three levels are only moderately excited with an L,p = 2 transfer in the (3He, p) reaction, especially in the present arrangement in which the proton detector is placed at forward angles. However, the counting efficiency is relatively high for the low-energy y-rays from these levels, and the spectra have low background. Consequently we have been able to study their )'-decay. The spin assignments of these levels (table 1) are either J~ -- ½- or ½-. Their 7decay had been studied in several earlier experiments: (i) They were populated in the radioactive decay 17) of 47V, whose ground state has spin J~ = ~r-- (ii) The 1.548 and 1.794 MeV levels with J~ = ½- or ~-- were excited is) by E1 )'-decay from the ½+ states in 47Ti from the thermal-neutron capture reaction 46Ti(n, 7)- (iii) The 1.548 MeV level was studied 6) by use of the (p, p')') reaction on 47Ti. Our measurements confirm the earlier conclusion that the 1.548 MeV state decays by the emission of two )'-rays: the ground-state transition with an energy of 1548_+ 2 keV and the 1391 -+2 keV transition to the first excited state. The 1.794 MeV level )'-decays in two branches: a ground-state decay (E~ = 17944- 2 3.2.1. The 0.157, 1.249 and 1.441 M e V levels.
STUDY OF 47Ti
17,18) and
k e Y ) in agreement with refs.
605
the transition ~s) to the 1.548 M e V state.
Since the latter is below the cut-off energy in our y-spectrum, we observe only the subsequent y-ray f r o m the 1.548 M e V level. The 2.160 M e V level decays predominantly to the ground state, although we could detect a y-ray leading to the first excited state. The latter transition was already indicated as a possibility in ref. ~ 7). 3.2.3. The 2.614, 2.835, 3.223 and 7.480 MeV levels. These levels have not been studied before. A l t h o u g h they are m u c h m o r e strongly populated than the 1.548, 130 511
4.
3
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GAMMA ENERGY (CHANNEL NUMBER)
Fig. 8. Spectrum ofF-rays in coincidence with the proton groups populating the 2.614, 2.835 and 3.223 MeV levels of "7Ti in the reaction 4sSc(SHe, p)4VTi. A typical },-peak width is about 10 channels at the base and about 6 channels at half maximum. The lines whose energies (keV) are indicated in parentheses are not prominent in this spectrum; those at 1.548 and 1.974 MeV have been definitely identified from our other }'-ray measurements, but the 2.835 MeV line is weak even in the best of the other spectra. The dashed lines represent either weak transitions or (in a few cases) those that could not be uniquely fitted into the level scheme. 1.794 and 2.160 M e V levels discussed in subsect. 3.2.2, their decay schemes are difficult to extract. In addition to difficulties due to possible complexity o f their decays and ambiguities in fitting the 7-rays into the level scheme (as mentioned in subsect. 3.1), m o s t o f these states are not populated by pure L,p = 0 transfer but have appreciable L,p = 2 contributions. Consequently the y-rays are not necessarily emitted isotropically and hence those in cascade need not be o f equal intensity. These intensities are therefore not a useful clue in the level-fitting procedure. In fig. 8 is the spectrum o f y-rays in coincidence with protons populating the 2.614,
606
L. MEYER-SCHIDTZMEISTER et al.
2.835 and 3.223 MeV levels, whose 7-decay should therefore be seen. Indeed the 7-rays whose energies are indicated are observed among others, although only two of them (2.457 and 2.678 MeV) are easily fitted into the 7-decay of the 2.835 and 2.614 MeV levels. They indicate strong transitions of both these states to the first excited state. The 1.287, 1.394 and 1.548 MeV 7-rays also are members of cascades from these two levels, and some possible combinations are shown in the insert of fig. 8. The 3.223 MeV level is about as strongly populated in the present experiment as is the 2.614 MeV level (as seen in fig. 1), yet no strong 7-rays belonging to this state are identified. In particular, we observe no strong 7-transition to the ground state or first excited state. However, a weak 7-ray populating the second excited state seems 7:%C I 511
[I i
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Fig. 9. Spectrum ofT-rays in coincidence with the proton group from the 45Sc(31-[e, p)47Ti reaction populating the analog state at 7.346 MeV. The three-pronged brackets for the high-energy7-rays indicate the photopeak and the single- and double-escape peaks. The 7-decay of the 7.480 MeV level is also seen. The parentheses and dashed lines have the same significance as in fig. 8. to be present. Consequently we assume that the 7-decay is complex, having many branches of about equal intensities. The 7.480 MeV level 7-decays predominantly to the ground state, in contrast to what is found for all other cases in which the 7-decay of a level populated by L,p = 0 or L,p = 0 + 2 transfer could be observed. 3.2.4. The isobaric analog state at 7.346 M e V . The 7-decay of this state is displayed in fig. 9. The two strong 7-rays leading to the 0.157 and 3.223 MeV levels have relative intensities of 2 and 3, respectively. Although no direct ground-state transition is indicated, the upper limit for the intensity of this transition is fairly high ( < 20 % of that of the 7.189 MeV ),-ray). Two additional strong 7-rays are observed at E = 1.284 and 1.092 MeV. Their
STUDY OF 47Ti
607
energies are the same as those attributed to the decay of the 2.835 MeV level (fig. 8), although we showed that neither this state nor the state at 2.613 MeV is directly excited in the ~-decay of the analog (i.e., the transition probabilities are smaller than 15 and 5%, respectively). In addition, the 1.092 and 1.284 MeV 7-rays are prominent in the spectra taken in coincidence with proton groups leading to excitations in the range E~ = 5-7.5 MeV. These lines could arise in two possible ways: (i)They could originate from the 1.441 and 1.249 MeV states which are not directly populated in the (3He, p) reaction (transition probability < 10 %) but must be populated through ;~-cascades via states at higher energy. (ii) They might well be emitted sequentially, as is indicated in the insert of fig. 9. This possibility requires no further assumptions to explain the experimental fact that these two lines have about equal intensities. The sum of the intensities of the two ~-rays is about the same as the combined strength of the transitions from the isobaric analog state to the 3.223 and 0.157 MeV states. 4.
