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Spin assignments to excited states of 56Fe using inelastic proton scattering
Nuclear Physics Al65 (1971) 225-239;
@ North-Holland
Publishing
Co., Amsterdam
Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPIN ASSIGNMENTS
TO EXCITED
USING INELASTIC
STATES
OF 56Fe
PROTON SCATTERING
G. S. MAN1 Schuster Laboratory,
Manchester
University,
Received 18 November
Manchester
1970
Abstract:
Inelastic proton scattering from 56Fe at 49.35 MeV has been studied with protons from a linear accelerator. Angular distributions for thirty excited states up to an excitation of 7.5 MeV in 56Fe were obtained. Spin and parity assignments to most of the states were made using DWBA analysis with first order collective form factors. The structure of this nucleus is discussed in the light of the present data.
E
NUCLEAR REACTIONS 56Fe(p, p’), E = 49.35 MeV; measured (E,‘, f3). 56Fe deduced levels, J, x and deformation parameters. Enriched targets.
1. Introduction The excitation energies, spins and parities for many states in 56Fe are known ‘). Inelastic proton scattering on this nucleus has been studied recently by Peterson ‘) for a proton energy of 17.5 MeV. Calculations for the excitation energies have been carried out by Vervier ‘), McGrory “) and Irvine and Skouras “). For 56Fe Vervier considers only a (If;*) configuration for protons and a (2~:) configuration for neutrons. The effective interaction for the proton-proton in the zf$ orbit is taken from the 54Fe spectrum, for the neutron-neutron in the VP+ orbit from 56Ni spectrum, and for the proton-neutron in the (zf;)(vpt) configuration, is deduced from 56Co levels. The agreement with observed levels in 5 6Fe was not very good. McGrory restricted the neutron configurations to the 2p,, 2ps and If+ singleparticle orbits and the protons were restricted to the (If;“) configuration. In his calculations the 71-z interaction was obtained from the 54Fe spectrum, the v-v interaction from the shell-model calculations of Cohen et al. “) for nickel isotopes and the n-v interaction from Vervier’s ‘) calculations for N = 29 nuclei. McGrory calculated the positive parity states in 56Fe and obtained quantitative agreements for level positions as well as cross sections for 54Fe(t, p)56Fe reactions for states up to 3 MeV in excitation. The positive and negative parity states in 5 6Fe were calculated by Irvine and Skouras “) using the same configurations as McGrory for positive parity states and by including the 1% single-particle orbit in the neutron configurations for the negative parity states. They used the Rosenfeld force mixture for the two-nucleon interaction 225 April 1971
G. S. MAN1
226
T
“.LU
0.15
d
3 9 ”
I i
0.K
>
9 0.5c
75
125
CHANNEL
Fig. 1. A typical
35
time spectrum from the spark solid line is the fit to the spectra
85
135 CHANNEL
t t
175
225
NUMBER
I
!
4
275
chamber for levels to 4.7 MeV using the NSPEC programme.
185 NUMBER
Fig. 2. A typical time spectrum from the spark chamber The solid line is the fit to the spectra using
excitation.
The
235
for levels from 4.5 MeV to 8.0 MeV. the NSPEC programme.
56Fe STATES
227
and calculated the spectra assuming the spacings for the single-particle orbits used. The agreement with observed excitation energies was reasonable. TABLE 1 Energy levels (MeV) Peak no.
This work &
1 2 3 4 5 6
and spin values obtained in the present work Ref. ‘)
J
0.849 2.118 2.695 2.986 2.986 3.159 3.411 3.411
4+ 2+ f6+)
7
3.635
2+
8
3.850
2+
9
4.124
4+
10 11
4.512 4.660
34+
12 13 14 15 16
4.860 5.106 5.195 5.266 5.535
4+ $1 4+ 2+
17 18
5.763 5.880
(5’) 4+
19 20 21
6.067 6.273 6.410
4’
22 23 24 25 26 27 28
6.635 6.870 6.966 7.080 7.189 7.312 7.415
Ref. Ii)
-57
7
4
J
0.85 2.08 2.65 2.94 2.96
2+
2+
2+ 4+ 2+ 0’ 2+
3.12 3.37 3.39
4+ 2* 6+
0.847 2.08 2.657 2.939 2.960 3.120 3.123 3.369
Cl+) 4+ 2+
3.443 3.599 3.605
3+ 0+ 2+
3.829 3.857
2+ 3+
3.60 3.75 3.83 4.04 4.10 4.19 4.40 4.46 4.51 4.61 4.69 4.73 4.88 5.15 5.20 5.26 5.51 5.58 5.69 5.73 5.83 5.90 6.00 6.30
2+
2+ 2+ 2+
4f c4*1 4’ 34+ 4+ 2’ c::, (3-j
(?4) 6.48 (3-I
c:, 41 (3.4) (3,4) (3-j
2(+)
228
G. S. MANI
In this paper we report the results obtained for excitation energies, spins and parities for levels in 5 ‘jFe up to an exe’nation of 7.5 MeV using inelastic scattering of 50 MeV protons. The study was undertaken to investigate the structure of 56Fe and to compare with calculations of Irvine and Skouras. The DWBA calculations using phenomenological Microscopic calculations in a later paper.
first order collective form factors are presented in this paper. using Irvine and Skouras’s wave functions will be reported
2. Experimental technique The experiment was performed using the 50 MeV proton beam from the proton linear accelerator at the Rutherford High Energy Laboratory, Chilton, Berkshire. The inelastically scattered protons were detected by an n = 3 double focussing magnetic spectrometer with an acoustic spark chamber assembly. Details of the experimental set up have been discussed in an earlier paper “). The target used in the present experiment was self-supporting and was 99 % enriched 56Fe which had a thickness of 2 mg/cm ‘. The target was obtained from the isotope division, AERE, Harwell. Since the focal plane of the spectrometer corresponds to 5 % in momentum at 50 MeV, that is, 5 MeV in energy, in order to study excitation up to 7.5 MeV in 5 6Fe the experiment was done twice with the magnetic rigidity adjusted to obtain the lowed excitation and the higher excitation regions. There was an overlap between the two cases so that one could extract consistent values for excitation energies and angular distributions. Typical time spectra for both the cases are shown in figs. 1 and 2. The full lines in the figures are the theoretical fits to the spectra using the computer programme NSPEC described in ref. “). The method for extracting differential cross sections and the corrections for 12C and 160 impurities as well as for the neutron background are described in ref. “).
