Nuclear structure studies of the chromium isotopes: The 52, 53Cr(p, p′), 53Cr(p, p′γ), 53Cr(d, d′) and 52Cr(d, p) reactions

Nuclear Physics A121 (1968) 1--37; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NUCLEAR THE

STRUCTURE

STUDIES

OF THE CHROMIUM

s2'SaCr(p, p ' ) , 5aCr(p, p ' ? ) , S3Cr(d, d ' ) A N D

ISOTOPES:

S2Cr(d, p) R E A C T I O N S

M. N. R A P t, j. RAPAPORT, A. SPERDUTO and D. L. SMITH t* Physics Department and Laboratory for Nuclear Science tl't, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA Received 19 August 1968

Abstract: The MIT-ONR electrostatic generator and the MIT multiple-gap spectrograph were used to study the level structure of 52Cr and 5~Cr by means of the (p, p'), (p, P'7'), (d, d') and (d, p) reactions with proton and deuteron bombarding energies of 7.5 MeV. A total of 14 levels in 52Cr and 26 levels in g3Cr from the (p, p') reactions and 102 levels in 53Cr from the (d, p) reactions are reported. Angular distributions of elastic and inelastic particle groups corresponding to the first five states in 53Cr have been obtained from both the (p, p') and (d, d') experiments. A comparison of the angular distributions of protons from the (d, p) reactions with calculations from zero-range DWBA has yielded information on the orbital angular momentum of the transferred neutron and transition strengths for 27 levels in 5~Cr up to 4.7 MeV in excitation. The deduced (d, p) strengths are compared with shell-model sum-rule limits. The experimental results from the five reactions investigated are compared with other experiments performed with higher bombarding energies. The properties of the low-lying levels in 53Cr are of particular interest and are discussed in terms of theoretical calculations based on the shell model and also the weak-coupling model.

E

N U C L E A R REACTIONS ~,53Cr(p, p), (p, p'), 53Cr(d, d), (d, d'), E = 7.5 MeV; measured a(Ep,, 0), ~r(Ea,,0); 53Cr(p, P'7), E = 6.5 MeV, measured 177; 52Cr(d, p), 52Cr(d, d), E = 7.5 MeV, measured a(Ev, 0). S2Cr deduced levels; 5aCr deduced levels, ln, ~, transition strengths. Enriched targets.

1. Introduction T h i s article is the s e c o n d in a series o f r e p o r t s f r o m this l a b o r a t o r y o n the n u c l e a r level s t r u c t u r e studies o f the c h r o m i u m i s o t o p e s a n d is c o n c e r n e d w i t h the 52'53Cr (P, P ' ) 5 2 ' S a C r , 53Cr(p, p ' ? ) 5 3 C r , 53Cr(d, d ' ) 5 3 C r a n d 52Cr(d, p ) 5 3 C r r e a c t i o n s . T h e r e is a c o n s i d e r a b l e a m o u n t o f e x p e r i m e n t a l w o r k r e p o r t e d in the l i t e r a t u r e on t h e level p r o p e r t i e s o f b o t h 52Cr a n d 5 3Cr b e g i n n i n g w i t h the earliest 1) m e a s u r e m e n t s o n t h e d e c a y o f 52Mn, inelastic p r o t o n s c a t t e r i n g 2) a n d slow n e u t r o n - c a p t u r e g a m m a r a y s 3) f r o m n a t u r a l c h r o m i u m targets. Precise m e a s u r e m e n t s o f a few level p o s i t i o n s ~ Present address: Nuclear Data Project, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA. tt Present address: Radiation Physics Branch, AMSMI-RRR, Physical Sciences Laboratory, Redstone Arsenal, Alabama, USA. ttt This work has been supported in part through funds provided by the U.S. Atomic Energy Commission under AEC Contract AT(30-1)-2098.

December 1968

1

2

M . N . RAO et al.

in 52, 53Cr have also previously been carried out in this laboratory 4, 5) by magnetic analysis of the light products in the reactions 55Mn(p, e)52Cr, 52Cr(p,p')52Cr, s 5Mn(d ' e)53Cr and S2Cr(d, p)5 aCr" A summary of the information on these nuclei at the time of the experiments is contained in ref. 6), while subsequent work is compiled in ref. v). More recent studies using the last three of the above reactions have been reported by Bjerregaard et al. 8), while a more extensive series of measurements by means of the (p, p') reactions from enriched targets of 52Cr and 53Cr and the (d, p) reactions from 52Cr have been carried out by Macgregor and Brown 9). Katsanos and Huizenga lo) have also obtained some very precise magnetic-spectrograph measurements of levels in 52Cr both by means of the 52Cr(p, p') and the 55Mn(p, ~) reactions. Other similar measurements, though with somewhat less precision, have been reported by Matsuda 11) and Veje et al. 12), both by means of the (p, p') reactions. Spins, parities and other properties of low-lying states in S2Cr have been deduced and confirmed recently la- 15) by observing the cascade gamma rays in the decay of 52Mn and in the study of the particle gamma coincidence reactions (n, n'7) 16) and (p, P'7) [refs. 17,18)]. Properties of low-lying levels in 5aCr have also been deduced from the (n, n'7) experiments 16), from angular correlations in the (n, 7) slow neutron-capture measurements 19), (d, p) stripping reactions 20-22), (d, P7) coincidence measurements 2a) and neutron pick-up reactions 24-27). Experiments involving one- and two-nucleon pick-up reactions have given important information on the ground-state configurations of 52Cr and s 3Cr as well as providing spectroscopic information on some of the excited states. Angular-distribution studies of the (p, d) reactions on natural chromium have been performed with 17.0 and 18.5 MeV incident protons by Legg and Rost 24), with 28 MeV incident protons by Sherr et al. 25) and on enriched S2Cr, 5aCr and 54Cr isotopes with 17.5 MeV incident protons by Whitten 26). Measurements from the neutron pick-up reactions (d, t) and (3He, ~) using 12 MeV deuterons and 18.0 MeV aHe particles have been reported by Bock et al. 27). The two-particle pick-up (p, t) reactions on the three isotopes have been studied by Whitten 26). Studies from inelastic scattering of protons, deuterons and alpha particles have been undertaken in an effort to determine the collective character of some of the lowlying levels in the chromium isotopes. Bock et al. 27) have used 7-12 MeV deuterons and have studied the excitation of the first four levels in SaCr by means of the (d, d') reactions. Meriwether et al. 28) using 50 MeV alpha particles obtained angulardistribution measurements of several inelastic particle groups populating states in S2Cr and 5aCr" Similar measurements using the (p, p') reactions with 17.5 MeV incident protons have been performed on 52Cr by Funston et aL 29) and on ~aCr by Whitten 26). In the present work, the energy-level positions of both S2Cr and 53Cr have been measured up to an excitation energy of about 4.0 MeV by means of the (p, p') reactions and in 53Cr up to about 6.7 MeV by means of the (d, p) reactions. Proton

