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Levels of 44Sc by the (3He, α) reaction on 45Sc
Nuclear Physics A168 (1971) 177---l 89; @ worth-lowland FL~bIishingCo., A~?~terdu?n Not to be reproduced
LEVELS
by photo~rint
or microfilm without written permission from the publisher
OF 44Sc BY THE (3He, a) REACTION ON 45Sc 3. RAPAPORT
Physics Department, Ohio. University, Athens, Ohio t T. A. BELOTE and D. E. BAINUMtt Physics department and Laboratory for Nuclear Science tt? ~ussachuset?s I~stitate of technology, Ca~zbridge, ~assac~asetts and W. E. DORENBUS~H Physics f)epartment, Wayne State University, Detroit, Michigan Received (Revised
IO December 1970 15 February 1971)
Abstract: The 45Sc(3He, o()~~SCreaction has been studied at an incident 3He energy of 13.0 MeV. A ground state Q-value of 9.249&0.015 MeV was measured for this reaction. Alpha-particle spectra were obtained at lab angles between 7.5” and 172.5’ for transitions to levels below 3.0 MeV excitation energy. A distorted-wave analysis was carried out to obtain I. values and spectroscopic strengths. The isobaric analog of 44Ca(0) was observed at an excitation energy of 2.763&0.020 MeV. The results are compared with other experimental data and with theoretical predictions. E
NUCLEAR
REACTIONS 45Sc(3He, dt), (3He, “He), ECHO= 13.0 MeV; measured u(E1, @), Q. %Sc deduced levels, J, z, t,, transition strengths.
1. Introduction
A considerable amount of experimental and theoretical work on lf; nuclei has been done in the last few years. McCullen ef al. ‘) using a slleli-model description can explain some of the low-lying properties of these nuclei, while Malik and Scholz ‘) assuming If+ con~gurations and the collective mode! with Coriolis coupling are able to describe at least qualitatively other features of low-lying odd nuclei in this region. The 44Sc nucleus with four lf+ nucleons outside a doubly magic 4oCa core should have a level structure similar to that of its cross conjugate, 52Mn. This latter nucleus has been studied previously in this laboratory by means of the (3He, p) and (d, z) reactions “)_ However, two low-lying states in 44Sc at 0.068 and 0.146 MeV reported by Ristinen and Sunyar “) had no observed counterparts in s2Mn. The neutron pickup reaction leading to states in 44Sc was therefore undertaken ‘. 7 Work supported in part by the US Atomic Energy Commission. tt Present address: Edgewood Arsenal, Maryland. ttt Part of this work was carried out under AEC Contract AT(30-l)-2098. $ Preliminary results of this work were presented at the APS meeting in Boston, February 1968 [ref. ‘)I. Those results have also been compiled by Ohnuma and Sourkes in their recent ‘%%(d, t) publication t1). 177
178
J. RAPAPORT
et
al.
Previously, Kashy “) reported ten levels below 1.66 MeV of excitation in 44Sc by means of the 45Sc(p, d) reactio n. Neutron groups from the 41K(a, n)44Sc reaction have been studied by Smith and Steigert ‘). Bjerregaard et al. “) report levels in “SC below 1.427 MeV observed by the 46Ti(d, a) reaction. More recently, Schwartz “) reported the t3He, d) proton stripping on 43Ca with high resolution up to an excitation energy of 5.5 MeV in 44Sc. Schlegel et al. lo) observed states in 44Sc up to 5.59 MeV of excitation excited by the 4”Ca(3He, P)~~SC reaction, while Ohnuma and Sourkes have reported the (d, t) neutron pick-up reaction ll). Using the atomic beam, magnetic-resonance method, Harris and McCulIen “) have determined the nuclear spins for the ground state and the isomeric state at E, = 271.3 F0.7 keV [ref. ‘“)I to be 2 and 6, respectively. Ristinen and Sunyar “) assign J” = 1 + both to the 0.068 and 0.146 MeV states from the 44Ti(0) decay. However, from a more recent determination 14) of the 44Ti(0) mass, the calculated logft to the 0.146 MeV level is 6.5 rather than < 4.4 as previously thought, therefore weakening this assignment. A J” = l- has also been postulated for this state 14). ___---
45sc+ 3Ha E
3t.k ---
c, ~
-
= 13.0 MeV set I set 2
IO"
60
90
120
I80
G&,{degrees) Fig. 1. Angular distribution for the elastic observed cross sections to the Rutherford indicate statistical uncertainties. The curves eters
scattering of 13.0 MeV 3He from ‘?Sc. The ratio of the cross section is presented versus angle. The error flags are optical-model fits to the data using the 3He paramgiven in table 2.
4io
Fig. 2. Alpha-particle
I-------
EXCITATION
ENERGY
(MeV)
DISTANCE
ALONG
PLATE
(cm)
IO
SPECTROGRAPH FIELD = II 896 EXPOSURE = 7 500 pC
E+*= 13.0 MeV
=30”
CI?%C
ANGLE
(‘He,
LA5
?3
_-3p_ .- ______--~____.. ,
GAUSS
Xi
__-_!p -----
spectrum from 45S~(3He, CL)~%Creaction at fYlab= 30”. Alpha-particle groups corresponding the numbers used to identify these states in table 1.
.~
-1
to states in “%c are labelled with
op _.-_
180
J. RAPAPORT
et al.
In the present experiment, the MIT multiple-gap spectrograph has been used to reaction. Data were obmomentum analyse a-particles from the 4sSc(3He, CX)~~SC tained for 18 levels up to 3.004 MeV excitation. The experimental procedure and results’are given in sect. 2; the distorted-wave (DWBA) analysis of the measured angular distributions is presented in sect. 3. A discussion of the level scheme of 44Sc, sum-rule analysis and comparison with other experiments is given in sect. 4. 2. Experj~ental procedure and results 2. I. TARGETS The target used in the present experiment was prepared by vacuum evaporation of metallic scandium, a monoisotopic element, onto a thin carbon-backing film. The 45Sc target thickness was measured to be 52 .ug/cm’. k
F i i?
0 Q=9.249 MeV B, =3
E,-&fiS MeV I,
I
3 =0.654 P, =3
I
=3
IS
e
cm
Meti
\
(degrees)
Fig. 3. Angular distributions of a-particles from ‘?SC(~H~, CX)~%C.The distributions are labelled with the numbers used to identify the correspon~ng states in table 1. Statistical uncertainties are indicated by error flags on the data points. The curves are DWBA predictions using the set of parameters 2a given in table 2.