Discussion
4.1. COMPARISON BETWEEN THE RESULTS OF (3He, p) EXPERIMENTS AND THOSE OF ONE-NUCLEON TRANSFER REACTIONS The 45Sc(3He, p)47Ti reaction populates many low-energy states in 47Ti by transferring the n-p pair into the lf~ and 2p~ shells of the target nucleus. If the pair goes into only one of the shells, the shape of the angular distributions is expected to reflect some contribution of Lnp -- 0 transfer; but if the two nucleons populate different shells, n o Lnp = 0 contributions are possible. Twelve angular distributions have shapes characteristic of orbital angular-momentum transfers Lnp = 0 o r Lnp ---- 0 + 2 and thus one might expect for states at low excitation energies a large ( 1 ~ ) 7 component in the nucleon configuration. This identification is indeed confirmed for a number of states by the one-nucleon transfer reactions - both the 46Ti(d, p)47Ti reaction 19-22) t and the 48Ti(3He, ~)47Ti reaction studied by Rao et al. 6). In these reactions the target nucleus has either a (lf~) 6 or a (lfk) 8 nucleon configuration. The transfer of one nucleon into or out of the lf~ shell leads to 7 - states in 47Ti with (lf~) 7 nucleon configurations. This process is reflected in an angular distribution whose shape is characteristic of an orbital angular-momentum transfer l, = 3. In table 1 the results of these reactions are compared with those of the (3He, p) reaction. We would like to point out that DWBA calculations indicate a larger (3He, p) reaction cross section for the transfer of a nucleon into the 2p~ shell than into the lf_~ shell (see table 3). Consequently even small admixtures of other nuclear components like (lf÷)5(2p~) 2 into a predominant (lf~) 7 nucleon configuration might influence the (3He, p) cross section appreciably 23). Of the twelve states populated by Lnp = 0 or L , , = 0 + 2 transfer in the (3He, p) reaction, the only ones seen in the one-nucleon transfer reactions are the five lowest ones (the states at 0.157, 2.614, 2.835, 3.223 and 3.246 MeV, of which the last two were * We are grateful to W. Haeberli for making some of the results of the 45Sc(d,p)*TTi polarization measurements by W. Haeberli and K. C. Kocher available to us prior to publication.
608
L. M E Y E R - S C H I ~ T Z M E I S T E R
et al.
not resolved in earlier work) and the analog at 7.346 MeV. That they are populated with In = 3 in the latter reactions, as expected, confirms the strong (lf~) 7 characters ot these states. The six states (those at 4.252, 4.705, 5.458, 6.530, 6.864 and 7.480 MeV) are not seen in either of the one-nucleon transfer reactions. It might well be that some of these states are in effect particle states with strong (lf~)~(2p) 2 components in the nucleon configuration. One also expects that one of them will be a state with spin 2~- , T = ½ formed by adding an n-p pair with spin 1 ÷, T = 0 to the 45Sc target with spin 7- T ~ (as explained in subsect. 4.2.4(c) below). Of special interest is the 7.346 MeV analog of the J~ = 7 - , T = ~ ground state of 47Sc. Since its formation should be restricted by isospin selection rules, we expect to find that (i) this state is not populated in the (d, p) reaction, (ii) it is populated freely in the (3He, 0t) reaction, (iii) it is excited in the (3He, p) reaction only if the n-p pair is absorbed in its singlet mode with S = 0, T = 1, and (iv) its excitation via the (3He, p) reaction is connected with an angular distribution of Lnp = 0 [ref. 11)]. TABLE 3 Calculated relative cross sections for a n u m b e r o f different n u c l e o n configurations Configuration
(1 f~_)2
Lnp 0 2 4
(2pgr) z
(lf~_) 2
AJnv = 1 1.0 0.12
(i f~_)2p~_ ZIJap = 3
7.8 0.31
0.27 0.02
1.4 0.04
I n the calculations the code T W O P A R so) a n d the optical potentials o f table 2 were used. T h e cross sections integrated f r o m 0 ° to 60 ° are given, the value for the (lf.~) z cross section has been arbitrarily set equal to 1.0. T h e isospin transfer equals ATnp = 0 a n d the total a n g u l a r m o m e n t u m transfer equals 3 J . p = 1 or 3.
Indeed all four of these predictions are borne out in the experimental results shown in table 1. We observe the same four restrictions for the 3.223 MeV state. For this reason we are tempted to conclude that the 3.223 MeV state has the same spin and spatial nucleon configuration as the analog state but that is has T = T<. That is, it appears to be the antianalog. Since in this case the antianalog is produced by transferring the n-p pair from the (3He, p) reaction into the f÷ nuclear shell already partiallypopulated, the cross section O'AAs is expected to be much less than the cross section a~As connected with the formation of the analog at 7.346 MeV. That is indeed true. The ratio 0"AAS/0"IAs is about 2-~, in rather good agreement with the theoretically estimated value* t W e w o u l d like to t h a n k D. K u r a t h for providing us with the theoretical value. T h e calculation is based o n the following a s s u m p t i o n s : (i) T h e 45Sc target nucleus has seniority 1 a n d is well described by a ~fk n u c l e o n configuration. (ii) T h e n-p pair is transferred in its singlet state with S = 0, T = I. (iii) T h e ratio was n o t corrected for the effect o f the different excitation energies o f the analog a n d antianalog. This latter a p p r o x i m a t i o n s h o u l d have little effect since the Q-value o f the reaction is high.