Cr NUCLEARSTRUCTURE

3

angular distribt~tions up to 4.7 MeV excitation in the (d, p) reactions have been obtained, and absolute differential cross sections have been measured. Distorted-wave calculations have been carried out and used to determine the transferred neutron angular momenta and the spectroscopic strengths for the transitions which exhibit a stripping character. Additional information in confirmation and support of some of the previous spin and parity assignments for the first four excited states in 53Cr has been obtained in the present study from the gamma-decay modes in the 5 aCr(p ' p,y) reaction and from measurements of cross sections of the (p, p') and (d, d') reactions on 53Cr. Comparison of these data with other experimental results and theoretical calculations will be made in sect. 3. 2. Experimental method and results 2.1. T A R G E T S A N D A P P A R A T U S

The targets were prepared by vacuum evaporation of enriched C r 2 0 3 material onto thin films of formvar. The chromium oxide was obtained from the Stable Isotopes Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee. An isotopic analysis of the samples used to prepare targets for the present experiments is given in table 1. The target thicknesses were determined by using elastic scattering of 3.0 MeV particles in the (p, p') and (d, d') experiments and 2.5 MeV deuterons in the (d, p) experiment. The Rutherford scattering predictions at these energies are assumed to be valid. The target thicknesses used in each of the experiments are given in table 1. TABLE 1 Isotopic analysis o f the c h r o m i u m targets Target thickness #g/cm ~

Isotope

s°Cr Target

~*Cr 5sCr sample (~)

55Cr (P, P')

~2Cr

0.01

99.90

0.01

0.01

7.1

58Cr

0.03

1.12

98.79

0.07

29.5

(P, P'7)

(d, p)

(d, d')

15.0 50.0

26.0

The incident proton and deuteron beams were obtained from the M I T - O N R generator 30). For the (p, p'), (d, d') and (d, p) experiments, the reaction products were magnetically analysed with the MIT multiple-gap spectrograph 31) and were recorded on 50 #m Eastman Kodak NTA nuclear emulsions at each of the 23 angles from 7,5 ° to 172.5 ° at intervals of 7.5 °. Appropriate thicknesses of aluminum foil were placed in front of the emulsions to stop the reaction deuterons for the (d, p) exposures. In the s 3Cr(p ' p,y)53Cr measurements, a high-intensity magnetic spectrometer 32) was placed in the target well of the multiple-gap spectrograph between the target and

4

M . N . RAO et

al.

the entrance slit of the 1.5 inch wide gap at 45 ° with respect to the incident beam direction. This combination permitted the realization of a solid angle of 3.2 x 10-2 sr, while at the same time preserving the high-energy resolution feature of the broadrange spectrograph. The proton groups scattered in the direction of the quadrupole spectrometer lens were focussed and directed into the 45 ° gap. With appropriate setting of the spectrograph field, a particular particle group is m o m e n t u m analysed and focussed onto a particle detector at the image surface of the 45 ° gap. The detector consisted of a 5 m m thick plastic scintillator integrally mounted onto a R C A 8054 phototube. The g a m m a rays were detected by a 7.6 cm x 7.6 cm NaI(T1) scintillator also integrally mounted onto a R C A 8054 phototube. This unit and the preamplifier module were held so that the axis of the scintillator was inclined at about 20 ° to the vertical through the target center. The front face of the NaI(T1) scintillator was at 7.5 cm from the target center. The large solid angle of acceptance of the g a m m a detector was required to smear out, at least in part, any spatial correlations that might exist between the protons selected at 45 ° to the beam and the de-excitation g a m m a rays. The relative intensities were not corrected for angular correlations between the protons and the g a m m a rays. The proton-gamma coincidences were performed using conventional double-delay line cross-over technique with a coincidence resolving time of 40 ns. Chance coincidence spectra were obtained simultaneously by employing an additional coincidence unit. The response of the NaI(T1) detector for mono-energetic g a m m a rays was measured by placing calibrated radioactive standard sources at the position of the target. The coincidence g a m m a spectra were analysed by a stripping procedure using the experimentally obtained response functions. The relative intensities were obtained from the areas of the full-energy peaks after correction for detector efficiency, and they have a probable error of 10 ~ to 20 ~o caused by statistics and uncertainties in the analysis. 2.2. EXCITATION ENERGIES FROM THE 52Cr(p, p') AND 5aCr(p,p') REACTIONS The angular distributions of 7.5 MeV protons elastically and inelastically scattered from the enriched 52Cr and s 3Cr targets were recorded and measured at all 23 angles of the multiple-gap spectrograph. A typical proton spectrum from each target at 52.5 ° is shown in figs. 1 and 2. Particle groups attributed to 52Cr in fig. 1 are numbered 1 to 14 and to 5 a c t in fig. 2, 1 to 26. In fig. 2 are also observed a few of the more prominent groups from the 1.12 ~ 52Cr impurity in the 5aCr target. These groups are identified with the circled number 52. Other unnumbered groups in both figures are assumed to arise from the usual target contaminants; namely, carbon, oxygen, sulfur, silicon and wolfram. Where identified, they are labelled by their respective chemical symbol. In fig. 3 are shown the experimental angular distributions of 7.5 MeV elastically scattered protons from s 2Cr and s 3Cr and an optical-model theoretical prediction based on parameters used in the (d, p) stripping analysis (see subsect. 2.6).

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The-measured + excitation energies in “Cr are given in table 2 together with the results of other precision measurements and include only those of the latter that fall within the limits of the present data. The positions of the energy levels measured here in the (p, p’) experiments are the arithmetic averages of measurements obtained at

P PROTON ELASTIC SCATTERING Ep = 7.50 MeV Optical

Model Porometers

V = 51.8

W’ = 45.0

ro = 1.25 a = 0.65

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Fig. 3. Angular distribution of 7.5 MeV elastically scattered protons from Wr and Wr. The solid curves represent the predicted distribution resulting from optical-model calculations using parameters extrapolated from the empirical formula of Perey 40). t The calibration of the MIT multiple-gap spectrograph is based on the value of 5.3042 MeV for the energy of *i”Po alpha particles. All energy measurements of (p, p’), (d, p) and contaminant reference energies are based on this number.