“SC LEVELS 2.2. ELASTIC
181
SCATTERING
Elastic scattering of 3He from 45Sc was observed at 13.0 and 5.0 MeV bombarding energies. The 5.0 MeV elastic scattering was used to determine the target thickness by assuming Rutherford scattering behavior. The 13.0 MeV results are shown in fig. 1 and were used to determine the optical-model parameters; the curves represent the DW prediction calculated for the two sets of 3He parameters (see subsect. 3.1). 2.3. THE
45Sc(3He,
cr)“‘%c REACTION
Reaction products were detected using 50 ,um Tlford KO nuclear emulsion plates at lab angles between 7.5” and 172.5” in 7.5” intervals; these plates were chosen because of their low sensitivity to protons and deuterons. The cc-particle spectrum obtamed at era,, = 30” after a 7500 PC exposure is shown in fig. 2. The energy resolution was 30 keV. Alpha-particle groups corresponding to a residual mass of 44 were identified from their kinematic shift with angle. Up to an excitation energy of 3.0 MeV, 18 transitions were identified. Above that energy, the level density, as well as the weakness of the transitions, did not allow unique level assignments. 1
r
:
i
P E,=l.424 MeV I” =(Z)
t
8
cm
(degrees)
Fig. 4. See caption
for fig. 3.
J. RAPAPORT
182
et al.
TABLE 1 4%c(3He, ~r)~~Sc results
Level
0
Q “) (MW 0
ClojdsZb) (mb/sr)
I, ‘)
c2s
J”
3 3 3 3 3 3 3
0.35 0.50 0.37 0.32 0.14 1.37 0.23
2+ d) 6+ d,
(:)
0.20 0.23
I (2) (3)
0.25 0.45
(:) (3) (2) (0)
0.32 0.30 0.15 0.19 0.12
(3_, 4-)
3
0.10
0+ (IAS)
(2)
0.20
9.249 8.980 8.905 8.595 8.493 8.273 8.206 8.068 7.825 7.718
0.269 0.344 0.654 0.756 0.976 1.043 1.181 1.424 1.531
0.22 0.35 0.28 0.26 0.11 1.09 0.18 0.20 0.08 0.24
11
7.567 7.139
1.682 2.110
0.18 0.17
12 13 14 15 16 17
7.039 6.665 6.553 6.486 6.342 6.245
2.210 2.584 2.696 2.763 2.907 3.004
0.10 0.03 ‘) 0.01 q 0.15 8) 0.06 0.14
1 2 3 4 5 6 7 8 9 10
(7)+ ‘)
“) The estimated error is &20 keV for levels l-17. The uncertainty for the ground state Q-value is &15 keV. ‘) Maximum observed cross section at Oiab= 7.5”, except as indicated. ‘) Tentative values in parentheses. “) Ref. 12). ‘) Ref. 6). ‘) At I!$.,,= 30”. ‘) At f&s = 22.5”. 2 parameters
TABLE
Optical-model Particle
“)
Set (&
(M:V) 3He
1 2
133.2 173.77 180.0 183.7 Y
4He E
“) The optical potential
12.18 16.21 31.65 26.0
1.36 1.14 1.22 1.40 1.25
0.633 0.734 0.796 0.560 0.65
used was of the form: V(r) = - V(eX+l)-l-iW(eX’+l)-‘+
1.74 1.604 1.63 1.48
(L)
rot (fm)
0.789 0.753 0.423 0.560
1.40 1.40 1.30 1.40
Vc(r,rc),
with r-roA113 x=-----, a
x’ =
r_r’,,AW a’
’
rc = rocA1’3.
b, Adjusted to give the transferred neutron a binding energy of -Q(3He,
~)+20.58
MeV.
“SC
LEVELS
183
The Q-values, excitation energies, and maximum observed cross sections are given in columns 2, 3 and 4 of table 1. Columns 5 and 7 give i, and f” assigned to the observed transitions, while in column 6 the deduced spectroscopic strengths are tabulated. To obtain the Q-values, a correction was made to the calibration of the spectrograph because of the high field used. This correction was obtained by observing a-groups from contaminants with known Q-values. The measured Q-value for the ground state transition was 9.249-tO.015 MeV, in good agreement with the value of Q = 9.259~0.007 MeV obtained from the mass table 1“). The angular distributions are shown in figs. 3 and 4. The curves shown are DW predictions using the set of parameters 2a given in table 2. 3. DWBA analysis 3.1.
ELASTIC
SCATTERING
The experimental 13.0 MeV elastic 3He scattering data were analysed with the optical-model search code ABACUS 16). The search was initiated with two sets of parameters. Set I was obtained starting from that of 13.0 MeV 3He elastic scattering by “4Fe [ref. I’)], while set 2 followed from the parameters given by Gibson ef al. 18). The DW elastic-scattering calculated curves are shown in fig. 1, where they are compared with the experimental data presented as the ratio of the observed cross sections to the Rutherford cross sections. 3.2. TRANSlTION
STRENGTHS
The relation between experimental and calculated cross section is given by (d~ld~)~~~ = NC%@), where S is the spectroscopic factor, C the isospin coupling coefficient, and ~(0) the calculated cross section. The value of N, which arises from the overlap integral between the ‘He and CIwave functions, is not too we11known. An empirically deduced value of N = 25 rt 5 was used in the analysis I’). The DW code TANYA developed at MIT and the code DWUCK were used to calculate cr(@)from the sets of parameters given in table 2. Two sets of 3He and two sets of a-particle potential parameters were used. The a-particle sets of parameters were obtained from the work of Stock et nl. 19). From the different combination of parameters, the caIculations done with sets la and 2a were very simiIar, although set ?a seemed slightly better and was therefore used throughout the strength analysis. A Woods-Saxon potential was used both for the neutron bound state and the “He and or-potentials. VoIume absorption was used for both the 3He and r-potentials. All calculations were performed with a zero-range interaction. No lower cut-offwas used. The values of the orbital angular momentum of the transferred neutron were deduced for the various rx-groups by comparing the shapes of the calculated and ob-
184
J. RAPAPORT
et al.
served angular distributions. The transition strengths listed in table 1 were obtained by matching the experimental cross sections summed over angles to the calculated cross-section sums. At about 2.0 MeV excitation energy, Q = 7.25 MeV, the calculated cross sections for 1, = 2 and I, = 3 are quite similar in shape. In some cases both fitted the observed angular distributions equally well (see fig. 4). Tentative values for 1, for these cases are given in parentheses. 4. Discussion 4.1. STRENGTH
FUNCTION
AND SUM RULE
Spectroscopic strengths extracted from the measured angular distributions are plotted versus excitation energy in fig. 5 are and compared with the theoretical cal-
“SC
Level
Scheme
c
ysc
J”
(He.a)P”
P,=O
x,=2
P,=3
J”
McCullen,,Bayman ond Zomck
Fig. 5. Strength function for 45Sc(3He, ~r)~%c reaction. An excitation energy scale is given on the left. States in 44Sc (see subsect. 4.2) are compared with the present data. The values of the transition strength C’S from table 1 are indicated.