3. Results and discussion In table 1 we present the list of energy levels observed in this experiment. These are compared with the states observed in the (p, p’) reaction by Peterson ‘) and in y-ray experiments ll). All the levels of ’ 6Fe observed through various reactions are not included since there are a large number of closely spaced levels which our experiment does not resolve and most of which are not strongly excited in (p, p’) reactions. The energies of excited states in 5 6Fe obtained in the present work have an overall error of 30 keV and our energy resolution was around 70 keV. The angular distributions were analysed using DWBA theory with first order collective form factors. The interaction between the nucleus and the projectile is
229
%lZe STATES
represented by an optical model of the form
The potential U in eq. (1) included real, complex and spin-orbit terms. Then, in first order, the form factor is given by
The deformation parameter jYtis related to the restoring force parameter C of the vibrations model by /$ = (21+1)$ 1
where ho is the energy of the excited state. For uniform charge distribution of deformation fi, the electromagnetic transition strength %(EL)f is given by ‘>
The first order form factor given in (3) could only be used for single-phoebe transitions. Double-phonon excitations would need higher order terms. The optimal-m~el parameters for the DWBA calculations were obt~ned from the analysis by Mani et al. I’>. The potentials used are given below: v, = 41.3 MeV
aR = 0.64 fm
rR = 1.20 fm
W, =
0.9 MeV
WD = 8.2 MeV
a, = OS6 fm
$t =
1.25 fm
V,,*_= 7.5 Met’
rr,,,, = 0.61 fm
r $0. =
1.16 fm
rc = 1.25 fm
where V,, a,, rR are the depths, surface thickness and radius parameter for the real part of the potential. Similarly Ws (volume), W, (surface) aI and rr define the imaginary part of the potential and I!,,,.+ CL_ and r,.,. are parameters for the spin-orbit part of the potential whiIe ri: is the Coulomb radius parameter. The DWBA calculations were done by using a computer code written by Sherif “). The full Thomas term for the spin-orbit coupling was used. The deformation was maintained the same for both the central and the spin-orbit term. It was found, by varying the ratio of the central to spin-orbit deformation, that the most consistent fits were obtained with the ratio equal to unity. Fig, 3 shows the angular distributions and DWl3A fits to al1 levels that we have established to have J = 2’. In table 2 we compare the results of this experiment with various other experiments for the first excited 2+ state in 56Fe. The values of the de-
230
0
Fig. 3. Angular
20
distributions
40 60 CENTER
80 0 OF MASS ANGLE
for 2 + levels, The solid lines represent using first order collective form factors. TABLE
Comparison
of strengths
(p, p’) “) (14.3, 17.3, 17.5, 19 MeV) (p, p’) “) (30 MeV, 150 MeV) t3He, 3He’) “) (38 MeV, 22 MeV) (u, bl’) “) (22 MeV) electromagnetic b> (e, e’) ‘> (60.20 MeV) Dopper shift “) present cxp. (p, p’) (50 MeV) (a, a’) “) Average
2
of the first excited 2+ state obtained
Method
82
0.25 0.22 0.20 0.20 0.23
0.2jr: 0.02 0.215
DWBA fits to the data
P2R
from a variety of experiments (fml
1.19 1.oo 1.20 0.94 1.06
0.92 fO.09 0‘986$ID.O8
B(E2) f (e2- fm4) llOOzkl65 830$125 690f 04 7401111 9001100 1250 f270 39Of 90 81QflOO 792f 121 8901135
“) Average values obtained from ref. I). Since no errors were quoted, we have taken an arbitrary value of IS ‘4 for the error. b, Average values given in ref. ‘). “) DWBA calculation 13). The earlier Orsay value of 720 e 2 9fm4 was obtained using PWBA and when corrected using DWBA [see ref. 13>] one obtains for B(E2)t the value 12405150 &2- fm4. d, Ref. $I>. ‘) Ref. 17)*
56Fe STATES
231
formation parameter &, the deformation distance fizR and the transition strength B(E2) are given in the table. The mean value from all the results is 890 e2 * fm4 with a probable error of around 15 ‘A. It is surprising that both the low-energy proton scattering and (e, e’) experiments yield a B(E2) value slightly higher than that obtained from high-energy proton scattering, 3He and alpha scattering and Coulomb excitation. Vervier “) has calculated B(E2) on the basis of the assumptions discussed in the introduction. Since the considers only a (lf:“) configuration for protons and a (2~;) configuration for neutrons, his matrix elements for the effective E2 transition operators involve only matrix elements for protons in the lf; orbit and for neutrons in the 2p3 orbit. Hence he requires matrix elements of the form
where Q4 and Qi are the E2 operators for protons and neutrons respectively, with effective charge included. These matrix elements are obtained from the experimental values ofB(E2) for the O+ -+ 2+ transitions in 50Ti, 54Fe and 58Ni. Using these values for the tr~sition 2: -+ 0: in 56Fe, he obtains a value for B(E2) lying between 1390 and 1200 e2 - fm”. Unfortunately Vervier’s calculation does not indicate what effective charge one needs. The agreement between the experimental and the theoretical value is reasonable. The calculation does not indicate the amount of core excitation since the matrix elements for the E2 operator were obtained from known experimental values of B(E2) as described above. The wave functions of Skouras “) for the 0: and 2: states show a large admixture of p+ and f+ configurations. It would be interesting to obtain B(E2) values using these wave functions. From fig. 3 it is seen that the L = 2 theoretical curve does not reproduce very well the data for the 3.411 MeV level at large angles. Peterson “) indicated that his results for this level are consistent with the assumption that it is a doublet with spins 2+ and 6+. Theoretical calculations “-“) do predict a 6+ state around this region of excitation. The 54Fe(t, P)~~F~ reaction does not excite this state at all, and it has been suggested by Cohen and Middleton ‘I) that this could be a three-phonon vibrational state. We have attempted to fit the data assuming a mixture of 2’ and 6+ contribution in the angular distribution, The angular distribution is not very much improved by such an assumption. If the 6+ state is a three-phonon vibrational state, then the first order form factor used by us would not reproduce its angular distribution. With the assumption of an L = 2 and an L = 6 mixing, we obtain pz = 0.054 which is very close to the value of & = 0.057 that is obtained with a pure L = 2 contribution alone, and we also get /Is = 0.037 in agreement with Peterson’s ‘) estimate of 0.03. The fact that we obtain reasonably good fits at all angles for the angular distributions of other 2+ states and that the data for the 3.411 MeV level is not well fitted, even with the assumption of a (2’, 6’) doublet, with the experimental cross sections at large angles always larger than the theoretical values, tend to con-
232
G. S. MAN1
firm Cohen
and Middleton’s
suggestion
of a three-phonon
vibrational
structure
for
the 6+ state. The 2.986 MeV level that we observe (see fig. 7) can be identified with the 2.957 MeV level of Peterson ‘). Peterson contains J” = 2+ for this state. The level around 2.96 MeV is known to be a doublet ‘,11) with excitation energies of 2.960 MeV and 2.939 MeV. The 2.939 MeV is known ‘O*‘l)tohave spin O+. Inthe 54Fe(t,p)56Fereaction10) two O+ levels below 4 MeV are observed, one at 2.939 MeV and the other at 3.6 MeV Comparison
(;eY)
TABLE 3 of strengths of all 2+ states known in s6Fe from a variety of experiments
This experiment B(E2)f 82
0.847 2.658
0.06
0.2
2.960
0.02 “)
(P, P’) Y 82
17.5 MeV B(E2)+
(e, e’) “) B(E2)
810 73
0.29 0.107
14980 200
1250 37
8
0.044
34
21 41
10 ;+;J - . 55 (+35)
17
13 -64
3.370
0.06
73
0.043
32
3.60 3.75
0.05
50
0.053 0.082
49 118 \
3.856 4.73 5.535
0.03
18
0.069 0.050
0.05
50
Dopper shift d, B(E2)T 893 *90 17 k5.5
C-15)
10
6.48
0.055
53
The B(E2)t values are given in units of e2 * fm4. “) Adopted values from ref. Is) where possible. b, Values from ref. I). ‘) Values from ref. ‘a). “) Values from ref. I’). ‘) This value is very approximate since, as explained in text, it is an unresolved doublet.