7

Cr NUCLEAR STRUCTURE

f o u r angles (52.5 °, 67.5 °, 97.5 ° a n d 120 °) with respect to the incident b e a m o f 7.5 M e V p r o t o n s . I n the earlier M I T m e a s u r e m e n t s 4) o f the 52Cr(p, p')52Cr experiment, level no. 5 h a d n o t been observed, a n d level nos. 8-14 were n o t r e p o r t e d . In the present m e a s u r e m e n t s , the excitation energy o f level no. 1 was t a k e n as 1.433 MeV, a n d the r e m a i n i n g levels calculated with respect to this value as the reference energy. The present m e a s u r e m e n t s are in excellent a g r e e m e n t with the earlier M I T values 4), with those o f M a c g r e g o r a n d B r o w n 9), those o f K a t s a n o s a n d H u i z e n g a l o ) a n d with the level p o s i t i o n s d e d u c e d f r o m the 52Mn decay schemes o f W i l s o n et al. 14) a n d F r e e d m a n et al. 1 s). These are all t a b u l a t e d in table 2. TABLE 2

Level positions of 5*Cr in MeV Present Level no. 0 1 2 3 4 5 6 7 8 9a 9b 10 11 12 13 14

Ref. ~)

Ref. 10)

Ref. 14)

Ref. 16)

Ref. 18)

(MeV) 4-0.007

(MeV) -4-0.005

(keV)

(keV)

(keV)

0 1.433 b) 2.368 2.645 2.765 2.963 3.113 3.162 3.417

0 1.437 2.372 2.650 2.768 2.964 3.119 3.162 3.413

0 1.434 2.371 2.650 2.767 2.965 3.114 3.163 3.416

0 1433.64-0.8 2368.7±1.3 2647.64-1.5 2766.2±1.1

0 1434.5-4-0.3 2370.34-0.3

3112.14-0.8

3114.6___0.3

3.474 3.614 3.771 3.947 4.011 4.036

3.470 3.617 3.772 3.948 4.013 4.038

3.472 3.619 3.772 3.947 4.016 4.040

data

(MeV) < 4-0.006

2768.8 :t:0.3

0 1434.14-0.6 2368.64-0.8 2646.94-0.8 2766.14-0.8 2965.64-0.8 3162.84-0.8 3413.2~1.0 3469.54-1.0 3472.54-1.0

3613.8±0.8

3617.7!0.3 3771.0&0.8

0+ 2+ 4-0+ 4+ 2+ 6+ 2+ (3+) (5+) 2 5+ 2+

a) Spin and parity assignments from refs. la-10). b) Reference energy from ref. 4) (see text). The excitation energies f r o m the 5 3Cr(p ' p,)53Cr reaction in the present experiments are listed in table 3. These m e a s u r e m e n t s are also based on the value (1.433 M e V ) o f the first excited state in 52Cr as the reference energy. T h e particle g r o u p corres p o n d i n g to this level is also observed f r o m the enriched ~ aCr target (1.12 ~ 52Cr) b o m b a r d m e n t (see fig. 2). In table 3 are also listed the level p o s i t i o n m e a s u r e m e n t s in 5 3Cr f r o m the present (d, p ) experiments (see subsect. 2.3) a n d the " m e a n " values obt a i n e d b y averaging the (p, p ' ) a n d (d, p ) measurements. Similar m e a n values deduced f r o m the (p, p ' ) a n d (d, p ) results o f M a c g r e g o r a n d B r o w n 9) are shown in c o l u m n 7 for c o m p a r i s o n . The m e a s u r e m e n t s o f o t h e r workers 8,11,12,22) are n o t included b u t are a d e q u a t e l y s u m m a r i z e d in ref. 9) a n d are in satisfactory a g r e e m e n t with the present d a t a and those o f refs. 9,1 o).

8

M . N . RAO e t

al.

TABLE 3 Level positions o f 5~Cr in MeV 53Cr(p, p')~3Cr Level no.

Present work ~)

Ref. 9) b)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 0.565 1.006 1.289 1.538 1,974 2.173 2.233 2.322 2.452 2.657 2.672 2.708 2.772 2.826 2.991

16 17

3.127 3,184

18 19 20

3.266 3,351 3.435

21 22 23 24

3,602 3.621 3.697 3.711

25 26 27 28 29

3.838 3.971

0 0.566 1.010 1.291 1.544 1.974 2,176 2.233 2.322 2.456 2.658 2.676 2.708 2.773 2.828 2,992 3.085 3.127 3.180 3.244 3.265 3.349 3,430 3.599 3.604 3.622 3.698 3.712 3.781 3.837 3.974 3.980 4.046 4.073 4.128 4.139 4.171 4.189 4.223 4.286 4.297 4.317 4.331 4.363

30 31 h) 32 33 34 35 36 37 h)

4.427 4.453

5~Cr(d, p)~zCr Present work e)

M e a n excitation energy

Ref. 9) a)

Present work

Ref. 9)

~) 0.564 1.007 1.289 1.538 1,975

2,999

0 0.565 1.008 1.285 1.537 1.971 2,169 2.227 2.324 2,454 2.664 2.676 2.715 2.782 2.826 2.998

3.155 3.196

3.151 3.191

3.146 3.190

3.276 3,358 3.442

3.270 3,355 3.438

3.271 3,354 3.438

3.629 1)

3.626

3.719

3.715

0 0.565 1 .O08 1.290 1.541 1.974 2.176 2.233 2.323 2.456 2.664 2.676 2.713 2.773 2,828 2.996 3.085 3,144 3.186 3,244 3,268 3,352 3.434 3.599 3.604 3.624 3,698 3.713 3.781 3.837 3,974 3.983 4.046 4.070 4.128 4.140 4.171 4.192 4.227 4.286 4.302 4.317 4.332 4.360

~) ~) 0.565 I) 1,009 I) 1.281 1.535 1.968 2.165 2.221 2.327 I) 2.456 2.669 I) 2.681 2.723 I) 2.793 2.825 3,005

2,324 2.669 2.676 2.718

3.602 3.625 3.697 3.715

3.985 4,047 4,067

3.986

3.844 3.971 3.985 4.047 4.067

4.136 1)

4.140

4.136

3.847

4.204 4.228 I) 4,290 4.308 4.340 4,390 4.435 I)

4.232 4.308 4.333 4.356 4.434

4.204 4.228 4.290 4.308 4,340 4,390 4.435

4.431 4,453

Cr NUCLEAR STRUCTURE TABLE 3 (continued) s3Cr(p, p')saCr Level no. 38 h) 39 40 41 42 43

44 45

46 47 48 49 50 51 52 53 54 55 56 57 58 h) 59 h) 60 61 62 63 64 65

Present work a)

Ref. 9) b) 4.484 4.500 4.522 4.530 4.570 4.610 4.642 4.661 4.675 4.690 4.699 4.745 4.790 4.804 4.815 4.884 4.929

5zCr(d, p)53Cr Present w o r k e)

Ref. 9) d)

4.489 4.516 4.551 4.610 r) 4.639 4.666

Mean excitation energy Present work 4.489

4.496 4.514

4.614 4.644

4.516 4.551 4.610 4.639 4.666

4.671 4.696 t) 4.736

4.812 4.850 4.873 4.906 4.934 4.967 5.001 5.047 5.093 5.123 5.174 5..208 5.225 5.265 5.310 5.330 5.397 r) 5.420 5.452 t) 5.471

66 67 68 69 70 71 72 73

5.596 5.624 5.674 5.701 5.736 5.750 5.805 5.843

74 75

5.877 5.900

4.700

4.802 4.817

4.931 4.962 5.005 5.084 5.128 5.181 5.210 5.268 5.274 5.320 5.326 5.396 5.418 5.456 5.557 5.584 5.593 5.665 5.697 5.734 5.742 5.792 5.835 5.862 5.886 5.937

4.696 4.736

4.812 4.850 4.873 4.906 4.934

Ref. 9) 4.484 4.498 4.518 4.530 4.570 4.612 4.643 4.661 4.673 4.690 4.700 4.745 4.790 4.803 4.816 4.884 4.930

10

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al.