STUDY OF '*TTi
609
of about 1 : 14. We would like to point out that Hansen and Nathan 24) have recently summarized the available experimental cross sections of (SHe, p) reactions on doubly even target nuclei leading to the 0 + analog and the corresponding antianalog states. In all these examples, the experimentally observed ratio aAAs/tr~As was smaller, often substantially, than the theoretical values given. This is also true in the present case but the discrepancy is relatively small and might well be due to the rough theoretical estimates. In this context it might be questionable if the 3.223 MeV state indeed can be identified with the antianalog. For this reason we have started to study the 45Sc(:~, d)*TTi reaction which should easily populate all states excited by the (3He, p) reaction with Lnp = 0 and Lnp = 0 + 2 transfers except the analog and the antianalog. Preliminary results 2s) of these measurements indicate that indeed the 3.223 MeV state is the ~- antianalog. The angular distributions for the (3He, p) reaction to the states at 1.548, 1.794, 2.168 and 3.919 MeV are characteristic of pure Lnp = 2 transfer. As pointed out earlier in this section, this might indicate a (lf~)62p nucleon configuration for the final states. Such a configuration with spin J = 3- or ½- should easily be excited by the (d, p) reaction with In = 1 but not by the (SHe, a) reaction. This in fact true, as seen in table 1, although the ~z- state at 1.548 MeV which shows most of the In = 1 strength in the (d, p) reaction is also populated by the (3He, ~) reaction, but only weakly. This fact probably indicates some impurity in the assumed nucleon configuration in either the final or the target nucleus or both. Although the ground state of 47Ti has an (f~)7 nucleon configuration 1, 2), it has an anomalous spin of ~- and is not expected to be populated by either the (d, p) or the (SHe, , ) reaction. Indeed it is only weakly excited. Since the same is expected to b~ true for the (SHe, p) reaction, its angular distribution will be discussed in subsect. 4.2.4(b). The states at 1.249 and 1.441 MeV also are only weakly excited in the (d, p) reactions 19) and are not reported in the (3He, ~) work 6). However, they are well populated by the s 0V(p, a)47Ti reaction 15), and this fact led to the assumption that the 1.249 and 1.441 MeV states are high-spin states (J~ -- { - and 1@-) that theory predicts 1, 2) in this energy region. Moreover, as discussed in subsect. 4.2.4(c), both of these states are only weakly populated in the (3He, p) reaction. The states at 1.823 and 2.371 MeV are excited by In = 2 and l~ = 0 transfer in the (3He, a) reaction; they are assumed to be ld~ and 2s½ hole states 6). Hence they should not be populated by the (SHe, p) reaction, and indeed they are hardly seen in it. They are not listed in table 1. 4.2. COMPARISON BETWEEN THEORETICAL PREDICTIONS AND EXPERIMENTAL RESULTS ON PARTICLE REACTIONS LEADING TO *TTi TWO theoretical approaches will be considered in the comparison with the experimental data. One by McCullen et al. 1) is based on shell-model calculations using only f~ nucleon configurations and thus excludes levels with nucleon excitation into higher shells. The other, by Malik and Scholz 2), is the Coriolis-coupling model which
610
L. MEYER-SCH{)TZMEISTER
et al.
includes configurations in which nucleons are excited to the p-shell as well. Both models have been used to calculate n o t only energy-level schemes and spectroscopic factors for some pick-up and stripping reactions but also electromagnetic transition probabilities. The c o m p a r i s o n between these theoretical results and the available experimental data thus constitutes a test o f the models. 3"~r
(MeV) l l
7/2---
Jf
(MeV)
--7.480
I~--7.346 ----6.884
712--- I~,S __ 6.64 //
----6.530 /,/
----5.45e -----5.372
5/2~'-//
- - ' ~
//
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7/24__---3.90
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3/2-, I / 2 - - - -
~3.919
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712~" .
/4.755 4.705
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jlr
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5/~ . . . . .
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~3.817 ./-3.246 ~3.223
7/2-~(5/2-)--
- - 2.835 .~2.614
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I/2 i --3.72 I/2~----.~. I--3.51 9/2-~_ __.J 3.26 7/z ~ / 3.14 5/2 --!
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1/2--3/2--~
- --I.794 --1.548 ~IA41
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7/2----5/2---
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.69
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t~-0.183 -- 0
MALIK
a SCHOLZ
Fig. 10. Experimental and theoretical level schemes of 47Ti. The experimental results include those of both the present investigations and refs. 17-22). The theoretical results are those of refs. 26-28). 4.2.1. Energy-level scheme. In the 47Ti level schemes shown in fig. 10, the energies measured in this experiment and their spin assignments - b o t h the established ones and (in parentheses) those suggested f r o m the present and earlier work 9,17-22) _ are c o m p a r e d with the calculated energies and spins f r o m refs. 26-28) t. Both models t We are grateful to B. F. Bayrnan and J. D. McCullen for providing us with the calculations
based on the MBZ model. The calculations based on the model of Malik and Scholz were provided by J. R. Comfort.
STUDY OF 47Ti
611
[refs. 1, 2)] are able to place both the ½- and ~- states close to the ground state along with the ~ - - and ~- as required by the experimental data. However, the level energies and the spin sequences are different. Of course, excitation energies and spin assignments do not reveal much information about the nucleon configuration associated with the states. Much more information will be obtained by comparing calculated and measured spectroscopic factors for nucleon-transfer reactions populating the states in question. 4.2.2. Spectroscopic factors for the 46Ti(d,p)47Ti reaction. Table 4 shows the experimental results reported in refs. 19 - 22) and the theoretical values from refs. 26.28 ). Since the calculations of ref. 26) are restricted to the lf~ nucleon configuration, they apply only to 1, = 3 transfers; but those of ref. 2a) include excitations into the lf~,~ and 2p~p, shells and hence predict spectroscopic factors for In --- 3 and In = 1 transfers. In both calculations the In = 3 strength of the lf~ shell is concentrated in the lowest -~- state, in good agreement with the experimental results. In fact, the measured 19,22) spectroscopic factor for the state at 0.157 MeV is (2Jr+ 1)5a ~ 5 although a value of 4 exhausts the shell-model sum rule 29). For this reason one might be tempted to assume that the states at 2.614 and 2.835 MeV, also populated by In = 3 transfer, have spin ~ - with a nucleon in the f~ shell. The calculations of ref. 2a) indeed predict such a state with a relatively large spectroscopic factor at an energy of about 2.5 MeV (as seen in table 4). However, recent experiments 20, 22) indicate that at least the 2.614 MeV state has J~ = ~-. The spin of the 2.835 MeV state is uncertain and might well be ~-. This result is somewhat unsatisfactory both because it implies that the experimental spectroscopic factors for the f~r shell are grossly overestimated (at least 50 % greater than the sum-rule limit) and because it is strange that so little strength for 1n = 3 transitions into the f~ shell is observed for excitation energies up to more than 5 MeV. The agreement between experimental and theoretical results is quite good for the In = 1 transitions leading into the p~ shell. More than half of the measured strength is concentrated on the ½- state at 1.548 MeV, while the rest is most likely for transitions to states with higher excitation energies. Many such states are populated by In = 1 transfers, but no spin assignments can be made at present. Theoretically, as seen in table 4, one finds that nearly half of the l --- 1 strength for transitions populating ½- states is concentrated on one state (the one at 1.84 MeV, which is the second ~ - state and is distinguished hereafter as ½2), and the rest is distributed anaong transitions to states at higher excitation energies. Reasonable agreement between theory and experiment is also observed for the l = 1 strength for the population of ½- states. About a third of that strength is experimentally associated with a low-energy state at 1.794 MeV, while theoretically about a fifth of the total strength is to a state at 1.69 MeV. 4.2.3. Spectroscopic factors for the 4aTi(3He, ~)4 7Ti reaction. In table 5 the measured spectroscopic factors reported in ref. 6) are compared with the ones calculated by use of the f~ shell model 1). The agreement between experiment and theory for the