and these have been confirmed from y-ray studies ‘l). The shell-model calculations of McGrory “) predict the lowest O+ level around 3 MeV while Skouras “) obtains for the lowest Of state an excitation energy of 3.4 MeV. The L = 2 DWBA prediction for the 2.957 MeV level is also shown in fig. 7. It is seen from this figure that this level cannot be a pure L = 2 transition and the discrepancy may be due to an admixture of the O+ state. This would imply a large cross section for the Of state compared to what one obtains for O+ states in nearby regions of nuclei. The angular distribution for the 6.635 MeV level is shown in fig. 3. This also is a known doublet ‘I) with excitation energies of 3.599 MeV (O+) and 3.605 MeV (2+). From the figure it is obvious that the contribution of O+ to the angular distribution of the 3.635 MeV is small. The core excited O+ level should also appear around 3 MeV excitation. Since inelastic proton scatteringstoO’stateswithlargecoreexcitationconfigurationshavealargecrosssection, our data suggests that the O+ state at 2.939 MeVis mainly due to core excitation and the
233
56Fe STATES 56 Fe (P. P’)~F~ Ep 4935hreV
0.00lL____ 0
Fig. 4. Angular
IO
distribution
I
SO 60 70 40 OF MASS ANGLE
20 30 CENTER
/
BO
3
for the lowest 4+ level in 56Fe. The solid line is the DWBA prediction for one-phonon excitation.
*%ep’l
I p, =F. Ep.4935M&
-J-i 11
4.860 4+
11’
t
4 660 4+
‘L,
t lt
1 Y 4 124 -@+f ad
h
iii
E
tt
t
t
\
I
P
tt
t’
IX 1 -
I
0 ,I
0.C )I
0
Fig. 5. Angular
20
distributions
,
40
,
60
80
0
for 4+ levels in 56Fe and DWBA fits with first order collective form factors.
234
G. S. MAN1
one at 3.599 MeV is to be identified with the shell-model state predicted by McGrory and Skouras. The 2+ level at 2.986 MeV is not reproduced in the calculation of both McGrory and Skouras and hence may also be created by core breaking. The 3.850 MeV level observed by us should be identified with the 3.839 MeV state of Seaman et al. 11) and of Peterson ‘). The assignment of 2+ to this level as shown by the data in fig. 3 is consistent with the other experiments quoted above. This level is also a doublet ‘I) with a 3+ state at 3.85 MeV. The small discrepancy between the theoretical and experimental angular distribution that we observe may be due to the admixture of the 3.856 MeV level. Peterson ‘) obtained more 2’ states at 3.75 MeV. 4.73 MeV and 6.48 MeV excitations. We did not observe these states. On the other hand we obtain the spin 2+ for a level at 5.535 MeV, the angular distribution for which is shown in fig. 3. Comparing the cross sections obtained by Peterson with ours, we are unable to explain how we could have missed the extra states unless they are impurity states. Also the 5.535 MeV level seen by us cannot be an impurity level. The pz, p2 R and B(E2) values extracted from our data are listed in table 3 and compared with other experiments. One sees from the table that the B(E2) from 50 MeV proton scattering is in general in better agreement with values obtained using electromagnetic methods than 17.5 MeV proton scattering data. This discrepancy between low-energy proton data and the present experiment may be due to the strong distortion effects at lower energies. The electromagnetic interaction has an equal amount of isoscalar and isovector components, while the alpha interaction is purely isoscalar and the proton interaction is mainly isoscalar with a small isovector component which arises from the V,(z, . z2) part of the two-nucleon interaction. Thus a study of these three reactions would yield information regarding the isospin composition of the states involved. If core excitation is assumed isoscalar, then the fact that our B(E2) values in general agree with values from electromagnetic measurements would tend to indicate core admixture in most of these states. Detailed microscopic calculations are underway to test these predictions. The second lowest 4+ state in 56Fe occurs at 2.085 MeV [ref. “)I. This level is known to be a two-phonon state both from alpha scattering 16) and inelastic proton scattering ‘). Fig. 4 shows the angular distribution for this state. The full line in the figure is the DWBA calculation for the one-phonon character for this level. A COW pled channel calculation is being attempted with two-phonon excitation taken into account. The angular distributions for states with L = 4 characteristics are shown in fig. 5. The 3.159, 4.124, 4.660 and 4.860 MeV levels can be identified with the 3.12, 4.10, 4.61 and 4.88 MeV levels of Peterson ‘) who also assigns spin 4+ to these states. Peterson observes two levels at 4.40 and 4.46 MeV excitation with J” = 4+ and we do not see them in our spectra. The cross sections for these two states, from Peterson’s work, are very small and hence could have been missed by us. The 5.266 MeV
I
0.1+
0
Fig. 6. Angular
-
.20
distributions
40
60 CENTER
0 20 40 80 OF MASS ANGLE
60
80
for 3- and 5- states in 56Fe and DWBA fits with first order coltective form factors.
CENTER
OF MASS
ANGLE
Fig. 7, Angular distributions for levels in 56Fe which are not due to single L transfers. various DWBA predictions using first order coliective form factors are also shown.
The
work
Of
s”-
x-4-
5-
4-
Of Theory 41
in S%
3”
States
3-
A3.4J
(3-1
Parity
Fig. 8. Comparison of negative parity levels observed in this experiment with the shell-model calculations of Irvine 4).
Present
------s-1 -“----l3.41
Negative
2’ potor~ort’”
-
~_
-
I
+
TtbeoryJ’
-4’
-2’
a’
r
-2 -6’
=;I
0’
I
6
------a+
Theory*’
--LL+
-4+ -2’
-6+
-.-&If -.
-4+
3
*
+ ,d+-$+ --.-.$--4’
2* 7*
-5’ -.
“s-----4+
Fig. 9. Comparison of levels observed in the present work with those observed by Peterson ‘). The shell-model predictions for positive parity states by Vervier 2, and McGrory 3, are also shown.
Present work
2’0.849
4’2.118
-4’
=
1,s
4’4.124
-
---+67 458805+-5.763
S6Fe STATES
237
Fig. 10. The relative strengths of 2+, 3- and 4+ levels in 56Fe.
level that we observe is probably the 5.26 MeV level quoted by Peterson ‘). From the angular distribution it is most probably a 4+ state. The 5.880, 6.067 and 6.273 MeV levels are to be associated with the 5.83, 6.00 and 6.30 MeV states of Peterson. The spins of these states have not been determined before and our angular distribution indicates, as seen from fig. 5, that they ‘have J” = 4+. The 3.12 MeV state is well established as a doublet with spin 4+ for the state at 3,123 MeV and possibly If for the level at 3.120 MeV. Our angular distribution indicates a 4+ value for J”. We would not detect any l+ admixture since cross sections to unnatural parity states are very small for inelastic proton scattering. The earlier assignment of 5- to this level by Cohen and Middleton lo) is inconsistent with (p, p’) experiments [ref. I) and present work] and with 56Fe(cc, a’) and 5gC~(~, 01) measurements. The angular distributions to 3- states are shown in fig. 6. The 4.512 MeV level is the lowest 3- state. The angular distribution for the 6.635 MeV level indicates that it might possibly be a doublet with 3- and 4’ as spin values. The 6.966 and 7.189 MeV levels favour 3- assignment though for the latter 4+ could not be ruled out. The 7.080 MeV level could be 3- though a better fit is obtained with the assumption of 4-. This is shown in fig. 6 by the dashed curve (L = 3 + 5) as compared with the full line which is for L = 3. The other possible candidates for 3- are shown in fig. 7.