TABLE 3 (continued) 6aCr(p, p')~aCr Level no.

Present work ~)

Ref. ~) b)

5~Cr(d, p)58Cr Present work c)

76 77

5.951 5.962

78 79 80 81

5.996 6.039 6.068 6.114

82 83

6.154 6.180

Ref. 9) a)

Mean excitation energy Present work

Ref. 9)

5.953 5.976

84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 a) b) e) d) e) t) g) ~)

6.231 6.258 ~) 6.305 6.335 6.370 6.387 6.415 6.430 6.445 6.460 6.495 6.524 6.550 6.575 6.600 6.630 6.665 6.700 6.735

6.039 6.061 6.123 6.135 6.165 6.216 6.224 6.255 6.290 6.329 6.377 6.395 6.417

6.493 6.511 6.546 6.599 6.628 6.661 6.694 6.728

<__0.006 MeV for all levels; reference energy, 52Cr first excited state, E x = 1.433 MeV (see text). -t-0.007 MeV for all levels, ref. 9). Estimated uncertainty ~ 0.010 MeV for all levels. 4-0.010 MeV for all levels, ref. 9). Ground-state Q-value, 5.7254-0.006 MeV. Reference energies from ref. 5) (see text). Ground-state Q-value, 5.723--0.015 MeV. Possible unresolved doublet.

2.3. EXCITATION ENERGIES FROM THE 52Cr(d, p) REACTION T h e 52Cr t a r g e t w a s b o m b a r d e d w i t h a 7.5 M e V d e u t e r o n b e a m . A t y p i c a l p r o t o n s p e c t r u m o b t a i n e d w i t h a 4 0 0 0 / ~ C e x p o s u r e is s h o w n in fig. 4. T h e p r o t o n e n e r g y r e s o l u t i o n was a b o u t 10 keV, and" t h e p r o t o n g r o u p s c o r r e s p o n d i n g to a r e s i d u a l m a s s o f 53 w e r e identified f r o m t h e i r k i n e m a t i c e n e r g y shift w i t h angle. S e v e r a l c o n t a m i n a n t p r o t o n g r o u p s w e r e o b s e r v e d a n d are d e s i g n a t e d by t h e i r c o r r e s p o n d i n g c h e m i c a l s y m b o l in fig. 4.

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12

M . N . RAO et al.

The ground-state Q-value adopted for the 52Cr(d, p)53Cr transition in the present work is the value of 5.725+_0.006 MeV previously measured 5) in this laboratory using the single-gap spectrograph. In ref. s), there were reported three other proton groups identified with the 52Cr(d, p)SaCr reactions and corresponding to levels in s 3Cr at 0.565, 1.008 and 2.327 MeV. Because of the effects of differential hysteresis in the multiple-gap spectrograph, these excitation energies were also considered more precise and were adopted as reference energies for the purpose of interpolating the energies of new and adjacent proton groups observed in the present experiment. In the earlier work, a number of additional proton groups had been observed but the data were insufficient for unambiguous isotopic assignments. With the aid of the (d, p) spectra from the present enriched 52Cr bombardment, the single-gap data were reexamined, and measurement and identification were made of several groups attributable to the 52Cr isotope. These level positions are so designated in table 3 and were also used as reference energies for measurements of the excitation energies of adjacent levels. In the 53Cr(p, p')53Cr reaction, 26 levels were observed up to an excitation energy of 3.971 MeV. Of these levels, nos. 21, 23 and 26 at 3.602, 3.697 and 3.971 MeV, respectively, were not observed in the present (d, p) work or in the (d, p) work of Macgregor and Brown 9). Up to an excitation energy of 6.735 MeV in 53Cr, a total of 102 levels (the numbered levels in table 3) have been measured in the present experiments as compared to 110 reported by Macgregor and Brown over the same region of excitation. In columns 6 and 7 of table 3 are listed the mean energies (as defined in subsect. 2.2) for the cases where the level was observed in both the (p, p') and (d, p) reactions. 2.4. ANGULAR DISTRIBUTIONS OF THE saCr(p, p') AND saCr(d, d') REACTIONS In an effort to obtain further information on the character of the low-lying levels in angular-distribution data from the (p, p') and (d, d') reactions for the first five excited states in SaCr have been analysed. Fig. 5 shows the absolute differential cross section as a function of angle for the excitation of these states using incident proton and deuteron energies of 7.50 MeV. At this energy, the proton excitation may be expected to reflect large contributions from compound-nucleus formation a3, a¢) while (d, d') reactions with 7.5 MeV deuterons in this mass region have been observed as) to display some direct interaction mechanism. Though both sets of distributions in the present case are lacking in characteristics that give evidence of the excitation mode of the specific states, their relative cross sections perhaps are significant. The (p, p') cross sections for state nos. 3 and 4 are approximately in the ratio of 4 : 1, while the (d, d') cross sections for the same states are approximately in the ratio of 30 : 1. Since (d, d') direct inelastic scattering preferentially excites states of vibrational or rotational type, this may indicate that state no. 3 at 1.285 MeV excitation has a more collective character than state no. 4 at 1.537 MeV excitation energy.