612
L. MEYER-SCH1]TZMEISTER et al.
- levels is g o o d . M o s t o f the s t r e n g t h is c o n c e n t r a t e d in the t r a n s i t i o n to t h e l o w e s t 7-
state at 0.157 M e V , a n d the s t r e n g t h f o r p o p u l a t i n g t h e 3.223 M e V state is in
r e a s o n a b l e a g r e e m e n t w i t h t h e p r e d i c t i o n s m a d e f o r t h e c a l c u l a t e d level at 2.78 M e V . TABLE 4 Spectroscopic factors (2Jr+ 1)6P for the 46Ti(d, p)47Ti reaction Measured refs. 19-21)
Calculated ref. 22)
Ex jrr (2J~+1)5¢ l,, J~r(ZJt-~l)SP (MeV) 0.0 ~0.157 ~-1.548 ~1.799 (½-) 2.160 2.530 2.614 2.789 2.835 3.545 3.676 3.919 ½-, ~4.637 4.924 5.013 5.580 5.810 5.810
5.1 2.36 0.71 0.06 0.32 1.32 0.25 0.89 0.20 0.48 0.82 0.21 0.1 0.13 0.32 0.31 0.33
3 I I
~-
4.64
1 1
3
~--
1.46
ref. 26)
ref. 28) jTr ( 2 J t q - l ) J 1,
E~
(MeV) 0 0.183 1.51 1.56 1.69
~~~-~½1.84 ~-2.46 ~2.52 ~2.75 ~-3.02 ~3.14 7z3.51 t3.72 ½4.020 ~4.34 ~4.54 :a-
0.009 3.20 0.06 0.67 0.41 1.75 0.05 2.0 0.11 2 x 1 0 -5 0.14 0.02 6 x 1 0 -7 0.12 1.40 1.4
Ex (MeV)
3 3 I 3 1
jz, (2jt_~l)Sa
l,
0.157 2.45 2.78
~½5-
3.94 0.04 0.016
3 3 3
3.90
~-
0.000
3
l
3 3 3 1 3 1 1 1 3 1
TABLE 5 Spectroscopic factor C25 a for the 4STi(3He, ~)47Ti reaction Measured a)
Calculated b)
Ex (MeV)
j~r
0.157
?z~-~--
3.18 0.17 0.29
3
,~½(.~-) ~-
0.25 0.43 0.54 0.19 0.76
3
2.614 2.835 3.223 3.558 7.346*
C26a
1
E~
jn
C2~ '
l
(MeV)
* Isobaric analog state.
~) Ref. 6).
3
3 3 3
0.16
'~1 -
4.77
3
2.45
']z-
0.14
3
2.78
~3-
0.55
3
6.64*
~-
0.40
3
~) Refs. t.6).
A t h i g h e x c i t a t i o n e n e r g y , the full s t r e n g t h f o r the t r a n s i t i o n to the a n a l o g state ( w h i c h is o b s e r v e d at 7.346 M e V t h o u g h the c a l c u l a t i o n s w o u l d p l a c e it at 6.64 M e V ) is p i e d i c t e d to be 0.4; t h e m e a s u r e d v a l u e is 0.76. T h e l a t t e r is m o s t likely a n o v e r -
STUDY OF 47Ti
613
estimate due to the difficulties in the extraction of spectroscopic factors, an explanation that is also indicated by the results obtained in the studies of the 4STi(p, d)47Ti reaction 30). The spectroscopic factors measured in this latter work are all somewhat lower than those of ref. 6); in particular, that for populating the analog state is 0.34, which is close to the theoretical limit of 0.4. In conclusion, the comparison between the measured and calculated transition strengths in the (d, p) and (3He, ~) reactions populating 47Ti levels leads to a more appropriate coordination of measured and calculated states than is obtained by comparing the measured and calculated level schemes shown in fig. 10. For example, the first calculated ½- level at 1.51 MeV surely does not represent the measured ~r- state at 1.548 MeV, but the calculated ½2 state at 1.84 MeV does (table 4). TABLE 6 Possible coordination between experimental and theoretical 47Ti levels as established by use of
spectroscopic factors for one-nucleon transfer reactions [refs. 6.19-22.26.2S)l Exp. Ez (MeV) 0.0 0.157 1.249 1.441 1.548 1.794 2.614 2.835 3.223 3.919 7.346*
jzr
~½~-, a~~ t - , ~.~½6(~--) 6½-, { 6-
MBZ Ex (MeV)
Jrrn
0.30 0.16 1.80
~-1½t~t-
2.45
62-
2.78
~3-
6.64
6- *
Malik and Scholz Ex (MeV) J% 0.0 0.183 1.02 1.83 1.84 1.69 1.56 2.52 2.46; 3.14 (4.54)
~l ½1~1~132½, 62~263;*({5-)
* Isobaric analog state.