185
“%c LEVELS
culations
of McCullen
et al. ‘). Recently,
similar
calculations
have been repeated
using two-particle matrix elements taken from the experimental spectrum of 42Sc [see refs. lo* “)I. Th is calculation, while only slightly changing the neutron transfer strength, gives the position of the first J” = 6+ state at 0.358 MeV, in closer agreement with the known J” = 6+ level at 0.271 MeV. In the left column, the 44Sc level scheme taken from the compilation of Endt and van der Leun ““) and up-dated with recent data 9-11) is indicated. The spin assignments are taken from the same sources (see also sect. 1). The (3He, IX) reaction on 45Sc excites states in 44Sc with T, = 1 and T, = 2. The Z, = 3 transition to the T, states is seen fragmented in at least nine states below 2.5 MeV excitation energy. The level at E, = 2.763 MeV has been identified ‘) as the analog of 44Ca(0) and carries all the T, l,, = 3 strength observed. No other isobaric analog state was identified in the present experiment. TABLE 3 Strength sums XC2S T, states
Exp. T, states
Exp .
orbit theory “) theory b, PI-k a) (d, t)
14 3.75 3.64 3.76 d, 3.65 *)
ld+ 3.0
orbit theory “) theory b,
lf; 0.25 0.18 0.10 “) 0.22 b)
ld+ 1.0
i We, ~4 (d, t) “)
“) Simple shell model. ‘) From ref. I). ‘) States nos. 8, 10, 11, 12 and 17. ‘) IAS no. 15.
1.21 “) 2.53 r)
2% 1.5 0.12 ‘) 0.75 ‘) 2% 0.5
d, States nos. 0 through 7 and 9. ‘) From ref. Ii). r) Includes several other states. *) State no. 13.
Since the 4sSc target has four neutrons and one proton in the If* shell, the simple shell-model sum-rule limit ” ) indicates that the I, = 3 strength is divided such that the T, strength is C’S = 3.75, while the T, strength is C2S = 0.25. The calculations of McCullen et al. ‘) for neutrons and protons in the f4 configuration predict the strengths indicated in fig. 5. The agreement between the observed Z, = 3 transitions and the calculated strengths is fair. This model, however, does not predict negative-parity states for which core-excitation configurations are needed. The deduced experimental sum strengths are compared with the theoretical predictions, as well as with the results of Ohnuma and Sourkes ‘I) in table 3. Two low-lying negative-parity states are excited in the 43Ca(3He, d)44Sc experiment “), A state at E, = 0.637 MeV is reported with Z,, = 0, while a state at E, = 1.683 MeV is reported with Z,, = 2. No I,, = 0 transition was observed in the present neutron pick-up experiment below 1.0 MeV excitation. Ohnuma and Sourkes “) report an
186
J. RAPAPORT
et nf.
I, = 2 transition to a state at E, = 0.632 MeV. If the state excited in the protontransfer reaction has mainly a 2s+ proton-hole configuration, it should be weakly excited in the neutron pick-up from “%c. If the spin of this state is J” = (3,4)-, it could be excited with an I, = 2 transfer as observed by Ohnuma and Sourkes. The i, = 3 transition at E, = 0.654 observed in this experiment is seen somewhat broader than other a-groups (see fig. 2), indicating an unresolved doublet. In the present experiment, an 1, = 2 transition is observed at E, = 1.682 MeV with a strength of C2S = 0.32 and several other transitions have been assigned tentativeiy as I,, = 2. A tentative I, = 0 is assigned to a transition observed at 2.584 MeV excitation energy. However, several /, = 0, as well as 2, = 0+2 transitions, are reported in the (d, t) experiment 11) as low as 1.012 MeV excitation energy in 44Sc. The isobaric analog of the 44Ca(g.s.) in 44Sc has previously been identified as a state at 2.796 MeV by Schwartz “) and at 2.784 MeV by Ohnuma and Sourkes Ii). Using our measured Q-value for the I,, = 3 transition to the 44Ca(g.s.) isobaric analog, and the 45Sc(t, x)“4Ca ground state Q-value is), we determined the Coulomb displacement energy to be AE, = 7.201 f0.025 MeV. The value is in agreement with AE, = 7.219+0.011 MeV reported by Ohnuma and Sourkes ii) obtained from a weighted average of three experimental values. 4.2. COMPARISON
WlTH OTHER EXPERIMENTS
Our results are in good agreement with the (p, d) results of Kashy “) and with the (d, t) results of Ohnuma and Sourkes ’ “). In certain cases, the latter authors have been able to assign a unique 1, value to certain transitions. It is known that Z-value assignments are more easily made by (d, t) reactions than in the (3He, a) reactions where the angular distributions for I,, = 3 and In = 2 are often very similar.The extracted vatues of strengths are in good agreement. A comparison of spectroscopic info~tion to levels in 44Sc below 3.0 MeV is presented in table 4. It is interesting to compare the proton stripping and neutron pick-up experiments leading to 44Sc; this comparison allows some spin assignments to be made. Both 45S~ and 43Ca have a ground state J” = z’ -. , therefore, a If, nucleon transfer allows the excitation of T, states with l+ 5 J” 5 7+, while f = 1 + 3 transi~ons must correspond to states with 2+ 5 Jn 5 5+. Pure f, = 3 and Ia = 3 transitions would likely correspond to final states with J” = 1+, 6+, or 7+. Four states below 1.0 MeV excitation energy are seen with pure I, = 3 and I,, = 3 transitions: (i) The ground state with a known I’) J” = 2+, in disagreement with the above conjecture. (ii) The E, = 0. 271 MeV isomeric state (T, = 2.44 d) with a known “) J” = 6’. (iii) The state at EX = 0.976 MeV, for which Kashy “) has suggested a J” = 7+ because of its (p, d) strength. (iv) The state at E, = 0.654 MeV which is a J” = 1’ state. This assignment is made on the basis of the observed L = O-t-2 transition in the 42Ca(3He, p) reaction [ref. ’ “)I*
187
++Sc LEVELS TABLE
Low-lying Level
states
in 44Sc with known
Jr
Stripping 43Ca(3He,
d)
4 spectroscopic reactions
czs
I.