G. S. MAN1
238
These are levels at 7.312 MeV, 7.475 MeV and 7.807 MeV excitations. The 7.312 MeV level yields as good a fit for the J = 3- as for the J = 4- assumption, The data for 7.475 and 7.807 MeV level are not sufficientIy extended in angles to make any definite prediction. The only 5- state we observe is at 5.106 MeV excitation. The angular distributions as well as DWBA fits are shown in fig. 6. Peterson observed two states, one at 5.15 MeV excitation with possible spin 4+ and another at 5.20 MeV with spin 3-. Our TABLE 4
Values of & and jf,R obtained in the present work L
BL
(ZeV)
3.159
4
0.087
3.411 4.124 4.400
(6) 4 (4)
(0.037) 0.045
AR “1 i-u 9 (fin) Cm)
0.4
4.46
4
4.512 4.66
3 4
4.69
4
4.86
4
0.039
0.18
5.106
5
0.041
0.19
5.266
4
0.59
(0.17) (0.14) 0.21 0.19 0.25
i%R “1 Cm)
0.050
0.71 0.33
I%
if&R 9
(fm)
0.32
5.763 d, 6+4
0.19
5.880 6.067 6.273
4 6 4
6.410 “) (3,4)
0.35 0.154 0.071
L
(MS) g 1;:; 0.039 0.037 0.053 5: z;.rl
BLR ‘1
(fm)
(0.14) 0.18 0.17 0.24 (0.18)
0.94 0.26
0.60
6.635 6.870
3 (3)
0.084
0.39
0.40
0.12
6.966
3
0.05
0.23
0.48
0.24
7.080e)
(3,4)
2 1 yoE
(0.21) ,& = 0.23
7.189e)
(3,4)
tz;;:
(0.21)
7.312d)
3-I-4
;; x ;;;;:
(0.18)
3
0.051
0.23
(0.22)
g4 = 0.36
0.23
0.21
7.475
0.23
“) r0 = 1.2 fm (present work). “) re = 1.23 fm [ref. I)]. ‘) re = 1.2fm [ref. I’)]. d, These are non-normal parity states. The cross section is defined to be u = @~,~e~rf@~~~~~ where CT& is the reduced cross section and is,, and & are deformations. ‘) The angular distributions fit equally well for two L-values and PI values for each of them are given.
data indicates also two states at 5.106 MeV and 5.195 MeV which probably are to be identified with the above two levels observed by Peterson. The angular distribution for the 5.195 MeV is shown in fig. 7, which the dashed curve is for a DWBA fit to a mixture of L = 3 and L = 5 while the full line is the L = 4 curve. Thus we see from the figure that J” = 4- is the most probable spin for the 5.195 MeV level. The angular distributions for the rest of the states observed by us are shown in fig. 7. The angular distribution for the 6.870 MeV level resembles somewhat the twophonon 4+ state distribution shown in fig, 4. It would be surprising to find a twophonon state at such a high excitation, if this were indeed true. The angular distri-
56Fe STATES
239
for the 7,668 MeV exhibits no structure and hence no definite spin assignment was possible. The 6.410 MeV level is possibly a doublet with spin 3- and 4’ as suggested by the DWBA fits to the angular distribution in fig. 7. The excitation energies for the negative parity states in 56Fe have been calculated by Irvine “> on the basis of the shell model using the assumptions described in the introduction. The configurations for the protons were taken to be (If;) and the neutrons (f+g& (p+g+) and (p+gs). The Rosenfeld force mixture was used for the twonucleon interaction. The single-particle spacing between h and fz was adjusted to obtain the position of the lowest 3- level and was found to be 4.04 MeV. In fig. 8, a comparison is made between Irvine’s calculations and the presentexperimentalrzsult. The lowest 5- and 4- observed at 5.106 MeV and 5.195 MeV are well reproduced by the theory. The second 5- at 6.15 MeV predicted by theory is not observed by us. On the other hand the level at 5.763 MeV (see fig. 7) might quite possibly have a 5component in it. The doublet at 6.410 MeV with spins 3- and 4+ (see fig. 7) may be identified with the predicted states at 6.4 MeV (3-) and 6.5 MeV (4-). The 5- at 7.15 MeV and the 4- at 7.55 MeV predicted by theory are not seen in this experiment. The experimental results suggests the possible existence of four negative parity states between 7.0 and 7.5 MeV though the evidence is not very strong. The levels up to 6.0 MeV in excitation in ’ 6Fe observed by us are shown in fig. 9 and compared with those obtained by Peterson “) and also with the theoretical predictions of Vervier “) and McGrory “) for the positive parity states. The relative strengths of 2+, 4+ and 3states obtained by us are shown in fig. IO. Our observed values of fi, PR and B(EL) where applicable to the levels in 56Fe , other than 2+ states, are given in table 4. bittion
The author is indebted to Dr. A. D. B. Dix and to Messrs. D. T. Jones and D. Jacques for their help in obtaining the above data. Also the author would wish to express his thanks to Drs. J. M. Irvine and L. D. Skouras for their shell-model calculations and for very helpful discussions. References 1) R. J. Peterson, Ann. of Phys. 53 (1969) 40, references to earlier work are given in this paper 2) J. Vervier, Nucl. Phys. 78 (1966) 497 3) J. B. McGrory, Phys. Rev. 160 (1967) 915 4) J. M. Irvine and L. D. Skouras, private communication 5) S. Cohen, R. D. Lawson, M. H. Macfarlane, S. Pandya and M. Saga, Phys. Rev. 160 (1967) 903 6) G. S. Mani, to be published 7) P. H. Stelson and L. Grodzins, Nucl. Data Al (1965) 21 8) H. Sherif and J. S. Blair, Phys. Lett. 26B (1968) 488; H. Sherif, Nucl. Phys. 131 (1969) 532 9) S. F. Eccles, H. F. Lutz and V. A. Madsen, Phys. Rev. 141 (1966) 1067 10) B. Cohen and R. Middleton, Phys. Rev. 146 (1966) 748 11) G. G. Seaman et al., Phys. Rev. 188 (1969) 1706 12) G. S. Mani, D. T. Jones and D. Jacques, to be published 13) R. J. Peterson, H. Thiessen and W. 3. Alston, Nucl. Phys. Al53 (1970) 610 14) J. Bellicard and P. Barrean, Nucl. Phys. 36 (1962) 476 15) Nuclear Data Sheets, Section B, 3 (1970) nos 3-4 16) G. Bruge et al., Phys. Lett. 22 (1966) 640 17) A. M. Bernstein, Advances in nuclear physics, vol. 3 (1969) 325
@ North-Holland
Publishing
Co., Amsterdam
Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPIN ASSIGNMENTS
TO EXCITED
USING INELASTIC
STATES
OF 56Fe
PROTON SCATTERING
G. S. MAN1 Schuster Laboratory,
Manchester
University,
Received 18 November
Manchester
1970
Abstract:
Inelastic proton scattering from 56Fe at 49.35 MeV has been studied with protons from a linear accelerator. Angular distributions for thirty excited states up to an excitation of 7.5 MeV in 56Fe were obtained. Spin and parity assignments to most of the states were made using DWBA analysis with first order collective form factors. The structure of this nucleus is discussed in the light of the present data.