As a result of this comparison between measurements and calculations, we have ten states that are reasonably well described by theory, as shown in table 6. For four of these states (those at 2.614, 2.835, 3.223 and 3.919 MeV), the coordination is uncertain - mostly because of their relatively small spectroscopic factors in the (d, p) and (3He, 00 reactions. 4.2.4. The two-nucleon (3He, p) transfer reaction. The cross sections and the angular distributions for the 45Sc(3He, p)47Ti reaction leading to a number of states in 47Ti were calculated in ref. 26) (MBZ). The results for a few ~-, ½-, 3 - and ~ states and the isobaric analog are shown in table 7. Since more than one total angular momentum Jnp of a transferred n-p pair can lead to a given final state, these calculations involve a summation over all Jnp terms. The strengths of the different J,p contri, butions are given for the reactions to a number of 47Ti levels. When the n-p pair is transferred in its singlet mode ( S = 0, T = 1), the orbital angular-momentum transfer is Lnp = Jnp; and since the only prominent states in our spectra are those populated
614
L. MEYER-SCHOTZMEISTER et aL
in the (3He, p) reaction without parity change, the Jnp values are even. However, for an n-p pair transferred in its triplet mode ( S = 1, T = 0) J,p is odd and the orbital angular-momentum transfer has the two values Lnp = J , p + 1. The angular distributions that follow from the J.p values of table 7 are calculated with the code TWOPAR ~0) by use of the optical potentials of table 2. A few of these angular distributions are shown in fig. 11 and their shapes and strengths will be compared with the experimental results. Most of these distributions are for reactions to states that were found to be well described by the MBZ model in subsects. 4.2.2 and 4.2.3. (a) The analog state. Several total angular-momentum transfers J,p contribute to the formation of most of the 47Ti states listed in table 7; no single J,p term predominates. An obvious exception is the analog state whose calculated excitation energy (MBZ) is 6.64 MeV. It is formed primarily o f J . p = 0 transfer so Lnp --- 0. Since the measured angular distribution of the analog state was well represented by a pure L,p = 0 transfer, as discussed in subsect. 2.3 and seen in fig. 2, the calculated angular distribution derived from table 7 is expected to fit the measured one well. In fact, it gives a slightly better fit since the weak contribution of higher J,p terms (table 7) will decrease the deep minimum at about 33 ° and bring the calculated and measured values even closer together. This is seen in fig. 1 la, in which the calculated curve is plotted as a solid line labeled by the measured excitation energy of 7.346 MeV, while the measured angular distribution is indicated by open circles. (b) The states with spin assignment ~- or ~-. In subsects. 4.2.1.-4.2.3, it was shown that the ground state and the first excited state are well described by the MBZ model, and that consequently the (3He, p) calculations might be able to predict the measured angular distributions of both states. This is indeed true for the ground state. Of all the ~- states indicated in table 7, only the ground state has an angular distribution that has a broad maximum at an angle of about 25 ° and fits the measured distribution within the experimental error. This is shown in fig. I ld, where the calculations are represented by a solid line and the measurements by crosses. However, the calculated angular distribution of the first excited state (the ~" state at E x = 0.16 MeV) deviates markedly from the measured one. The ~ - and ~2 states at the MBZ energies 0.16 and 2.45 MeV show nearly fiat distributions because high J.p terms play an important role. The calculated distribution for the ~- state is shown as a solid line in fig. 1 lc; the measured angular distribution of the 0.157 MeV state is indicated by open circles. In contrast to the calculated angular distributions, it seems to show a strong L,p = 0 contribution. In fact, all known ~ - levels show measured angular distributions with strong L,p = 0 contributions (as seen in table 1). This discrepancy between the m~asured and calculated angular distributions is seen for the ½~" and ~ states, for example. However, the theoretical curve in fig. 1 lb shows a strong L,p = 0 contribution to the k~ state at Ex(MBZ) = 2.78 MeV, which may correspond to the measured level at 3.223 MeV. But even for this state, the measured and calculated angular distributions disagree markedly. In fact, with the exception of the analog, 11o calculated angular distribution for a 7-z state shows a pure L.p = 0 transfer similar
STUDY OF *TTi
615
to that measured for this 3.223 MeV state. Note that pure Lap = 0 transfers are calculated not only for the ~- analog state but also for the {~ and {~ states (as seen in table 7). However, these two states cannot be associated with the 3.223 MeV state whose rather strong population in the (3He, ~) reaction makes the { - and { - spin assignments most unlikely for this state. (c) The ~- states. The states at 1.249 and 1.441 MeV are considered to be the first states with spin as high as J = { - or ~ - . They have small cross sections, and consequently their measured angular distributions are uncertain. In fig. 1le, the mea'
400i
1
'
I
'
I
'
:_
7.348 MeV (7/2-, I A S I
-
2
4C
o
2C
2
IC
'
I
'
I
' j
0 • 57Me
7
j.
I)
I--
IOC ~' 6C =
I
4
o
20(
'
O.:.~_..
d g.s. ( 5/2t-1
2L-
~
T
T
~
_
E e 3
4
~
2
0.
3.223 MeV(7/2£)
.J.
o*
f~ 1.441MeV
2~-~.[
0.E
0.4
1.2
T
O.
,
f,
I
io*
zo*
,
°"4I-,~1 ~,
,
30*
40*
o*
io*
I,
20*
I , -
30*
40*
Oe.m.
Fig. 11. Comparison of calculated and measured angular distributions for the 45Sc(3He,p)*TTi reactions leading to a few selected *TTilevels. Circles and crosses represent the data, solid and dashed lines the calculations. The experimentally established levels are marked by their excitation energies; their theoretical identifications are in parentheses. In angular distribution (e), the crosses are the values for the 1.441 MeV state, the circles are those for the 1.249 MeV state.