53Cr, the

CrNUCLEARSTRUCTURE

13

2.5. THE saCr(p, p'y) MEASUREMENTS The inelastic proton-gamma coincidence measurements were carried out with an incident proton beam of 6.5 MeV. Figs. 6a-c show the results of these studies. The normalized shapes of single gamma-ray energies obtained with the help of radioactive standard sources are indicated in these figures by dotted lines. El = 7.50 MeV

530r (p, p') 53Cr

2of ,.o

0.8 o.6

53Cr (d,d')53Cr Level No.5

} {{

~{

{'}~}{11 { 11

E× =1.971MeV 0.08

{{{1{

0.4 I

I

I

I

o6I

--£

I Level

]

No.4

J

,

E~ =1.557 MeV

0.4

002

0.2

°°"I {~

I

I

i

i Level

I

No.3

0.6 1.0I

{{{{{{{

{{{{{}

{

{

0.2 r

I

I

i

I

I

Level

No. 2

I

°3o, f

0"6 I O4 I

I

{{{}

I

I

I Level

I

No. I

0.2

}{{{

{

0.05 i Ex = 0.565 MeV 0"4 1

§{

I

I

~

I

tI

{

{ i

{ { { { ~{{{{{{{ I

}{ {{

I

i

i

I

90

i

I

l

180 0 8C.M.(degrees)

I

I

I

90

I

}{{

{{11{{,

o.~ I

I

Ex =.I.008 MeV

o~

o"

2'0 1.0f 0.8 0.6 0.4 0

{

Ex = t.285 MeV

o.8

I . 2"0 f .8 b~ 01.0 0.6 "o 0.4

I

0.01

I

vE

{

I

I

I

{{ I

180

Fig. 5. Angular distributions of protons and deuterons from the (p, p') and (d, d') reactions corresponding to the first five states in 58Cr. The 1.008 MeV level decays (B) mainly to the ground state with no observable branching to the 0.565 MeV first excited state (fig. 6a). The 1.285 MeV decay shows clearly a branching (D) to the 1.008 MeV level (fig. 6b) in addition to the direct

14

M. N. RAO e t al.

1.008

(6e)

[ o0,0

150

B 1.008

.(,

I00 5SCr

I

50

** ee .*

•

00

.-*

** q["*"

• Oeoo

~-000

ff'~"-'--l"

oe

.

4'0 logo

m

•

I

/"

•e • •

I

'1

\

90 oe

...,r'

• 00

I

*

I

200

A 0.565

IOC

T ~ , T|

0.565

I a

J

I

A

|

..,

o!

.'.,',.,.~ .-'-" .-.....,_'

-* "l 20

"T"

* I

40

60 Ch0nnel

*

153Cr 120

I 80 I00 Number

(~

I 140

C 1.285 ,q

0 E (1) -0

(6b)

ft I

c-

60C

,,

-

0 0 1.285

0 400--

D

B 1,008

D o.ze

14%

B

E Z

1.008

C86% 0,565

,o

° o

200

-

% .o oo o~O o o Oo oo oo ¢Ooo oo o oo ~'7"-~ o

~

't

f

I

0 SSCr

I

I

I

20

40

60

~'--'1

Chonnel

~I

80

I00

I~

I

120

140

Number

Fig. 6. Gamma spectra. (a) in coincidence with inelastically scattered protons exciting levels in "Cr at (A) 0.565 MeV and (B) 1.008 MeV. (b) in coincidence with the proton group leading to excitation of the 1.285 MeV state in "Cr.

15

Cr NUCLEAR STRUCTURE

(6c)

E 0.53 o

600

Fi

F 0.25

1,557

',,, F

,

1,285

400 E

28%

1.0~

72% 0,565

i o

200

8 1.008

C

B

I o

~

io

,,o/

',

'

60 ~o o

,

0

,

CI.285

53Cr

~ C_.,_ - - ~_oe' o , ....~ ,_ o ~ ~ , .... ,......\°* _,..-,o _._~__,

........

2'0

40

60 80 I00 Channel Number

120

140

Fig. 6. Gamma spectra. (c) in coincidence with the proton group leading to excitation of the 1.537 MeV state in 58Cr. transition (C) to the ground state. The presence of the g a m m a rays of energy 0.53 MeV (E) and 1.0 MeV (B) indicate that the 1.537 MeV state decays to the 1.008 MeV level (fig. 6c). There is also a weaker transition (F) to the level at 1.285 MeV. The relative intensities of these branchings are indicated in the figures. No direct transitions to the ground state and to the first excited state were observed from the 1.537 MeV level. This is in agreement with the (d, PT) observations 23). These results are also consistent with the evidence from the inelastic scattering indicating that the 1.537 MeV state exhibits little or no collective character; otherwise an enhanced E2 transition to the ground state should be expected. Earlier measurements have suggested spins and parities of ½-, ~-, -~- and ½- for the first four excited states in 5aCr at 0.565, 1.008, 1.285 and 1.537 MeV, respectively. The present (p, p'), (d, d'), (p, P'7) and (d, p) (see subsect. 2.6) data further support these assignments. 2.6. THE s2Cr(d, p) STRIPPING ANALYSIS The angular distribution of the elastically scattered deuterons from 52Cr was measured at an incident energy of 7.5 MeV to provide information on the opticalmodel parameters for use in the D W B A calculations. The automatic search code ABACUS was used to generate sets of deuteron parameters to fit the experimental data. Two starting potentials were used. Set 1 (table 4) was generated using the B4 set obtained for the Ti experiments 36). Subsequent sum-rule analyses of both the Ti(d, p) [ref. 37)] and 5°Cr(d, p)SlCr [ref. 38)] indicated that the spectroscopic strengths were consistently high particularly for the I. = 3 transitions. (See refs. 37, 38) for further details.) Set 2 (table 4) was generated by starting the automatic search

16

RAO et aL

M.N.

using parameters set 2 of ref. 38). The fit to the experimental data for set 2 is shown in 7.

fig.

TABLE 4 Optical-model p a r a m e t e r s used in the 52Cr(d, p)~aCr analysis Particle d d p n

Set

V (MeV)

r0 (fro)

a (fm)

r'0 (fro)

a' (fm)

W' (MeV)

roe (fm)

1 2

102.0 114.2 51.8 a)

1.0 1.0 1.25 1.25

0.88 0.76 0.65 0.65

1.41 1.37 1.25

0.64 0.69 0.47

97.1 52.78 45.0

1.3 1.3 1.25

T h e optical potential used was o f the f o r m d V(r) =

-- V(eX+l)-a+iW

( e ~ ' + l ) - X + Vc(r, re),

' ~,,

with r--ro A~ - -a,

X

X"

r - - r ' o A Jr - a ,r

--

r e =roeA4:.

Vc is the C o u l o m b potential f r o m a h o m o g e n e o u s l y charged sphere o f radius r e . a) A d j u s t e d to give the transferred n e u t r o n a b i n d i n g energy o f Q(d, p ) + 2 . 2 2 4 MeV. 104 8

6

SZcr (d ,d )SZcr Ed = 7.50 MeV

4

Deuteron

2

~2,, V ro a 114.2 1.0 0.76

~o~

Parameters i

r~ [.37

i

a W re 0.695 52.78 1.50

8

6 4 2

~

,02 6 4

x \ \ (

~\~.,

Ruther f°rd

\ \ \ -.