E
NUCLEAR REACTIONS 56Fe(p, p’), E = 49.35 MeV; measured (E,‘, f3). 56Fe deduced levels, J, x and deformation parameters. Enriched targets.
1. Introduction The excitation energies, spins and parities for many states in 56Fe are known ‘). Inelastic proton scattering on this nucleus has been studied recently by Peterson ‘) for a proton energy of 17.5 MeV. Calculations for the excitation energies have been carried out by Vervier ‘), McGrory “) and Irvine and Skouras “). For 56Fe Vervier considers only a (If;*) configuration for protons and a (2~:) configuration for neutrons. The effective interaction for the proton-proton in the zf$ orbit is taken from the 54Fe spectrum, for the neutron-neutron in the VP+ orbit from 56Ni spectrum, and for the proton-neutron in the (zf;)(vpt) configuration, is deduced from 56Co levels. The agreement with observed levels in 5 6Fe was not very good. McGrory restricted the neutron configurations to the 2p,, 2ps and If+ singleparticle orbits and the protons were restricted to the (If;“) configuration. In his calculations the 71-z interaction was obtained from the 54Fe spectrum, the v-v interaction from the shell-model calculations of Cohen et al. “) for nickel isotopes and the n-v interaction from Vervier’s ‘) calculations for N = 29 nuclei. McGrory calculated the positive parity states in 56Fe and obtained quantitative agreements for level positions as well as cross sections for 54Fe(t, p)56Fe reactions for states up to 3 MeV in excitation. The positive and negative parity states in 5 6Fe were calculated by Irvine and Skouras “) using the same configurations as McGrory for positive parity states and by including the 1% single-particle orbit in the neutron configurations for the negative parity states. They used the Rosenfeld force mixture for the two-nucleon interaction 225 April 1971
G. S. MAN1
226
T
“.LU
0.15
d
3 9 ”
I i
0.K
>
9 0.5c
75
125
CHANNEL
Fig. 1. A typical
35
time spectrum from the spark solid line is the fit to the spectra
85
135 CHANNEL
t t
175
225
NUMBER
I
!
4
275
chamber for levels to 4.7 MeV using the NSPEC programme.
185 NUMBER
Fig. 2. A typical time spectrum from the spark chamber The solid line is the fit to the spectra using
excitation.
The
235
for levels from 4.5 MeV to 8.0 MeV. the NSPEC programme.
56Fe STATES
227
and calculated the spectra assuming the spacings for the single-particle orbits used. The agreement with observed excitation energies was reasonable. TABLE 1 Energy levels (MeV) Peak no.
This work &
1 2 3 4 5 6
and spin values obtained in the present work Ref. ‘)
J
0.849 2.118 2.695 2.986 2.986 3.159 3.411 3.411
4+ 2+ f6+)
7
3.635
2+
8
3.850
2+
9
4.124
4+
10 11
4.512 4.660
34+
12 13 14 15 16
4.860 5.106 5.195 5.266 5.535
4+ $1 4+ 2+
17 18
5.763 5.880
(5’) 4+
19 20 21
6.067 6.273 6.410
4’
22 23 24 25 26 27 28
6.635 6.870 6.966 7.080 7.189 7.312 7.415
Ref. Ii)
-57
7
4
J
0.85 2.08 2.65 2.94 2.96
2+
2+
2+ 4+ 2+ 0’ 2+
3.12 3.37 3.39
4+ 2* 6+
0.847 2.08 2.657 2.939 2.960 3.120 3.123 3.369
Cl+) 4+ 2+
3.443 3.599 3.605
3+ 0+ 2+
3.829 3.857
2+ 3+
3.60 3.75 3.83 4.04 4.10 4.19 4.40 4.46 4.51 4.61 4.69 4.73 4.88 5.15 5.20 5.26 5.51 5.58 5.69 5.73 5.83 5.90 6.00 6.30
2+
2+ 2+ 2+
4f c4*1 4’ 34+ 4+ 2’ c::, (3-j
(?4) 6.48 (3-I
c:, 41 (3.4) (3,4) (3-j
2(+)
228
G. S. MANI
In this paper we report the results obtained for excitation energies, spins and parities for levels in 5 ‘jFe up to an exe’nation of 7.5 MeV using inelastic scattering of 50 MeV protons. The study was undertaken to investigate the structure of 56Fe and to compare with calculations of Irvine and Skouras. The DWBA calculations using phenomenological Microscopic calculations in a later paper.
first order collective form factors are presented in this paper. using Irvine and Skouras’s wave functions will be reported
2. Experimental technique The experiment was performed using the 50 MeV proton beam from the proton linear accelerator at the Rutherford High Energy Laboratory, Chilton, Berkshire. The inelastically scattered protons were detected by an n = 3 double focussing magnetic spectrometer with an acoustic spark chamber assembly. Details of the experimental set up have been discussed in an earlier paper “). The target used in the present experiment was self-supporting and was 99 % enriched 56Fe which had a thickness of 2 mg/cm ‘. The target was obtained from the isotope division, AERE, Harwell. Since the focal plane of the spectrometer corresponds to 5 % in momentum at 50 MeV, that is, 5 MeV in energy, in order to study excitation up to 7.5 MeV in 5 6Fe the experiment was done twice with the magnetic rigidity adjusted to obtain the lowed excitation and the higher excitation regions. There was an overlap between the two cases so that one could extract consistent values for excitation energies and angular distributions. Typical time spectra for both the cases are shown in figs. 1 and 2. The full lines in the figures are the theoretical fits to the spectra using the computer programme NSPEC described in ref. “). The method for extracting differential cross sections and the corrections for 12C and 160 impurities as well as for the neutron background are described in ref. “).