c2s
2
3
0.35
3
0.35
4
3 1
3 3
0.50 0.37
2
0.48 0.03 0.35 0.06
2 3 3
0.13 0.32 0.20
3 3
0.32 0.14
3
1.29
3
1.37
0
0.02 0.04 0.25 0.03 0.26 0.41
3
0.23
3
0.23
(2)
0.20
(2) (3)
0.45 0.25
426
112
1
632
f
+3 +3
(2,‘l, 4, 5)+
971 980
i 4d) f20 ‘)
(7)+ ‘) 3+
1012 1056
f10d) f 5 d,
(3,4)_ (3,4, 5)+
0 3 1 +3 3
*
7d)
(2,354,
5)+
1415
f10d)
1434
*
5 d)
(2,394, (2, 3,4,
5)5)+
1512
f
9”)
(2, 3,4,
5)’
1534
+
5d)
(2, 3,4,5)+
1560
i
1598
i-13
sd)
+3
0+2
2+4
i-3
0.170 0.340 0.024 0.490
1 -+3 1 +3 1 +3
0.010 0.070 0.020 0.141 0.038 0.756
1 $3
1187
1
4
1 ‘3 1 +3 2
1 +3 0
(3,4)-
+2 b,
a)
‘)
&I
0.34 0.023 0.450 0.004 0.084 0.04 0.15 0.055 0.166 1.62
5 d,
45Sc(3He,
L
3 1
f
t)
?
strength
0.28
765 669
YSc(d,
reactions
1,
3
(3,4)_
p)
‘)
2+ ‘) 67%*0.03 ‘) I+h ) 146.25+ 0.04 ‘) I+ ‘) 239 &12 ‘) 270.6 + 0.6 p, 6+ ‘) 353 + 5 d) (3,4, 5)’
5 d,
“)
Pick-up
“2Ca(3He,
b,
“)
information
(2, 394, 5)-
1 +3
1653 *12 b) (2, 394, 5)+ 1654 flOd) (3,4)1688 & 6d) (2, 3,4, 5)-Several other higher excited states ‘WZa(O). 2784 110”) 0’
1
0.014 0.043 0.014
2 0.17 are seen in these 3
0.04 0.15 0.05 0.12
0.11
0 2 reactions. 0
Listed
below 3
0.01 0.41 is only 0.22
0.32 2 the analog of 3
0.10
“) See a more detailed discussion in subsect. 4.2. d, Ref. II). “) Ref. 9). ‘) Ref. I”). ‘) This work. Also see table 1. r) Ref . I’) . “) Refs. z’s 4). e, From ref. “). ‘) Refs. 22* *3* 4). ‘) Ref. *). ‘) A level at 429&13 keV with Zp = 1+3 is reported in ref. 9); a level at 427*8 keV is reported in ref. I’). Either a close-lying doublet or because of the weakness of the observed transitions a missassigned I-value transfer. ‘) Ref. 6).
188
J. RAPAPORT
et al.
Schlegel et al. lo) also report an L = 2+4 transition to a level at 0.98 MeV, which would correspond to a state with J” = 3’. Both in the proton stripping, as well as in the neutron pick-up, the observed I = 3 transition to a state at E, = 0.976 MeV is the strongest, thus supporting a high J-value. A state with J” = 7+ is also predicted from the shell-model calculations ‘) at about 1.0 MeV excitation energy. However, because of the high L-transfer required, this state should be very weakly excited in the (3He, p) reaction. Thus, it is very likely that there are two close-lying states at E, = 0.98 MeV with J” = 3+ and 7+. States at E, = 0.344 and 1.043 MeV are excited with I,, = 3 in the present experiment, with I, = 1 + 3 in the (3He, d) reaction ‘), and with L = 4 in the (jHe, p) reaction. This limits their spins to J” = 3+, 4+ or 5+. The two low-lying states at E, = 0.068 and 0.146 MeV were not excited in the present experiment. It is interesting to note that they have been seen only in the decay of 44Ti [ref. 4)], in the 46Ti(d, a) reaction done by Bjerregaard ef al. “) with 3 to 4.3 MeV incident energy, and in the 44Ca(p, n) reaction reported by Glass and Kliwer [ref. ““)I. They made an assignment of J = 1 for the 0.068 MeV state from correlation measurements of the gammas from the decay of 44Ti. Brandi et al. ‘“) excited the 0.146 Me\’ isomeric state (T+ = 49.6 ps) by means of the 45Sc(y, n) reaction. These states have not been excited by a direct process in either single- or two-nucleon transfer reactions. This points towards a rather complex configuration for these states. The use of the DW code TANYA from the MIT cyclotron group is acknowledged. One of us (J.R.) would like to thank Dr. P. D. Kunz at the University of Colorado for the use of his DWBA computer code DWUCK. The help of Robert Lilley at the Ohio University Computer Center is greatly appreciated. We wish to thank A. P. Luongo for the careful fabrication of the 4sSc target. References 1) J. D. McCullen, B. F. Bayman and L. Zamick, Phys. Rev. 134 (1964) B515 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
15)
F. B. Malik and W. Scholz, Phys. Rev. 150 (1966) 919 J. Rapaport, W. E. Dorenbusch and T. A. Belote, Nucl. Phys. A109 (1968) 657 R. A. Ristinen and A. W. Sunyar, Phys. Rev. 153 (1967) 1209 D. E. Bainum, J. Rapaport, T. A. Belote and W. E. Dorenbusch, Bull. Am. Phys. Sot. 13 (1968) 174 E. Kashy, Enys. Rev. 134 (1964) B378 A. M. Smith and F. E. Steigert, Phys. Rev. 122 (1961) 1527 J. H. Bjerregaard, P. F. Dahl, 0. Hansen and G. Sidenius, Nucl. Phys. 51 (1964) 641 J. J. Schwartz, Phys. Rev. 175 (1968) 1453 W. Schlegel, D. Schmitt, R. Santo and F. Puhlhofer, Nucl. Phys. Al53 (1970) 502 H. Ohnuma and A. M. Sourkes, Phys. Rev. C3 (1971) 158 D. L. Harris and J. D. McCullen, Phys. Rev. 132 (1963) 310 J. A. Bruner and L. M. Langer, Phys. Rev. 79 (1950) 606 J. J. Simpson, W. R. Dixon and R. S. Storey, Phys. Lett. 30B (1969) 478; J. Rapaport, J. B. Ball, R. L. Auble, T. A. Belote and W. E. Dorenbusch, Bull. Am. Phys. Sot. 15 (1970) 528 J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67 (1965) 1
-SC LEVELS
189
16) E. H. Auerbach, Brookhaven National Laboratory, Report BNL 6562, unpublished 17) A. Trier, L. Gonzalez, J. Rapaport, T. A. Belote and W. E. Dorenbusch, Nucl. Phys. All1 (1968) 241 18) E. P. Gibson, B. W. Ridley, J. J. Kraushaar, M. E. Rickey and R. H. Bassel, Phys. Rev. 155 (1967) 1194 19) R. Stock, R. Bock, P. David, H. H. Duhm and T. Tamura, Nucl. Phys. A104 (1967) 136 20) P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 1 21) J. B. French and M. H. Macfarlane, Nucl. Phys. 26 (1961) 168 22) J. C. Glass and J. K. Kliwer, Nucl. Phys. A115 (1968) 234 23) K. Brandi el al., Nucl. Phys. 59 (1964) 33
LEVELS
by photo~rint
or microfilm without written permission from the publisher
OF 44Sc BY THE (3He, a) REACTION ON 45Sc 3. RAPAPORT
Physics Department, Ohio. University, Athens, Ohio t T. A. BELOTE and D. E. BAINUMtt Physics department and Laboratory for Nuclear Science tt? ~ussachuset?s I~stitate of technology, Ca~zbridge, ~assac~asetts and W. E. DORENBUS~H Physics f)epartment, Wayne State University, Detroit, Michigan Received (Revised
IO December 1970 15 February 1971)
Abstract: The 45Sc(3He, o()~~SCreaction has been studied at an incident 3He energy of 13.0 MeV. A ground state Q-value of 9.249&0.015 MeV was measured for this reaction. Alpha-particle spectra were obtained at lab angles between 7.5” and 172.5’ for transitions to levels below 3.0 MeV excitation energy. A distorted-wave analysis was carried out to obtain I. values and spectroscopic strengths. The isobaric analog of 44Ca(0) was observed at an excitation energy of 2.763&0.020 MeV. The results are compared with other experimental data and with theoretical predictions. E
NUCLEAR
REACTIONS 45Sc(3He, dt), (3He, “He), ECHO= 13.0 MeV; measured u(E1, @), Q. %Sc deduced levels, J, z, t,, transition strengths.