2 O\

tO 8 6 --

4 2

0

Optical Model

I

30

610

Fit

i

90 eC.M. (degrees)

r

120

i

150

180

Fig. 7. A n g u l a r distribution o f 7.5 MeV elastically scattered deuterons f r o m ~ C r . T h e solid curve results f r o m D W B A calculations using the deuteron p a r a m e t e r s (set 2) o f table 4.

Cr NUCLEAR STRUCTURE

17

The D W B A calculations were performed using the code J U L I E 39). The parameters for the optical potential for the outgoing protons were extrapolated from the empirical formula of Perey 4o) and are indicated in table 4. The captured neutron in the final state was described as moving in a Saxon well without a spin-orbit term. Table 4 gives the parameters used for the captured net~tron bound state. The magnitude V of the real potential for the neutron-wave function was adjusted so as to have the transferred neutron binding energy equal the Q-value for the stripping reaction leading to the state plus 2.224 MeV. The D W calculations were performed with a zero lower cut-off on the radial integrals. The relation between the experimental differential cross sections (da/df2)exp and the calculated D W B A results a(O) for a zero-spin target is given by (da/dQ)exp = 1.48 ( 2 J + 1)S a(O), where J is the spin of the final nuclear state, S the spectroscopic factor for the stripping transition and ( 2 J + I ) S the transition strength. The numerical factor 1.48 is associated with the use of the Hulth6n wave function to describe the deuteron. The spectroscopic transition strength ( 2 J + 1)S for each level was evaluated by taking the ratio of the maximum of the experimental cross section to the m a x i m u m of the predicted cross section. In the case of In = 0 transitions, the 15 ° data points were used. Angular distributions were obtained for most of the first 45 levels of 53Cr up to 4.7 MeV excitation and are presented in figs. 8-13. The stripping distributions have been grouped according to their In values. Some of the distributions give indication of a stripping pattern, but theoretical fits have not been made because some crucial experimental points were not available for these cases. This was due to the interference of contaminant peaks in most cases and to the fact that the corresponding proton groups appeared at or near the edges of the emulsion plates and hence could not be completely scanned. These latter distributions have been grouped together in fig. 13 with the distributions which have no obvious stripping pattern. The results of the stripping analysis from the present experiment are summarized in table 5. The transition strengths ( 2 J + 1)S deduced from both parameter sets 1 and 2 for each level that displays a stripping character are listed in columns 6 and ?, respectively. In an effort to maintain a consistent treatment of M I T data for the chromium isotopes and to permit evaluation and comparison with other nuclei, only the results from parameter set 2 will henceforth be quoted in this paper in the summation of spectroscopic strengths. In table 5, for comparison are also shown the results of Bock et al. 22)(columns 8-10). In the last column are shown the probable spin and parity assignments, some obtained from the literature and in other cases tentatively assigned from the present data. In the latter cases, they are enclosed in parentheses. The transition strengths ( 2 J + 1)S from set 2 are indicated in fig. 14, where they are compared with the spectroscopic factors obtained from the (p, d) pick-up experiment of Whitten 26). The

~ . N. RAO et al.

18

C3

0

~

v

V

V

V

w

v

V

w

19

Cr NUCLEAR STRUCTURE

i " ~ ""

~

+ "~ "~ +

+

,..~ , ~

r;

+

~"

)L,+

0

0

,.o

o

~

~

4

~

~

d VVV

d

4

d VV

d~

20

M.N. RAO et al.

simple shell-model sum-rule results are summarized in table 6. In the following paragraphs, our analysis of the observed angular distributions is discussed. TABLE 6 Summed strengths ( 2 J + 1)S 2s~ exp. theory

lf½

2p

2pk

2p~

lfff

lg~

2d~

3s~

0.08 a) 0.89 e) 0.03 b)

5.1 d)

4.1 e)

1.0 r)

2.9 g)

5.2 h)

1.04 l)

0.12J)

6

4

0

0

2

6

10

6

2

a) State no. 38. b) State no. 37. e) State nos. 3, 4, 19 and 20. d) All In = 1 transitions, e) State nos. 0, 8, 22 and 41. ~) State nos. 1, 9, 11, 12, 17, 20, 28, 29 and 41. g) State nos. 2, 10, 15 and 43. h) State no. 24. i) State nos. 16, 18, 27, 30, 32 and 42. J) State no. 44.

2.6.1. The I, = 1 distributions. Shown in fig. 8 is a group of 12 angular distributions that exhibit patterns characteristic of (d, p) stripping where the captured neutron has one unit of orbital angular momentum. From simple shell-model considerations, ,SZ4Crz8 consists of the doubly magic 4~Ca28 core plus four protons in the lf~ shell. Apart from higher-order excitations, the transfer of a neutron to 52Cr in the (d, p) reaction would be expected to excite states in the shell-model orbitals 2p~t, 2p~, lf~, lg~, 3% and higher. The angular distributions of the transitions depicted in fig. 8 are most likely attributed to the 2p~ and 2p~ orbitals. The spin and parity of the ground state of 53Cr have been measured 4t) to be 3-. From the particle-gamma coincidence experiments 16,23) and the (n, ~) angular correlation measurements 19), the spins and parities of the ground state and the excited states in 53Cr at 0.565, 2.324 and 3.625 MeV (nos. 0, 1, 8 and 22) have been given 3-, ½-, 3- and 3- assignments, respectively. From J-dependence effects in In = 1 (d, p) angular distributions, Lee and Schiffer 42) and Andrews et al. 21) report a "dip" (thus J = ½-) in the back-angle distribution for the level at 0.565 MeV and "no dip" in the ground-state distribution (thus J = 3-). The same effects are observed in the present data for these two states (see fig. 8). In addition, the above ~- assignments for the 2.324 and 3.625 MeV states are consistent with the absence of a back-angle dip in the l n = 1 distributions reported here and also by Andrews et al. 21). Because of other factors that may affect the character of the angular distributions (ref. 38)), the presence or absence of a dip in the cross section at the back angles cannot always unambiguously suggest the spin assignments. The 2.715 MeV level (no. 12), for example, exhibits an unnatural back-angle distribution, yet from the (n, ~) angular correlation measurements 19), a spin of ½ is indicated. The 2.454 MeV level (no. 9) depicts a nonstripping back-angle effect but is judged here on the basis of its forward-angle pattern to be an In = 1 transition. Interference from contaminant peaks in the case of the 3.190 MeV level (no. 17) at the critical