3. Results and discussion In table 1 we present the list of energy levels observed in this experiment. These are compared with the states observed in the (p, p’) reaction by Peterson ‘) and in y-ray experiments ll). All the levels of ’ 6Fe observed through various reactions are not included since there are a large number of closely spaced levels which our experiment does not resolve and most of which are not strongly excited in (p, p’) reactions. The energies of excited states in 5 6Fe obtained in the present work have an overall error of 30 keV and our energy resolution was around 70 keV. The angular distributions were analysed using DWBA theory with first order collective form factors. The interaction between the nucleus and the projectile is
229
%lZe STATES
represented by an optical model of the form
The potential U in eq. (1) included real, complex and spin-orbit terms. Then, in first order, the form factor is given by
The deformation parameter jYtis related to the restoring force parameter C of the vibrations model by /$ = (21+1)$ 1
where ho is the energy of the excited state. For uniform charge distribution of deformation fi, the electromagnetic transition strength %(EL)f is given by ‘>
The first order form factor given in (3) could only be used for single-phoebe transitions. Double-phonon excitations would need higher order terms. The optimal-m~el parameters for the DWBA calculations were obt~ned from the analysis by Mani et al. I’>. The potentials used are given below: v, = 41.3 MeV
aR = 0.64 fm
rR = 1.20 fm
W, =
0.9 MeV
WD = 8.2 MeV
a, = OS6 fm
$t =
1.25 fm
V,,*_= 7.5 Met’
rr,,,, = 0.61 fm
r $0. =
1.16 fm
rc = 1.25 fm
where V,, a,, rR are the depths, surface thickness and radius parameter for the real part of the potential. Similarly Ws (volume), W, (surface) aI and rr define the imaginary part of the potential and I!,,,.+ CL_ and r,.,. are parameters for the spin-orbit part of the potential whiIe ri: is the Coulomb radius parameter. The DWBA calculations were done by using a computer code written by Sherif “). The full Thomas term for the spin-orbit coupling was used. The deformation was maintained the same for both the central and the spin-orbit term. It was found, by varying the ratio of the central to spin-orbit deformation, that the most consistent fits were obtained with the ratio equal to unity. Fig, 3 shows the angular distributions and DWl3A fits to al1 levels that we have established to have J = 2’. In table 2 we compare the results of this experiment with various other experiments for the first excited 2+ state in 56Fe. The values of the de-
230
0
Fig. 3. Angular
20
distributions
40 60 CENTER
80 0 OF MASS ANGLE
for 2 + levels, The solid lines represent using first order collective form factors. TABLE
Comparison
of strengths
(p, p’) “) (14.3, 17.3, 17.5, 19 MeV) (p, p’) “) (30 MeV, 150 MeV) t3He, 3He’) “) (38 MeV, 22 MeV) (u, bl’) “) (22 MeV) electromagnetic b> (e, e’) ‘> (60.20 MeV) Dopper shift “) present cxp. (p, p’) (50 MeV) (a, a’) “) Average
2
of the first excited 2+ state obtained
Method
82
0.25 0.22 0.20 0.20 0.23
0.2jr: 0.02 0.215
DWBA fits to the data
P2R
from a variety of experiments (fml
1.19 1.oo 1.20 0.94 1.06
0.92 fO.09 0‘986$ID.O8
B(E2) f (e2- fm4) llOOzkl65 830$125 690f 04 7401111 9001100 1250 f270 39Of 90 81QflOO 792f 121 8901135
“) Average values obtained from ref. I). Since no errors were quoted, we have taken an arbitrary value of IS ‘4 for the error. b, Average values given in ref. ‘). “) DWBA calculation 13). The earlier Orsay value of 720 e 2 9fm4 was obtained using PWBA and when corrected using DWBA [see ref. 13>] one obtains for B(E2)t the value 12405150 &2- fm4. d, Ref. $I>. ‘) Ref. 17)*
56Fe STATES
231
formation parameter &, the deformation distance fizR and the transition strength B(E2) are given in the table. The mean value from all the results is 890 e2 * fm4 with a probable error of around 15 ‘A. It is surprising that both the low-energy proton scattering and (e, e’) experiments yield a B(E2) value slightly higher than that obtained from high-energy proton scattering, 3He and alpha scattering and Coulomb excitation. Vervier “) has calculated B(E2) on the basis of the assumptions discussed in the introduction. Since the considers only a (lf:“) configuration for protons and a (2~;) configuration for neutrons, his matrix elements for the effective E2 transition operators involve only matrix elements for protons in the lf; orbit and for neutrons in the 2p3 orbit. Hence he requires matrix elements of the form
where Q4 and Qi are the E2 operators for protons and neutrons respectively, with effective charge included. These matrix elements are obtained from the experimental values ofB(E2) for the O+ -+ 2+ transitions in 50Ti, 54Fe and 58Ni. Using these values for the tr~sition 2: -+ 0: in 56Fe, he obtains a value for B(E2) lying between 1390 and 1200 e2 - fm”. Unfortunately Vervier’s calculation does not indicate what effective charge one needs. The agreement between the experimental and the theoretical value is reasonable. The calculation does not indicate the amount of core excitation since the matrix elements for the E2 operator were obtained from known experimental values of B(E2) as described above. The wave functions of Skouras “) for the 0: and 2: states show a large admixture of p+ and f+ configurations. It would be interesting to obtain B(E2) values using these wave functions. From fig. 3 it is seen that the L = 2 theoretical curve does not reproduce very well the data for the 3.411 MeV level at large angles. Peterson “) indicated that his results for this level are consistent with the assumption that it is a doublet with spins 2+ and 6+. Theoretical calculations “-“) do predict a 6+ state around this region of excitation. The 54Fe(t, P)~~F~ reaction does not excite this state at all, and it has been suggested by Cohen and Middleton ‘I) that this could be a three-phonon vibrational state. We have attempted to fit the data assuming a mixture of 2’ and 6+ contribution in the angular distribution, The angular distribution is not very much improved by such an assumption. If the 6+ state is a three-phonon vibrational state, then the first order form factor used by us would not reproduce its angular distribution. With the assumption of an L = 2 and an L = 6 mixing, we obtain pz = 0.054 which is very close to the value of & = 0.057 that is obtained with a pure L = 2 contribution alone, and we also get /Is = 0.037 in agreement with Peterson’s ‘) estimate of 0.03. The fact that we obtain reasonably good fits at all angles for the angular distributions of other 2+ states and that the data for the 3.411 MeV level is not well fitted, even with the assumption of a (2’, 6’) doublet, with the experimental cross sections at large angles always larger than the theoretical values, tend to con-
232
G. S. MAN1
firm Cohen
and Middleton’s
suggestion
of a three-phonon
vibrational
structure
for
the 6+ state. The 2.986 MeV level that we observe (see fig. 7) can be identified with the 2.957 MeV level of Peterson ‘). Peterson contains J” = 2+ for this state. The level around 2.96 MeV is known to be a doublet ‘,11) with excitation energies of 2.960 MeV and 2.939 MeV. The 2.939 MeV is known ‘O*‘l)tohave spin O+. Inthe 54Fe(t,p)56Fereaction10) two O+ levels below 4 MeV are observed, one at 2.939 MeV and the other at 3.6 MeV Comparison
(;eY)
TABLE 3 of strengths of all 2+ states known in s6Fe from a variety of experiments
This experiment B(E2)f 82
0.847 2.658
0.06
0.2
2.960
0.02 “)
(P, P’) Y 82
17.5 MeV B(E2)+
(e, e’) “) B(E2)
810 73
0.29 0.107
14980 200
1250 37
8
0.044
34
21 41
10 ;+;J - . 55 (+35)
17
13 -64
3.370
0.06
73
0.043
32
3.60 3.75
0.05
50
0.053 0.082
49 118 \
3.856 4.73 5.535
0.03
18
0.069 0.050
0.05
50
Dopper shift d, B(E2)T 893 *90 17 k5.5
C-15)
10
6.48
0.055
53
The B(E2)t values are given in units of e2 * fm4. “) Adopted values from ref. Is) where possible. b, Values from ref. I). ‘) Values from ref. ‘a). “) Values from ref. I’). ‘) This value is very approximate since, as explained in text, it is an unresolved doublet.