1. Introduction
A considerable amount of experimental and theoretical work on lf; nuclei has been done in the last few years. McCullen ef al. ‘) using a slleli-model description can explain some of the low-lying properties of these nuclei, while Malik and Scholz ‘) assuming If+ con~gurations and the collective mode! with Coriolis coupling are able to describe at least qualitatively other features of low-lying odd nuclei in this region. The 44Sc nucleus with four lf+ nucleons outside a doubly magic 4oCa core should have a level structure similar to that of its cross conjugate, 52Mn. This latter nucleus has been studied previously in this laboratory by means of the (3He, p) and (d, z) reactions “)_ However, two low-lying states in 44Sc at 0.068 and 0.146 MeV reported by Ristinen and Sunyar “) had no observed counterparts in s2Mn. The neutron pickup reaction leading to states in 44Sc was therefore undertaken ‘. 7 Work supported in part by the US Atomic Energy Commission. tt Present address: Edgewood Arsenal, Maryland. ttt Part of this work was carried out under AEC Contract AT(30-l)-2098. $ Preliminary results of this work were presented at the APS meeting in Boston, February 1968 [ref. ‘)I. Those results have also been compiled by Ohnuma and Sourkes in their recent ‘%%(d, t) publication t1). 177
178
J. RAPAPORT
et
al.
Previously, Kashy “) reported ten levels below 1.66 MeV of excitation in 44Sc by means of the 45Sc(p, d) reactio n. Neutron groups from the 41K(a, n)44Sc reaction have been studied by Smith and Steigert ‘). Bjerregaard et al. “) report levels in “SC below 1.427 MeV observed by the 46Ti(d, a) reaction. More recently, Schwartz “) reported the t3He, d) proton stripping on 43Ca with high resolution up to an excitation energy of 5.5 MeV in 44Sc. Schlegel et al. lo) observed states in 44Sc up to 5.59 MeV of excitation excited by the 4”Ca(3He, P)~~SC reaction, while Ohnuma and Sourkes have reported the (d, t) neutron pick-up reaction ll). Using the atomic beam, magnetic-resonance method, Harris and McCulIen “) have determined the nuclear spins for the ground state and the isomeric state at E, = 271.3 F0.7 keV [ref. ‘“)I to be 2 and 6, respectively. Ristinen and Sunyar “) assign J” = 1 + both to the 0.068 and 0.146 MeV states from the 44Ti(0) decay. However, from a more recent determination 14) of the 44Ti(0) mass, the calculated logft to the 0.146 MeV level is 6.5 rather than < 4.4 as previously thought, therefore weakening this assignment. A J” = l- has also been postulated for this state 14). ___---
45sc+ 3Ha E
3t.k ---
c, ~
-
= 13.0 MeV set I set 2
IO"
60
90
120
I80
G&,{degrees) Fig. 1. Angular distribution for the elastic observed cross sections to the Rutherford indicate statistical uncertainties. The curves eters
scattering of 13.0 MeV 3He from ‘?Sc. The ratio of the cross section is presented versus angle. The error flags are optical-model fits to the data using the 3He paramgiven in table 2.
4io
Fig. 2. Alpha-particle
I-------
EXCITATION
ENERGY
(MeV)
DISTANCE
ALONG
PLATE
(cm)
IO
SPECTROGRAPH FIELD = II 896 EXPOSURE = 7 500 pC
E+*= 13.0 MeV
=30”
CI?%C
ANGLE
(‘He,
LA5
?3
_-3p_ .- ______--~____.. ,
GAUSS
Xi
__-_!p -----
spectrum from 45S~(3He, CL)~%Creaction at fYlab= 30”. Alpha-particle groups corresponding the numbers used to identify these states in table 1.
.~
-1
to states in “%c are labelled with
op _.-_
180
J. RAPAPORT
et al.
In the present experiment, the MIT multiple-gap spectrograph has been used to reaction. Data were obmomentum analyse a-particles from the 4sSc(3He, CX)~~SC tained for 18 levels up to 3.004 MeV excitation. The experimental procedure and results’are given in sect. 2; the distorted-wave (DWBA) analysis of the measured angular distributions is presented in sect. 3. A discussion of the level scheme of 44Sc, sum-rule analysis and comparison with other experiments is given in sect. 4. 2. Experj~ental procedure and results 2. I. TARGETS The target used in the present experiment was prepared by vacuum evaporation of metallic scandium, a monoisotopic element, onto a thin carbon-backing film. The 45Sc target thickness was measured to be 52 .ug/cm’. k
F i i?
0 Q=9.249 MeV B, =3
E,-&fiS MeV I,
I
3 =0.654 P, =3
I
=3
IS
e
cm
Meti
\
(degrees)
Fig. 3. Angular distributions of a-particles from ‘?SC(~H~, CX)~%C.The distributions are labelled with the numbers used to identify the correspon~ng states in table 1. Statistical uncertainties are indicated by error flags on the data points. The curves are DWBA predictions using the set of parameters 2a given in table 2.