sured angular distributions for the 1.441 and 1.249 MeV levels are given by crosses and open circles, respectively, and the calculated ones for the 1.80 and 2.17 MeV levels (the first two { - states from the MBZ calculation) are plotted as the solid and the dashed line, respectively. Although the uncertainty in the measurements is too great for a good comparison, it is obvious that neither the experimental nor the calculated angular distribution shows a strong Lap = 0 contribution. Neither in theory nor in fact, therefore, does the lowest { - state include an appreciable component corresponding to the nucleon configuration of the target nucleus into which an n-p
616
L. MEYER-SCHOTZMEISTER et aL
pair in its S = I, T = 0 state has been transferred with Lnp = 0. In the MBZ calculation, the state formed by transfer of this latter n-p pair is the 2~; level at a calculated energy of 3.87 MeV, as indicated in table 7 by its angular distribution with strong Lnp = 0 contributions. Since such a state is not expected to be populated by onenucleon transfer reactions, it is most likely one of the six states observed at higher excitation energy. As mentioned in subsect. 4.1, these states are indeed not populated by a one-nucleon transfer reaction and their angular distributions in the (3He, p) reaction show strong Lnp = 0 contributions. (d) Transition strengths in the (3He, p) reaction. As a measure of the transition strengths in the (3He, p) reaction populating different 47Ti states, we have formed the sums ~ Y . and ~ Y . sin 0., where Y. is the yield at the angles 0. = 5 °, 10 °, 15°, 20 °, 30 ° and 40 ° and the sum is over these six angles. These sums for the calculated 2 6) and for the measured results are listed in table 7. The measured results are also shown in table 1. The values are normalized to the analog state, whose value was set to 1.00. The peculiar set of angles was chosen in order to de-emphasize the larger angles, at which the yields Y. often are small and the associated errors are large. The experimental Y. values were obtained from a smooth curve drawn through the measured points of the angular distribution. Although the use of ~ Y . sin 0n or ~ Y . to compare transition strengths is rather arbitrary, some firm conclusions can be drawn from thevalues in table 7. The measured transition strength to the analog state is very much larger than that for any other state, but the calculated strength for the analog is comparable to those of the others. For a few states that are reasonably well described by the MBZ model (especially the J = ~ - ground state, the 7 - state at 0.157 MeV and the ~2 - state either at 1.249 or 1.441 MeV), the experimental strength is at most a few percent of that for the analog; but their calculated strengths are comparable to (though smaller than) that of the analog state. In conclusion, we find that the MBZ calculations of the (3He, p) reactions are able to reproduce the angular distributions for some states that are reasonably well described by the theory. However, the calculated transition strengths show much less variation than the experimental ones do. In particular, the theory does not predict either the strong enhancement of the transfer leading to the analog state or the weak transitions to the ~ - ground state and to the ~ - state at 1.249 or 1.441 MeV. This failure to indicate the strong enhancement of the transfer leading to the analog state, is a fact which agrees well with the observations 31) in the (t, p) reactions of f~ nuclei. Here also the measured cross sections of the ground-state transitions (orbital angular momentum transfer L . . = 0) are larger (by a factor of six) than the ones calculated by the MBZ theory. 4.3. GAMMA-DECAYS OF STATES IN 47Ti The comparison between the calculated and measured v-decays tests the validity of the theoretical models even more stringently than does the comparison between the
~-
~-
]27,-3 -
-,]-4-
2.17 3.87 0.16 2.45 2.78 3.90 6.64* 0.30 1.60 3.09 5.52 1.01 2.16 2.71
1.80
0.0380 0.2823 0.0021 0.0067 0.0778 0.0213 0 0.0019 0.0930 0.1021 0.1126
0.0470 0 0.0336 0.1344 0.0211 0.043 0.0337 0.0742 0.3334 0.0360 0.0011 0.108 0.0594 0.2676
0.0139
2
0.0944 0 0.1555 0.00783 0.0330 0.0422 0 0.1847 0.0232 0.0481 0.0015 0.1412 0.039 0.0160
0.0363
3
0.0160 0.0364 0.3479 0.4243 0.0007 0.0008 0 0.0482 0.0007 0.0242 0.0022 0.3136 0.0781 0.0627
0.0449
5
0.0460 0.0157 0.3885 0.0000 0.0157 0.0002 0.0001 0.1271 0.1108 0.0029 0.0004
0.1576
6
7
0.1312 0.0247 0.0732 0.0523 0.0019 0.0030 0
0.1139
b) Tentative correlation.
0.0065 0.0009 0.2289 0.1331 0.0305 0.0018 0.0667 0.0755 0.0273 0.0767 0.0001 0.1505 0.6075 0.0444
0.3148
4
Calculated strength contributed by J,p t e r m
0.0048
1
a) T w o alternative values,
0.0155 0.0224 0.0196 0.0003 0.4889
F~ (MBZ) Jop = 0 (MeV)
* Isobaric analog state,
t
~t
] ~•
•.~
T
~2-
½-
TABLE 7
Yn
1.44
1.00
0.45 0.67 0.44 0.30 0.41 0.19 0.19
1.00
0.26 0.49 0.36 0.29 0.22 0.10 0.11
1.15 0.87 0.48
1.30
0.66 0.53 0.41
0.60
0.50
7.346 0.00
0.157 2.614 b) 3.223 b)
1.249 1.441 a)
1.00 0.01
0.02 0.04 0.05
0.01 0.01 "~)
Y' Yn n=l
6
n=l
1.00 0.02
0.03 0.05 0.06
0.01 0.02 ")
Yn sin
M e a s u r e d (table 1)
~ Yn sin 0, Ex *~1 (MeV)
0.43
0.26
,=1
6
Calculated
Calculated strengths 26) contributed by total a n g u l a r - m o m e n t u m transfers J~p = 0 - 7 in 45Sc(aHe, p)47Ti reactions leading to several 47Ti levels (which are listed in order o f decreasing If )
0,,
©
,q
O~
618
L. MEYER-SCH(JTZMEISTER et aL