and these have been confirmed from y-ray studies ‘l). The shell-model calculations of McGrory “) predict the lowest O+ level around 3 MeV while Skouras “) obtains for the lowest Of state an excitation energy of 3.4 MeV. The L = 2 DWBA prediction for the 2.957 MeV level is also shown in fig. 7. It is seen from this figure that this level cannot be a pure L = 2 transition and the discrepancy may be due to an admixture of the O+ state. This would imply a large cross section for the Of state compared to what one obtains for O+ states in nearby regions of nuclei. The angular distribution for the 6.635 MeV level is shown in fig. 3. This also is a known doublet ‘I) with excitation energies of 3.599 MeV (O+) and 3.605 MeV (2+). From the figure it is obvious that the contribution of O+ to the angular distribution of the 3.635 MeV is small. The core excited O+ level should also appear around 3 MeV excitation. Since inelastic proton scatteringstoO’stateswithlargecoreexcitationconfigurationshavealargecrosssection, our data suggests that the O+ state at 2.939 MeVis mainly due to core excitation and the
233
56Fe STATES 56 Fe (P. P’)~F~ Ep 4935hreV
0.00lL____ 0
Fig. 4. Angular
IO
distribution
I
SO 60 70 40 OF MASS ANGLE
20 30 CENTER
/
BO
3
for the lowest 4+ level in 56Fe. The solid line is the DWBA prediction for one-phonon excitation.
*%ep’l
I p, =F. Ep.4935M&
-J-i 11
4.860 4+
11’
t
4 660 4+
‘L,
t lt
1 Y 4 124 -@+f ad
h
iii
E
tt
t
t
\
I
P
tt
t’
IX 1 -
I
0 ,I
0.C )I
0
Fig. 5. Angular
20
distributions
,
40
,
60
80
0
for 4+ levels in 56Fe and DWBA fits with first order collective form factors.
234
G. S. MAN1
one at 3.599 MeV is to be identified with the shell-model state predicted by McGrory and Skouras. The 2+ level at 2.986 MeV is not reproduced in the calculation of both McGrory and Skouras and hence may also be created by core breaking. The 3.850 MeV level observed by us should be identified with the 3.839 MeV state of Seaman et al. 11) and of Peterson ‘). The assignment of 2+ to this level as shown by the data in fig. 3 is consistent with the other experiments quoted above. This level is also a doublet ‘I) with a 3+ state at 3.85 MeV. The small discrepancy between the theoretical and experimental angular distribution that we observe may be due to the admixture of the 3.856 MeV level. Peterson ‘) obtained more 2’ states at 3.75 MeV. 4.73 MeV and 6.48 MeV excitations. We did not observe these states. On the other hand we obtain the spin 2+ for a level at 5.535 MeV, the angular distribution for which is shown in fig. 3. Comparing the cross sections obtained by Peterson with ours, we are unable to explain how we could have missed the extra states unless they are impurity states. Also the 5.535 MeV level seen by us cannot be an impurity level. The pz, p2 R and B(E2) values extracted from our data are listed in table 3 and compared with other experiments. One sees from the table that the B(E2) from 50 MeV proton scattering is in general in better agreement with values obtained using electromagnetic methods than 17.5 MeV proton scattering data. This discrepancy between low-energy proton data and the present experiment may be due to the strong distortion effects at lower energies. The electromagnetic interaction has an equal amount of isoscalar and isovector components, while the alpha interaction is purely isoscalar and the proton interaction is mainly isoscalar with a small isovector component which arises from the V,(z, . z2) part of the two-nucleon interaction. Thus a study of these three reactions would yield information regarding the isospin composition of the states involved. If core excitation is assumed isoscalar, then the fact that our B(E2) values in general agree with values from electromagnetic measurements would tend to indicate core admixture in most of these states. Detailed microscopic calculations are underway to test these predictions. The second lowest 4+ state in 56Fe occurs at 2.085 MeV [ref. “)I. This level is known to be a two-phonon state both from alpha scattering 16) and inelastic proton scattering ‘). Fig. 4 shows the angular distribution for this state. The full line in the figure is the DWBA calculation for the one-phonon character for this level. A COW pled channel calculation is being attempted with two-phonon excitation taken into account. The angular distributions for states with L = 4 characteristics are shown in fig. 5. The 3.159, 4.124, 4.660 and 4.860 MeV levels can be identified with the 3.12, 4.10, 4.61 and 4.88 MeV levels of Peterson ‘) who also assigns spin 4+ to these states. Peterson observes two levels at 4.40 and 4.46 MeV excitation with J” = 4+ and we do not see them in our spectra. The cross sections for these two states, from Peterson’s work, are very small and hence could have been missed by us. The 5.266 MeV
I
0.1+
0
Fig. 6. Angular
-
.20
distributions
40
60 CENTER
0 20 40 80 OF MASS ANGLE
60
80
for 3- and 5- states in 56Fe and DWBA fits with first order coltective form factors.
CENTER
OF MASS
ANGLE
Fig. 7, Angular distributions for levels in 56Fe which are not due to single L transfers. various DWBA predictions using first order coliective form factors are also shown.
The
work
Of
s”-
x-4-
5-
4-
Of Theory 41
in S%
3”
States
3-
A3.4J
(3-1
Parity
Fig. 8. Comparison of negative parity levels observed in this experiment with the shell-model calculations of Irvine 4).
Present
------s-1 -“----l3.41
Negative
2’ potor~ort’”
-
~_
-
I
+
TtbeoryJ’
-4’
-2’
a’
r
-2 -6’
=;I
0’
I
6
------a+
Theory*’
--LL+
-4+ -2’
-6+
-.-&If -.
-4+
3
*
+ ,d+-$+ --.-.$--4’
2* 7*
-5’ -.
“s-----4+
Fig. 9. Comparison of levels observed in the present work with those observed by Peterson ‘). The shell-model predictions for positive parity states by Vervier 2, and McGrory 3, are also shown.
Present work
2’0.849
4’2.118
-4’
=
1,s
4’4.124
-
---+67 458805+-5.763
S6Fe STATES
237
Fig. 10. The relative strengths of 2+, 3- and 4+ levels in 56Fe.
level that we observe is probably the 5.26 MeV level quoted by Peterson ‘). From the angular distribution it is most probably a 4+ state. The 5.880, 6.067 and 6.273 MeV levels are to be associated with the 5.83, 6.00 and 6.30 MeV states of Peterson. The spins of these states have not been determined before and our angular distribution indicates, as seen from fig. 5, that they ‘have J” = 4+. The 3.12 MeV state is well established as a doublet with spin 4+ for the state at 3,123 MeV and possibly If for the level at 3.120 MeV. Our angular distribution indicates a 4+ value for J”. We would not detect any l+ admixture since cross sections to unnatural parity states are very small for inelastic proton scattering. The earlier assignment of 5- to this level by Cohen and Middleton lo) is inconsistent with (p, p’) experiments [ref. I) and present work] and with 56Fe(cc, a’) and 5gC~(~, 01) measurements. The angular distributions to 3- states are shown in fig. 6. The 4.512 MeV level is the lowest 3- state. The angular distribution for the 6.635 MeV level indicates that it might possibly be a doublet with 3- and 4’ as spin values. The 6.966 and 7.189 MeV levels favour 3- assignment though for the latter 4+ could not be ruled out. The 7.080 MeV level could be 3- though a better fit is obtained with the assumption of 4-. This is shown in fig. 6 by the dashed curve (L = 3 + 5) as compared with the full line which is for L = 3. The other possible candidates for 3- are shown in fig. 7.