“SC LEVELS 2.2. ELASTIC
181
SCATTERING
Elastic scattering of 3He from 45Sc was observed at 13.0 and 5.0 MeV bombarding energies. The 5.0 MeV elastic scattering was used to determine the target thickness by assuming Rutherford scattering behavior. The 13.0 MeV results are shown in fig. 1 and were used to determine the optical-model parameters; the curves represent the DW prediction calculated for the two sets of 3He parameters (see subsect. 3.1). 2.3. THE
45Sc(3He,
cr)“‘%c REACTION
Reaction products were detected using 50 ,um Tlford KO nuclear emulsion plates at lab angles between 7.5” and 172.5” in 7.5” intervals; these plates were chosen because of their low sensitivity to protons and deuterons. The cc-particle spectrum obtamed at era,, = 30” after a 7500 PC exposure is shown in fig. 2. The energy resolution was 30 keV. Alpha-particle groups corresponding to a residual mass of 44 were identified from their kinematic shift with angle. Up to an excitation energy of 3.0 MeV, 18 transitions were identified. Above that energy, the level density, as well as the weakness of the transitions, did not allow unique level assignments. 1
r
:
i
P E,=l.424 MeV I” =(Z)
t
8
cm
(degrees)
Fig. 4. See caption
for fig. 3.
J. RAPAPORT
182
et al.
TABLE 1 4%c(3He, ~r)~~Sc results
Level
0
Q “) (MW 0
ClojdsZb) (mb/sr)
I, ‘)
c2s
J”
3 3 3 3 3 3 3
0.35 0.50 0.37 0.32 0.14 1.37 0.23
2+ d) 6+ d,
(:)
0.20 0.23
I (2) (3)
0.25 0.45
(:) (3) (2) (0)
0.32 0.30 0.15 0.19 0.12
(3_, 4-)
3
0.10
0+ (IAS)
(2)
0.20
9.249 8.980 8.905 8.595 8.493 8.273 8.206 8.068 7.825 7.718
0.269 0.344 0.654 0.756 0.976 1.043 1.181 1.424 1.531
0.22 0.35 0.28 0.26 0.11 1.09 0.18 0.20 0.08 0.24
11
7.567 7.139
1.682 2.110
0.18 0.17
12 13 14 15 16 17
7.039 6.665 6.553 6.486 6.342 6.245
2.210 2.584 2.696 2.763 2.907 3.004
0.10 0.03 ‘) 0.01 q 0.15 8) 0.06 0.14
1 2 3 4 5 6 7 8 9 10
(7)+ ‘)
“) The estimated error is &20 keV for levels l-17. The uncertainty for the ground state Q-value is &15 keV. ‘) Maximum observed cross section at Oiab= 7.5”, except as indicated. ‘) Tentative values in parentheses. “) Ref. 12). ‘) Ref. 6). ‘) At I!$.,,= 30”. ‘) At f&s = 22.5”. 2 parameters
TABLE
Optical-model Particle
“)
Set (&
(M:V) 3He
1 2
133.2 173.77 180.0 183.7 Y
4He E
“) The optical potential
12.18 16.21 31.65 26.0
1.36 1.14 1.22 1.40 1.25
0.633 0.734 0.796 0.560 0.65
used was of the form: V(r) = - V(eX+l)-l-iW(eX’+l)-‘+
1.74 1.604 1.63 1.48
(L)
rot (fm)
0.789 0.753 0.423 0.560
1.40 1.40 1.30 1.40
Vc(r,rc),
with r-roA113 x=-----, a
x’ =
r_r’,,AW a’
’
rc = rocA1’3.
b, Adjusted to give the transferred neutron a binding energy of -Q(3He,
~)+20.58
MeV.
“SC
LEVELS
183
The Q-values, excitation energies, and maximum observed cross sections are given in columns 2, 3 and 4 of table 1. Columns 5 and 7 give i, and f” assigned to the observed transitions, while in column 6 the deduced spectroscopic strengths are tabulated. To obtain the Q-values, a correction was made to the calibration of the spectrograph because of the high field used. This correction was obtained by observing a-groups from contaminants with known Q-values. The measured Q-value for the ground state transition was 9.249-tO.015 MeV, in good agreement with the value of Q = 9.259~0.007 MeV obtained from the mass table 1“). The angular distributions are shown in figs. 3 and 4. The curves shown are DW predictions using the set of parameters 2a given in table 2. 3. DWBA analysis 3.1.
ELASTIC
SCATTERING
The experimental 13.0 MeV elastic 3He scattering data were analysed with the optical-model search code ABACUS 16). The search was initiated with two sets of parameters. Set I was obtained starting from that of 13.0 MeV 3He elastic scattering by “4Fe [ref. I’)], while set 2 followed from the parameters given by Gibson ef al. 18). The DW elastic-scattering calculated curves are shown in fig. 1, where they are compared with the experimental data presented as the ratio of the observed cross sections to the Rutherford cross sections. 3.2. TRANSlTION
STRENGTHS
The relation between experimental and calculated cross section is given by (d~ld~)~~~ = NC%@), where S is the spectroscopic factor, C the isospin coupling coefficient, and ~(0) the calculated cross section. The value of N, which arises from the overlap integral between the ‘He and CIwave functions, is not too we11known. An empirically deduced value of N = 25 rt 5 was used in the analysis I’). The DW code TANYA developed at MIT and the code DWUCK were used to calculate cr(@)from the sets of parameters given in table 2. Two sets of 3He and two sets of a-particle potential parameters were used. The a-particle sets of parameters were obtained from the work of Stock et nl. 19). From the different combination of parameters, the caIculations done with sets la and 2a were very simiIar, although set ?a seemed slightly better and was therefore used throughout the strength analysis. A Woods-Saxon potential was used both for the neutron bound state and the “He and or-potentials. VoIume absorption was used for both the 3He and r-potentials. All calculations were performed with a zero-range interaction. No lower cut-offwas used. The values of the orbital angular momentum of the transferred neutron were deduced for the various rx-groups by comparing the shapes of the calculated and ob-
184
J. RAPAPORT
et al.
served angular distributions. The transition strengths listed in table 1 were obtained by matching the experimental cross sections summed over angles to the calculated cross-section sums. At about 2.0 MeV excitation energy, Q = 7.25 MeV, the calculated cross sections for 1, = 2 and I, = 3 are quite similar in shape. In some cases both fitted the observed angular distributions equally well (see fig. 4). Tentative values for 1, for these cases are given in parentheses. 4. Discussion 4.1. STRENGTH
FUNCTION
AND SUM RULE
Spectroscopic strengths extracted from the measured angular distributions are plotted versus excitation energy in fig. 5 are and compared with the theoretical cal-
“SC
Level
Scheme
c
ysc
J”
(He.a)P”
P,=O
x,=2
P,=3
J”
McCullen,,Bayman ond Zomck
Fig. 5. Strength function for 45Sc(3He, ~r)~%c reaction. An excitation energy scale is given on the left. States in 44Sc (see subsect. 4.2) are compared with the present data. The values of the transition strength C’S from table 1 are indicated.