transition strengths in nucleon-transfer reactions. Of course, the only states one can hope to understand are those with rather simple nucleon configurations: A few such states in table 6 are singled out by their large spectroscopic factors in nucleon-transfer reactions, and the ones whose y-decay we were able to study will now be discussed. In the decay scheme shown in fig. 12, our data are at the right and the earlier results [refs. 17. ~8)] are at the left. Most of the y-rays studied so far proceed from levels with spin assignment J~ = ½- or ~:- since the observations were made by using the reaction 46Ti(n, y)gYTi, which leads through a ½+ resonance ~7), or by studying the radioactive decay x6) of 47V whose spin is ~--. Two exceptions are the high-spin states at 1.249 and 1.441 MeV, which had been investigated by the (p, p'y) reaction 6) and by heavy-ion Coulomb excitation ~6). The 47Ti states whose y-decay was studied in the present experiment but not in earlier ones include some with spins ~ - and ~-. Of these, the analog state is especially important since its y-decay is observed and its simple nucleon configuration allows the calculation of this y-decay. The results shown in fig. 12 indicate that, as had been observed for isobaric analogs in many other fp shell nuclei 32-34), the y-decay is complex. In the sd shell nuclei, however, several strong M1 transitions from the analog state to its antianalog have been observed. Ern6 et al. 35) were the first to see and recognize such a transition (in 38Ar) and have related it to the process in which an unpaired f~ nucleon recouples in isospin space to an inert (d~)" core in such a way that the isospin decreases by one unit and the antianalog state results. More recently, Kurath 36) has shown that such strong M1 transitions are unlikely in fp shell nuclei since the core consists of f~ nucleons that will participate in the y-decay. Interferences between the y-transition amplitudes of the core and those of the unpaired nucleon might cause strong population of states other than the antianalog and consequently the transition strength to the latter will be reduced. This agrees well with our results that we see the y-decay to the antianalog, but that this transition is not dominant. 4.3.1. M B Z calculations. Since the MBZ model restricts its configuration space to the f~ nuclear shell, only the ground state of 47Ti, the first excited state, and a few of the others listed in table 6 are well described by this model. As a test of the model, therefore, the most important state whose y-decay we have studied in the analog. Its y-decay and that of a few others predicted by MBZ calculation 27) are shown in fig. 13. The MBZ states and those found experimentally are coordinated according to table 6. There is little doubt that the .}~-, ½l- and 97 states represent the experimental states at 0.0, 0.157 and 1.249 or 1.441 MeV, respectively, and we assume that the ~2 and ~3 states correspond to the levels at 2.614 and 3.223 MeV. A comparison between figs. 12 and 13 shows that in agreement with the MBZ calculations, the analog has a rather complex y-decay and, in particular, shows two strong transitions (with about the right intensity ratio) leading to the states at 0.157 and 3.223 MeV; no direct transition to either the 1.249 or 1.441 MeV state is observed. However, the predicted y-rays leading to the 2.614 MeV state and the ground state have not been detected in our experiment.
S T U D Y O F 47Ti
619
The absence or low intensity of any direct ground-state transition is observed not only for the analog but also in all other ~- and ½- low-energy states (namely those at 2.614, 2.835 and 3.223 MeV) which we were able to study by the (3He, p?) reaction, Ex (keV) 7480 7346
j~
~2--
2O 5340 3925 3685 3556 32:>3 2835 2"798 2614 2556 2533 2160 17"94 1548 144 I 1249 157 0
112. 312-
! 1I
(5/2-)-7/23/2-
I/2-
3/2"
T
4) 1~ .
9/2-, 11/2-
.
-
/
7/2-~ 5
/
2
r
-
~
m
_1
4 7T i Fig. 12. G a m m a decay o f 47Ti. T h e decay indicated on the r i g h t - h a n d side represents the present results, that on the left-hand side shows the results f r o m refs. 6, 17, 18). Each vertical line represents y-transitions to t h e final state indicated by the arrow point; a n arrow that does n o t e n d on one o f the levels in the d i a g r a m represents a transition that c a n n o t be fitted uniquely into the level scheme. T h e circles m a r k the levels f r o m which the y-rays originate; the transitions indicated by filled circles are definite, those indicated by open circles are weak or uncertain. 27
(MeV} 7. 346
....
(MBZ) 7/2-, IAS
7/2; 9/21
7/2 i 0
v
5/27
Fig. 13. T h e y-decay o f a few 47Ti levels as calculated by use o f the M B Z m o d e l 27).
while the MBZ calculations display a strong direct ground-state transition for the 52 state. The only direct ground-state transition which we were able to observe belongs to a state at the high excitation energy Ex = 7.480 MeV.
620
L. MEYER-SCHtJTZMEISTER et al.
4.3.2. Calculations with the Coriolis-coupling model. The 47Ti levels that seem to be reasonably well described by this model are shown in table 6. For most of these states, both measured and calculated ?-decay schemes are available. The calculated ones are shown in fig. 14, where the measured energies of the levels are given on the left and the theoretical spins and parities are at the right. For the 3.223 MeV level, we consider two possible states: ~3 and ~-. The isobaric analog is also included although the model does not produce analog states. In calculating the decay of this 47Ti state, the wave function used was that of the corresponding state, namely the 47Sc ground state. The strengths of the ~-ray transitions to the different 47Ti levels were then calculated, and the decay scheme of this nucleus was derived by using the measured level energies. (MeV) 7.346 .
3.223--
Ref. 28 .
.
.
.
.
'
7/2~ 4
5/z? Fig. 14. The ~,-decay of some 47Ti levels as calculated by applying the Coriolis-coupling model =8).