Cr NUCLEAR STRUCTURE

21

forward angles prevents making a more positive assignment in this case. The calculated D W distributions for this group shown in fig. 8 are for l n = 1, 3 and 4. These are examples of cases where the ln assignments are based largely on the judgment of the experimenter. Both groups (nos. 9 and 17), however, are relatively weak and have little effect on the sum-rule results below. The proton groups corresponding to the 2.664 and 2.676 MeV levels (nos. 10 and 11) were not completely resolved (12 keV spacing) at all angles. The sum of the yields are shown plotted in fig. 8 where the appropriate ratio from ln = 1 and In = 3 D W predictions were used as a guide to fit the sum curve. The two proton groups corresponding to these states were resolved at 37.5 ° and 45 °. This is the region where maximum cross section is expected for an l n = 3 transition. A peak shape analysis of this doublet indicated that the intensity of the higherenergy component diminished toward lower angles while the yield of the lower-energy component increased. This change in the asymmetry established group no. 11 at E x = 2.676 MeV as the l n = 1 transition. The sum of the transition strengths ( 2 J + 1)S for the 12 levels shown in fig. 8 is 5.1 (total of In = 1 states in column 7, table 5). With the combined uncertainty in the experimental and D W predictions, the value of 5.1 may be considered reasonable in comparison with the sum-rule prediction of 6.0 [ref. 43)]. In an effort to determine the unperturbed single-particle energies Ej. for both 2p~ and 2p4r states, the spin assignments from table 5 have been assumed. The first three ~ - states together appear to have the full 2p~ strength with ~ S = 0.99 and E~ = 1.27_+0.1 MeV. The remaining 1n = 1 transitions shown in fig. 9 (if all are J = k) represent only about one half ( ~ S = 0.57) of the remaining 2p~ strength expected with E~ = 1.74__ 0.3 MeV. With the 2p~-2P½ spacing in 49Ca being 2.01 MeV [ref. 44)] and approximately 1.60 MeV in 51Cr [ref. 38)], it would seem unlikely that in 53Cr this spacing should be only 0.47 MeV. However, it is quite possible that other p~ transitions have been missed (see fig. 13) or perhaps occur at higher excitations than examined in the present work. In the work of Bock e t al. 22), where the angular distribution analysis is extended to 7.2 MeV, three additional In = 1 levels are reported in the region above 5.5 MeV. These three states appear to contribute only about 20 ~ of the missing strengths and would raise the 2p~-2p~ spacing to approximately 1.0 MeV, Except for the few possible ambiguous In assignments from the present work shown in parentheses in table 5, there is very good agreement with the data of Bock et al. 22). 2.6.2. T h e I n = 3 d i s t r i b u t i o n s . In fig. 9a are shown four angular distributions which have been identified with states populated by the transfer of three units of angular m o m e n t u m in the (d, p) reaction on 52Cr. The curves drawn representing the D W predicted distribution for neutron transfer to the I f orbital show very good agreement with the data in the cases where the cross sections are high, such as the 1.008 and 4.666 MeV levels (nos. 2 and 43). A probable In = 3 assignment is given to the 2.998 MeV level (no. 15) because of the good D W match near the angle of m a x i m u m cross section. The back-angle behaviour here is not typical of (d, p) stripping usually

22

M. N. ~ o

e t al.

52Cr(d,p ) 53Cr IOI / ~

~,ooodS,o,e

_

Ed

=7.5 MeV Level No. I Ex =0.565 MeV

!

~e::o ooo MeV

l. = I

i0 °

I

io° "C

I0 9

'

I

I

I

[

ISO

T

90

Level No. I0 Ex =2.664 MeV --In=3

j,~.~.

I

I

~

El

180

Level No. 12 Ex = 2.715 MeV

~

/n=l

~

Id

}

F Level No. II

"

\

E~=2.6Z6M~V ',

"\

\

r ~

'~ ....

"10 v

t_'.~

\

0 I0 =

I

I

I 90

~,

I

I

180

I

I

~ 9

Level No.22

I

I 180

Level No. 28 Ex = 4.047 MeV

Ex =5.625 MeV In = I

~n=(I)

IOc

Id o

I

I

[ 90

I

I

180

I

I

p 90

"I ~

I 180

G¢.m.(de9 ) Fig. 8(a). Angular distributions of proton groups from the s=Cr(d, p)SaCr reactions assigned In = 1 orbital angular momentum transfer. The curves are DWBA predictions calculated from parameter set 2 of table 4.

Cr NUCLEAR

23

STRUCTURE

52Cr(d,p)53Cr- Ed---7.5MeV I0'

Level No. 8 Ex: 2 . 3 2 4 MeV ~n: I

I0"l

Level No. 9 Ex =2.454 MeV

I

In:(~l

I0°

90

0

Level N0, 17 Ex : 3.190 MeV

~X _~

~"

IBO

,t n : ( I )

90

tSO

T

Level No. 20

L-

Ex : 3,438 MeV

~E,O'/'~, \ Ivz ~

I

I

0

I

i

i

I

o ~

I

I

i

-I~~

90

I

I

'~r 180

9O

r

~n:11}

Io-z

1

i80

~i:'2:i:eV

I ~

0

I

90

Io°

~~

LZoT°o°Mev

Id'

180 Oc.m,(de

I

0

I

I 90

c])

Fig. 8(b). For caption see fig. 8(a).

I

~L 180

M, ~ . R ~ o e t al.

24

m

<

>

o~

/"'/

3~ ~"i=

.J

i I

IilIII I~I

~

JlllIl

'_o

o .

o

m~

o >

I

i

Ii

~

I,IL,

I

I

I

I

I

''

"--o

0

L

t~

o

~-~

'

v

£

.£

~1

I

[ II

I

I

I

[

[

(J~/qw) ~~( ZSPI-°p)