185
“%c LEVELS
culations
of McCullen
et al. ‘). Recently,
similar
calculations
have been repeated
using two-particle matrix elements taken from the experimental spectrum of 42Sc [see refs. lo* “)I. Th is calculation, while only slightly changing the neutron transfer strength, gives the position of the first J” = 6+ state at 0.358 MeV, in closer agreement with the known J” = 6+ level at 0.271 MeV. In the left column, the 44Sc level scheme taken from the compilation of Endt and van der Leun ““) and up-dated with recent data 9-11) is indicated. The spin assignments are taken from the same sources (see also sect. 1). The (3He, IX) reaction on 45Sc excites states in 44Sc with T, = 1 and T, = 2. The Z, = 3 transition to the T, states is seen fragmented in at least nine states below 2.5 MeV excitation energy. The level at E, = 2.763 MeV has been identified ‘) as the analog of 44Ca(0) and carries all the T, l,, = 3 strength observed. No other isobaric analog state was identified in the present experiment. TABLE 3 Strength sums XC2S T, states
Exp. T, states
Exp .
orbit theory “) theory b, PI-k a) (d, t)
14 3.75 3.64 3.76 d, 3.65 *)
ld+ 3.0
orbit theory “) theory b,
lf; 0.25 0.18 0.10 “) 0.22 b)
ld+ 1.0
i We, ~4 (d, t) “)
“) Simple shell model. ‘) From ref. I). ‘) States nos. 8, 10, 11, 12 and 17. ‘) IAS no. 15.
1.21 “) 2.53 r)
2% 1.5 0.12 ‘) 0.75 ‘) 2% 0.5
d, States nos. 0 through 7 and 9. ‘) From ref. Ii). r) Includes several other states. *) State no. 13.
Since the 4sSc target has four neutrons and one proton in the If* shell, the simple shell-model sum-rule limit ” ) indicates that the I, = 3 strength is divided such that the T, strength is C’S = 3.75, while the T, strength is C2S = 0.25. The calculations of McCullen et al. ‘) for neutrons and protons in the f4 configuration predict the strengths indicated in fig. 5. The agreement between the observed Z, = 3 transitions and the calculated strengths is fair. This model, however, does not predict negative-parity states for which core-excitation configurations are needed. The deduced experimental sum strengths are compared with the theoretical predictions, as well as with the results of Ohnuma and Sourkes ‘I) in table 3. Two low-lying negative-parity states are excited in the 43Ca(3He, d)44Sc experiment “), A state at E, = 0.637 MeV is reported with Z,, = 0, while a state at E, = 1.683 MeV is reported with Z,, = 2. No I,, = 0 transition was observed in the present neutron pick-up experiment below 1.0 MeV excitation. Ohnuma and Sourkes “) report an
186
J. RAPAPORT
et nf.
I, = 2 transition to a state at E, = 0.632 MeV. If the state excited in the protontransfer reaction has mainly a 2s+ proton-hole configuration, it should be weakly excited in the neutron pick-up from “%c. If the spin of this state is J” = (3,4)-, it could be excited with an I, = 2 transfer as observed by Ohnuma and Sourkes. The i, = 3 transition at E, = 0.654 observed in this experiment is seen somewhat broader than other a-groups (see fig. 2), indicating an unresolved doublet. In the present experiment, an 1, = 2 transition is observed at E, = 1.682 MeV with a strength of C2S = 0.32 and several other transitions have been assigned tentativeiy as I,, = 2. A tentative I, = 0 is assigned to a transition observed at 2.584 MeV excitation energy. However, several /, = 0, as well as 2, = 0+2 transitions, are reported in the (d, t) experiment 11) as low as 1.012 MeV excitation energy in 44Sc. The isobaric analog of the 44Ca(g.s.) in 44Sc has previously been identified as a state at 2.796 MeV by Schwartz “) and at 2.784 MeV by Ohnuma and Sourkes Ii). Using our measured Q-value for the I,, = 3 transition to the 44Ca(g.s.) isobaric analog, and the 45Sc(t, x)“4Ca ground state Q-value is), we determined the Coulomb displacement energy to be AE, = 7.201 f0.025 MeV. The value is in agreement with AE, = 7.219+0.011 MeV reported by Ohnuma and Sourkes ii) obtained from a weighted average of three experimental values. 4.2. COMPARISON
WlTH OTHER EXPERIMENTS
Our results are in good agreement with the (p, d) results of Kashy “) and with the (d, t) results of Ohnuma and Sourkes ’ “). In certain cases, the latter authors have been able to assign a unique 1, value to certain transitions. It is known that Z-value assignments are more easily made by (d, t) reactions than in the (3He, a) reactions where the angular distributions for I,, = 3 and In = 2 are often very similar.The extracted vatues of strengths are in good agreement. A comparison of spectroscopic info~tion to levels in 44Sc below 3.0 MeV is presented in table 4. It is interesting to compare the proton stripping and neutron pick-up experiments leading to 44Sc; this comparison allows some spin assignments to be made. Both 45S~ and 43Ca have a ground state J” = z’ -. , therefore, a If, nucleon transfer allows the excitation of T, states with l+ 5 J” 5 7+, while f = 1 + 3 transi~ons must correspond to states with 2+ 5 Jn 5 5+. Pure f, = 3 and Ia = 3 transitions would likely correspond to final states with J” = 1+, 6+, or 7+. Four states below 1.0 MeV excitation energy are seen with pure I, = 3 and I,, = 3 transitions: (i) The ground state with a known I’) J” = 2+, in disagreement with the above conjecture. (ii) The E, = 0. 271 MeV isomeric state (T, = 2.44 d) with a known “) J” = 6’. (iii) The state at EX = 0.976 MeV, for which Kashy “) has suggested a J” = 7+ because of its (p, d) strength. (iv) The state at E, = 0.654 MeV which is a J” = 1’ state. This assignment is made on the basis of the observed L = O-t-2 transition in the 42Ca(3He, p) reaction [ref. ’ “)I*
187
++Sc LEVELS TABLE
Low-lying Level
states
in 44Sc with known
Jr
Stripping 43Ca(3He,
d)
4 spectroscopic reactions
czs
I.
c2s
2
3
0.35
3
0.35
4
3 1
3 3
0.50 0.37
2
0.48 0.03 0.35 0.06
2 3 3
0.13 0.32 0.20
3 3
0.32 0.14
3
1.29
3
1.37
0
0.02 0.04 0.25 0.03 0.26 0.41
3
0.23
3
0.23
(2)
0.20
(2) (3)
0.45 0.25
426
112
1
632
f
+3 +3
(2,‘l, 4, 5)+
971 980
i 4d) f20 ‘)
(7)+ ‘) 3+
1012 1056
f10d) f 5 d,
(3,4)_ (3,4, 5)+
0 3 1 +3 3
*
7d)
(2,354,
5)+
1415
f10d)
1434
*
5 d)
(2,394, (2, 3,4,
5)5)+
1512
f
9”)
(2, 3,4,
5)’
1534
+
5d)
(2, 3,4,5)+
1560
i
1598
i-13
sd)
+3
0+2
2+4
i-3
0.170 0.340 0.024 0.490
1 -+3 1 +3 1 +3
0.010 0.070 0.020 0.141 0.038 0.756
1 $3
1187
1
4
1 ‘3 1 +3 2
1 +3 0
(3,4)-
+2 b,
a)
‘)
&I
0.34 0.023 0.450 0.004 0.084 0.04 0.15 0.055 0.166 1.62
5 d,
45Sc(3He,
L
3 1
f
t)
?