G. S. MAN1
238
These are levels at 7.312 MeV, 7.475 MeV and 7.807 MeV excitations. The 7.312 MeV level yields as good a fit for the J = 3- as for the J = 4- assumption, The data for 7.475 and 7.807 MeV level are not sufficientIy extended in angles to make any definite prediction. The only 5- state we observe is at 5.106 MeV excitation. The angular distributions as well as DWBA fits are shown in fig. 6. Peterson observed two states, one at 5.15 MeV excitation with possible spin 4+ and another at 5.20 MeV with spin 3-. Our TABLE 4
Values of & and jf,R obtained in the present work L
BL
(ZeV)
3.159
4
0.087
3.411 4.124 4.400
(6) 4 (4)
(0.037) 0.045
AR “1 i-u 9 (fin) Cm)
0.4
4.46
4
4.512 4.66
3 4
4.69
4
4.86
4
0.039
0.18
5.106
5
0.041
0.19
5.266
4
0.59
(0.17) (0.14) 0.21 0.19 0.25
i%R “1 Cm)
0.050
0.71 0.33
I%
if&R 9
(fm)
0.32
5.763 d, 6+4
0.19
5.880 6.067 6.273
4 6 4
6.410 “) (3,4)
0.35 0.154 0.071
L
(MS) g 1;:; 0.039 0.037 0.053 5: z;.rl
BLR ‘1
(fm)
(0.14) 0.18 0.17 0.24 (0.18)
0.94 0.26
0.60
6.635 6.870
3 (3)
0.084
0.39
0.40
0.12
6.966
3
0.05
0.23
0.48
0.24
7.080e)
(3,4)
2 1 yoE
(0.21) ,& = 0.23
7.189e)
(3,4)
tz;;:
(0.21)
7.312d)
3-I-4
;; x ;;;;:
(0.18)
3
0.051
0.23
(0.22)
g4 = 0.36
0.23
0.21
7.475
0.23
“) r0 = 1.2 fm (present work). “) re = 1.23 fm [ref. I)]. ‘) re = 1.2fm [ref. I’)]. d, These are non-normal parity states. The cross section is defined to be u = @~,~e~rf@~~~~~ where CT& is the reduced cross section and is,, and & are deformations. ‘) The angular distributions fit equally well for two L-values and PI values for each of them are given.
data indicates also two states at 5.106 MeV and 5.195 MeV which probably are to be identified with the above two levels observed by Peterson. The angular distribution for the 5.195 MeV is shown in fig. 7, which the dashed curve is for a DWBA fit to a mixture of L = 3 and L = 5 while the full line is the L = 4 curve. Thus we see from the figure that J” = 4- is the most probable spin for the 5.195 MeV level. The angular distributions for the rest of the states observed by us are shown in fig. 7. The angular distribution for the 6.870 MeV level resembles somewhat the twophonon 4+ state distribution shown in fig, 4. It would be surprising to find a twophonon state at such a high excitation, if this were indeed true. The angular distri-
56Fe STATES
239
for the 7,668 MeV exhibits no structure and hence no definite spin assignment was possible. The 6.410 MeV level is possibly a doublet with spin 3- and 4’ as suggested by the DWBA fits to the angular distribution in fig. 7. The excitation energies for the negative parity states in 56Fe have been calculated by Irvine “> on the basis of the shell model using the assumptions described in the introduction. The configurations for the protons were taken to be (If;) and the neutrons (f+g& (p+g+) and (p+gs). The Rosenfeld force mixture was used for the twonucleon interaction. The single-particle spacing between h and fz was adjusted to obtain the position of the lowest 3- level and was found to be 4.04 MeV. In fig. 8, a comparison is made between Irvine’s calculations and the presentexperimentalrzsult. The lowest 5- and 4- observed at 5.106 MeV and 5.195 MeV are well reproduced by the theory. The second 5- at 6.15 MeV predicted by theory is not observed by us. On the other hand the level at 5.763 MeV (see fig. 7) might quite possibly have a 5component in it. The doublet at 6.410 MeV with spins 3- and 4+ (see fig. 7) may be identified with the predicted states at 6.4 MeV (3-) and 6.5 MeV (4-). The 5- at 7.15 MeV and the 4- at 7.55 MeV predicted by theory are not seen in this experiment. The experimental results suggests the possible existence of four negative parity states between 7.0 and 7.5 MeV though the evidence is not very strong. The levels up to 6.0 MeV in excitation in ’ 6Fe observed by us are shown in fig. 9 and compared with those obtained by Peterson “) and also with the theoretical predictions of Vervier “) and McGrory “) for the positive parity states. The relative strengths of 2+, 4+ and 3states obtained by us are shown in fig. IO. Our observed values of fi, PR and B(EL) where applicable to the levels in 56Fe , other than 2+ states, are given in table 4. bittion
The author is indebted to Dr. A. D. B. Dix and to Messrs. D. T. Jones and D. Jacques for their help in obtaining the above data. Also the author would wish to express his thanks to Drs. J. M. Irvine and L. D. Skouras for their shell-model calculations and for very helpful discussions. References 1) R. J. Peterson, Ann. of Phys. 53 (1969) 40, references to earlier work are given in this paper 2) J. Vervier, Nucl. Phys. 78 (1966) 497 3) J. B. McGrory, Phys. Rev. 160 (1967) 915 4) J. M. Irvine and L. D. Skouras, private communication 5) S. Cohen, R. D. Lawson, M. H. Macfarlane, S. Pandya and M. Saga, Phys. Rev. 160 (1967) 903 6) G. S. Mani, to be published 7) P. H. Stelson and L. Grodzins, Nucl. Data Al (1965) 21 8) H. Sherif and J. S. Blair, Phys. Lett. 26B (1968) 488; H. Sherif, Nucl. Phys. 131 (1969) 532 9) S. F. Eccles, H. F. Lutz and V. A. Madsen, Phys. Rev. 141 (1966) 1067 10) B. Cohen and R. Middleton, Phys. Rev. 146 (1966) 748 11) G. G. Seaman et al., Phys. Rev. 188 (1969) 1706 12) G. S. Mani, D. T. Jones and D. Jacques, to be published 13) R. J. Peterson, H. Thiessen and W. 3. Alston, Nucl. Phys. Al53 (1970) 610 14) J. Bellicard and P. Barrean, Nucl. Phys. 36 (1962) 476 15) Nuclear Data Sheets, Section B, 3 (1970) nos 3-4 16) G. Bruge et al., Phys. Lett. 22 (1966) 640 17) A. M. Bernstein, Advances in nuclear physics, vol. 3 (1969) 325