For the initial calculations, the parameters of ref. 2) were used. Most of the results were very similar to those displayed in fig. 14, which were calculated with the set of parameters used in the final calculations. The exception was the ~-decay of the ½2 state at 1.548 MeV, for which a very different decay scheme was predicted by the initial calculations. They called for a predominant M 1 transition to the ground state. However, the fact that the measured intensities of the ~-rays to the first excited state and to the ground state are about equal indicates strong electric-quadrupole contributions. Since the calculated ~}2 state and the measured state at 1.548 MeV are very strongly populated in the (d, p) reaction with 1, = 1 transfer, no mistake in the coordination between experiment and theory (table 4) seems possible. The discrepancy in the ~,decay must then indicate that this level is not well described by the Coriolis-coupling model with the parameters of ref. 2). Comfort 28) was kind enough to repeat the calculation with different parameters. In fact, the changes in these parameters were slight and in agreement with his earlier studies ~ ) , and they produced hardly any variation in the spectroscopic factors of any of the levels under consideration. Even the decay schemes and the branching ratios shown in fig. 14 were not appreciably
STUDY OF 47Ti
621
changed for any level except the ] 2 state. Its branching ratio changed drastically while the lifetime varied over two orders of magnitude. This indicates that this level with a large p~ nuclear component is only poorly described by the Coriolis-coupling model. In contrast to this anomalous behavior of the ½2 state at 1.548 MeV, the ½7 state - whose reasonably large spectroscopic factor for the (d, p) reaction with 1. = 1 transfer indicates a P~r nuclear component - showed only small changes when the parameters were varied as described; its lifetime varies only by a factor of 2. Thus this state seems to be well described by the Coriolis-coupling model, although (as seen in figs. 12 and 14) the experimental and theoretical 7-decay schemes do not agree well. The experiment shows a strong electric quadrupole transition to the ground state, while theoretically the M1 transition to the state at 1.548 MeV dominates by far. In this case, however, the coordination of the ½~- state to the 1.794 MeV level is less certain than that of the ½2 state to the 1.548 MeV level. The Coriolis-coupling predictions of the y-decays of the ~ - and ~- levels at 2.614, 2.835 and 3.223 MeV are similar to those from the MBZ calculations in that the most pronounced transitions are those to the ground state and first excited state. However, the experiment indicates no ground-state transition except a possible weak one from the 2.835 MeV state. The strong transitions to the first excited state are in agreement with the theory. The measured and the calculated y-spectra of the analog state at 7.346 MeV agree in that both show a complicated decay with a relatively strong branch to the first excited state. However, much as in the MBZ results, the Coriolis-coupling model shows a reasonably strong transition to the ground state - strong enough that it should be observed in the experiment. Actually, however, it is not; the calculated intensity of this decay branch is at least 2-3 times the experimental upper limit. Although the calculations do not predict the experimentally observed y-decay from the analog to the 3.223 MeV state, theory and experiment agree that there is no transition (or at most a weak one) either to the ½2 state at 1.548 MeV or to the ~7 state at 1.249 MeV. 5. Conclusion
Both the MBZ and the Coriolis-coupling models are able to produce a level scheme for ~VTi that agrees reasonably well with energies and spin assignments of levels obtained experimentally. For some of these levels, both theory and experiment indicate large spectroscopic factors in one-nucleon transfer reactions, and hence a correlation between some of these theoretically and experimentally established states is possible. For the (d, p) reaction, the spectroscopic factors calculated with the MBZ model 26) are more strongly concentrated on the first ~-- state than are the experimental ones. The theoretical spectroscopic factors for the (3He, c~) reaction, however, are quite consistent with the experimental values 2, 6). The MBZ calculations for some ~- and ~ - states populated by the 45Sc(3He, p)47Ti
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reaction 26) display rather flat angular distributions because of strong contributions of high orbital angular momentum L.p in the n-p pair transfer. Experimentally, however, all but one of the known 3 - and ~- levels are associated with forward-peaked angular distributions indicating strong L,p = 0 contributions. The one exception, the 3 - ground state, shows a rather flat distribution which is fitted well within the experimental error by the curve calculated from the MBZ model. An even better fit between the calculated and measured angular distribution is obtained for the analog state at 7.346 MeV, which is excited with almost pure L.p = 0 transfer. The measured relative transition strengths of the (3He, p) reactions leading to the 47Ti levels differ greatly from those calculated with the MBZ model 26) Experimentally, the analog is populated far more strongly than is any other state, at least by a factor of 5 and in many cases by a factor of about 50. However, the MBZ theory predicts that the transition strengths to most studied levels are comparable with that of the analog state. In only a few cases does the calculated strength differ by a factor 5-10. Thus the 45Sc(3He ' p)47Ti reaction is actually much more selective in populating the analog than the MBZ model predicts. This fact is already indicated by (t, p) reactions on f~_ shell nuclei. The observed L.n = 0 transitions 31) are by a factor six stronger than those calculated by the MBZ model. The (d, p) spectroscopic factors predicted by the Coriolis-coupling model - not only for levels with the nucleon configuration (fg_)" but also for those with p~,~ f~-1 o r f ~g_ f , - 1 configuration - seem to satisfactorily fit the experimental results reported in refs. 19-22). Difficulties arise, however, when the calculated y-decays of the p~_ and pa states are compared with the observed ones. For the ~ - state at 1.84 MeV, the calculated ~-decay varies strongly with small changes of the parameters chosen for the calculation, while the calculated y-strength for the ½~-, 2~z, 22,3,4-, 79 - and _1~_~ 2I states hardly vary at all in response to the same changes. This behavior indicates that the latter states might be well described by the Coriolis-coupling model in its present state but that the p~ state at 1.84 MeV is not. Similar discrepancies are observed for the first p~ state, if indeed it can be identified with the state at 1.794 MeV. Theoretically, this state is supposed to decay by a dominant M1 transition to the 51~ state at 1.84 MeV, but experimentally a strong E2 transition to the ground state is observed in addition to the y-ray leading to the 1.548 MeV state. The analog state at 7.346 MeV shows a complex y-decay and has no dominant 7branch leading to any one low energy level. The complex y-decay of the analog is predicted by both the MBZ and the Coriolis-coupling model, and both also call for two strong y-transitions that indeed are seen experimentally. However, the predicted transitions to the ground state and to some low-lying ~ - states are not seen in our experiment. We wish to thank Dr. B. F. Bayman, Dr. J. D. McCullen and Dr. J. R. Comfort not only for the calculations of some properties in the production and in the 7-decay of the 47Ti nucleus but also for many fruitful discussions. We are also indebted to
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D r . D . K u r a t h , D r . R . D . L a w s o n a n d D r . F. B. M a l i k f o r s t i m u l a t i n g discussions. W e are v e r y g r a t e f u l to D r . W . H a e b e r l i f o r m a k i n g us a w a r e o f s o m e o f his results o n t h e r e a c t i o n 46Ti(d, p ) 4 7 T i b e f o r e final p u b l i c a t i o n . O n e o f us (G. H . ) wishes to t h a n k t h e W e s t e r n M i c h i g a n U n i v e r s i t y Office o f R e s e a r c h S e r v i c e s f o r p a r t i a l supp o r t o f this w o r k t h r o u g h a f a c u l t y r e s e a r c h grant.
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