strength
0.28
765 669
YSc(d,
reactions
1,
3
(3,4)_
p)
‘)
2+ ‘) 67%*0.03 ‘) I+h ) 146.25+ 0.04 ‘) I+ ‘) 239 &12 ‘) 270.6 + 0.6 p, 6+ ‘) 353 + 5 d) (3,4, 5)’
5 d,
“)
Pick-up
“2Ca(3He,
b,
“)
information
(2, 394, 5)-
1 +3
1653 *12 b) (2, 394, 5)+ 1654 flOd) (3,4)1688 & 6d) (2, 3,4, 5)-Several other higher excited states ‘WZa(O). 2784 110”) 0’
1
0.014 0.043 0.014
2 0.17 are seen in these 3
0.04 0.15 0.05 0.12
0.11
0 2 reactions. 0
Listed
below 3
0.01 0.41 is only 0.22
0.32 2 the analog of 3
0.10
“) See a more detailed discussion in subsect. 4.2. d, Ref. II). “) Ref. 9). ‘) Ref. I”). ‘) This work. Also see table 1. r) Ref . I’) . “) Refs. z’s 4). e, From ref. “). ‘) Refs. 22* *3* 4). ‘) Ref. *). ‘) A level at 429&13 keV with Zp = 1+3 is reported in ref. 9); a level at 427*8 keV is reported in ref. I’). Either a close-lying doublet or because of the weakness of the observed transitions a missassigned I-value transfer. ‘) Ref. 6).
188
J. RAPAPORT
et al.
Schlegel et al. lo) also report an L = 2+4 transition to a level at 0.98 MeV, which would correspond to a state with J” = 3’. Both in the proton stripping, as well as in the neutron pick-up, the observed I = 3 transition to a state at E, = 0.976 MeV is the strongest, thus supporting a high J-value. A state with J” = 7+ is also predicted from the shell-model calculations ‘) at about 1.0 MeV excitation energy. However, because of the high L-transfer required, this state should be very weakly excited in the (3He, p) reaction. Thus, it is very likely that there are two close-lying states at E, = 0.98 MeV with J” = 3+ and 7+. States at E, = 0.344 and 1.043 MeV are excited with I,, = 3 in the present experiment, with I, = 1 + 3 in the (3He, d) reaction ‘), and with L = 4 in the (jHe, p) reaction. This limits their spins to J” = 3+, 4+ or 5+. The two low-lying states at E, = 0.068 and 0.146 MeV were not excited in the present experiment. It is interesting to note that they have been seen only in the decay of 44Ti [ref. 4)], in the 46Ti(d, a) reaction done by Bjerregaard ef al. “) with 3 to 4.3 MeV incident energy, and in the 44Ca(p, n) reaction reported by Glass and Kliwer [ref. ““)I. They made an assignment of J = 1 for the 0.068 MeV state from correlation measurements of the gammas from the decay of 44Ti. Brandi et al. ‘“) excited the 0.146 Me\’ isomeric state (T+ = 49.6 ps) by means of the 45Sc(y, n) reaction. These states have not been excited by a direct process in either single- or two-nucleon transfer reactions. This points towards a rather complex configuration for these states. The use of the DW code TANYA from the MIT cyclotron group is acknowledged. One of us (J.R.) would like to thank Dr. P. D. Kunz at the University of Colorado for the use of his DWBA computer code DWUCK. The help of Robert Lilley at the Ohio University Computer Center is greatly appreciated. We wish to thank A. P. Luongo for the careful fabrication of the 4sSc target. References 1) J. D. McCullen, B. F. Bayman and L. Zamick, Phys. Rev. 134 (1964) B515 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
15)
F. B. Malik and W. Scholz, Phys. Rev. 150 (1966) 919 J. Rapaport, W. E. Dorenbusch and T. A. Belote, Nucl. Phys. A109 (1968) 657 R. A. Ristinen and A. W. Sunyar, Phys. Rev. 153 (1967) 1209 D. E. Bainum, J. Rapaport, T. A. Belote and W. E. Dorenbusch, Bull. Am. Phys. Sot. 13 (1968) 174 E. Kashy, Enys. Rev. 134 (1964) B378 A. M. Smith and F. E. Steigert, Phys. Rev. 122 (1961) 1527 J. H. Bjerregaard, P. F. Dahl, 0. Hansen and G. Sidenius, Nucl. Phys. 51 (1964) 641 J. J. Schwartz, Phys. Rev. 175 (1968) 1453 W. Schlegel, D. Schmitt, R. Santo and F. Puhlhofer, Nucl. Phys. Al53 (1970) 502 H. Ohnuma and A. M. Sourkes, Phys. Rev. C3 (1971) 158 D. L. Harris and J. D. McCullen, Phys. Rev. 132 (1963) 310 J. A. Bruner and L. M. Langer, Phys. Rev. 79 (1950) 606 J. J. Simpson, W. R. Dixon and R. S. Storey, Phys. Lett. 30B (1969) 478; J. Rapaport, J. B. Ball, R. L. Auble, T. A. Belote and W. E. Dorenbusch, Bull. Am. Phys. Sot. 15 (1970) 528 J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67 (1965) 1
-SC LEVELS
189
16) E. H. Auerbach, Brookhaven National Laboratory, Report BNL 6562, unpublished 17) A. Trier, L. Gonzalez, J. Rapaport, T. A. Belote and W. E. Dorenbusch, Nucl. Phys. All1 (1968) 241 18) E. P. Gibson, B. W. Ridley, J. J. Kraushaar, M. E. Rickey and R. H. Bassel, Phys. Rev. 155 (1967) 1194 19) R. Stock, R. Bock, P. David, H. H. Duhm and T. Tamura, Nucl. Phys. A104 (1967) 136 20) P. M. Endt and C. van der Leun, Nucl. Phys. A105 (1967) 1 21) J. B. French and M. H. Macfarlane, Nucl. Phys. 26 (1961) 168 22) J. C. Glass and J. K. Kliwer, Nucl. Phys. A115 (1968) 234 23) K. Brandi el al., Nucl. Phys. 59 (1964) 33