Cr NUCLEAR STRUCTURE

25

observed for In = 3 transfer. The level at 2.664 MeV (no. 10) is the In = 3 component of the doublet described in subsect. 6.1.1. F r o m simple shell-model considerations, these transitions at 1.008, 2.664, 2.998 and 4.666 MeV (nos. 2, 10, 15 and 43, respectively) most probably arise from neutron occupation of the lf~ orbital. The sum of transition strengths for these states (column 7, table 5) indicates that only about one half of the expected strength is observed ( ~ S = 0.48) in the excitation region covered in the present work. In the region up to 7.2 MeV in excitation, Bock et al. 22) make no additional l n = 3 assignments. Shown in fig. 9b is a group of four angular distributions which display characteristics not generally considered typical for In = 3 (d, p) transitions under the present experimental conditions. Particularly at the forward angles, there is noted a departure from the usual decreasing cross sections normally observed experimentally and also observed in the prediction from D W B A calculations. Except for the satisfactory agreement with D W predictions between 30 ° and 90 ° in the case of the 1.285 and t.587 MeV levels (nos. 3 and 4), it would not be possible to make unambiguous In = 3 assignments from the present (d, p) angular-distribution data. These levels have been given probable spin and parity assignments of ~- from the (d, p?) coincidence studies of Rollefson et al. 23), and the results of our present (p, P'?) measurements (see subsect. 2.5) are consistent with their analysis. F r o m both (p, d) and (3He, e) pick-up experiments, all four levels of fig. 9b have exhibited angular distributions characteristic of In = 3 neutron pick-up. The levels at 3.354 and 3.438 MeV (nos. 19 and 20) may be assumed to be those corresponding to the In = 3 pick-up transitions reported by Whitten 26) at 3.339 and 3.422 MeV from the (p, d) reactions and by Bock et al. 27) reported at 3.36 and 3.44 MeV from the (3He, c0 reactions. It is noted that level no. 20 is also given a tentative ln = 1 assignment and thus included among the l n = 1 distributions of fig. 8. It is conceivable that there is an unresolved component in the region of this level which corresponds to the transition observed in the pick-up experiments. However, neither in the (p, p') nor in the (d, p) measurements from the present experiments was there sufficient evidence for establishing two states at this energy (3.438 MeV). The behaviour of the angular distribution up to 37.5 ° for this level does, however, bear some resemblance to that of the other three groups of fig. 9b and thus lends support to the fact that this may indeed be the In = 3 state seen in the pick-up reaction. The spectroscopic information from the pick-up reactions for these levels is shown in fig. 14 with the (d, p) results of the present work. Assuming that the transitions shown in fig. 9b are lf~ neutron hole in character, the sum of transition strengths for these states from column 7 of table 5 is 0.89. 2.6.3. The In = 2 distributions. In fig. 10 is shown a group of six distributions assigned as In = 2 on the basis of matching the angle for the m a x i m u m experimental cross section with the maximum D W theoretical predictions. In the case of the 3.146 MeV level (no. 16) contaminant groups interfered at angles below 30 °, and thus only a probable In = 2 assignment can be made from the present data. The most prominent

26

M.N. RAO et al. ~2Cr ( d , p ) 53Cr - E d = 7 . S M e V Level NO. 16 Ex = 3.146 MeV in : (2)

Level No. 18 Ex = 3,271 MeV In= 2

Id'

10-2

~z

9O

0 ~.
90

180 Level NO. 27 Ex = 3.985 MeV

*80

Level No. 30 Ex" 4,136 MeV

E

"7

I0°

E

°\

10-2 I

I

I

1

I

90

i0c

180

I

16' 0

I

I 90

Level NO, 3~. Ex= 4.228 MeV

f ~

I

I

180

Level No. 42 E x = 4.639MeV

~rl" 2

IO-'

I

0

I

I

°,0

I

I

I

180

0

I

I

90

I

I J 180

Oc.m ( d e g )

Fig. 10. A n g u l a r d i s t r i b u t i o n s o f p r o t o n g r o u p s from the 5~Cr(d, p)saCr re a c t i ons assigned In = 2 o r b i t a l a n g u l a r m o m e n t u m transfer. The solid curves are D W B A p r e d i c t i o n s c a l c u l a t e d f r o m p a r a m e t e r set 2 o f t a b l e 4.

Cr NUCLEAR STRUCTURE

27

I, --- 2 distribution is that for level no. 30 at 4.136 MeV. The D W prediction for this transition seems to be in excellent agreement with the data. It may be noted that the discrepancies are greater with other levels, particularly in the cases where the cross sections are lower and the statistics are poor. No spin measurements for any of these levels are known. However, from simple shell-model considerations, the present results would suggest occupation of the 2d orbital and, therefore, spin and parity ~+ or ~+ with the former more likely. The sum of the transition strengths for these levels depicted in fig. 10 is 1.0, only 16 of the shell-model prediction of 6.0, i.e. if all are attributed to the 2d~ shell. Bock et al. 22) report several additional In = 2 transitions between 4.6 and 7.2 MeV excitation giving further evidence that the major strength of the 2d~ orbital lies above 7 MeV. The fact that none of these states is reported in the pick-up experiments 26,27) rules out the possibility that any of them may arise from ld~ hole-state configurations. Whitten 26) reports only one l, = 2 distribution from the 54Cr(p, d)53Cr reaction, and it is at an excitation energy of 4.68 MeV. Bock et aL 27) also observes an In = 2 distribution from the S4Cr(3He, 00 s 3Cr reaction at 4.7 Me¥. Their deduced spectroscopic factors for this level are in good agreement, S = 0.85 from ref. 26) and S = 0.69 from ref. 27). A possible candidate for the (d, p) transition "stripping" to this ld~ hole state is level no. 45 at 4.736 MeV. The average differential cross section at angles about 90 ° is 0.015 mb/sr. Interference with oxygen and nitrogen groups at forward angles prevented further data analysis for this level. Our group no. 42 at 4.639 MeV excitation with an In = 2 distribution is probably not the level in question since the spectroscopic strength deduced here (0.36) (table 5) assuming a ld~ transition seems large compared to the In = 2, ld~ strength (0.02) observed in the 5°Cr(d, p)51Cr experiment 38). 2.6.4. The In = 4 distribution. A strong l n = 4 transition occurring at 3.715 MeV (level no. 24, fig. 11) indicates, presumably, the occupation of the lg~ orbital. The assignment of a spin and parity of ~+ z to this state is consistent with the gamma-decay results of Rollefson et al. 23). The (d, p) transition strength deduced for this level in the present work is 5.2 as compared to 9.5 reported by Bock et al. 22). No other In = 4 transitions have been observed. 2.6.5. The In = 0 distributions. In the region of excitation energy analysed in the present work, only one level (no. 44) at 4.696 MeV appears to exhibit an angular distribution typical of l n = 0 stripping character. This is in agreement with the results of Bock et al. 22), who report, in addition, six other l n = 0 transitions at excitation energies above 6.0 MeV. The transition strength deduced here for the 4.696 MeV state is 0.12, about 6 ~ of that expected for the 3s~ orbital. In the (p, d) [ref. 26)] and (3He, ~) [ref. 27)] experiments, this state is not reported and thus is consistent with our assignment of a 3s orbital. In the (p, d) experiments of Whitten 26), a strong (S = 1.40) l, = 0 distribution is observed at an excitation energy of 4.41 +0.02 MeV. Bock et al. 27) also observe an l, = 0 distribution from the (3He, e) reaction at an excitation energy of 4.43 MeV and with approximately the same spectroscopic

28

M.N. RAO et al.

strength. Assuming the wave function of this state to be described in terms of a 2s hole in 54Cr, their observed strength can account for about 70 % of the singleparticle prediction 43). In an effort to identify this 2% neutron hole state in the present (d, p) experiment, the region in the vicinity of 4.4 MeV excitation in 53Cr was carefully examined. Unfortunately, at the critical forward angles of 7.5 ° and 15 ° the presence of intense contaminant groups from both oxygen and nitrogen obscured the excitation region of interest. In addition, at the forward angles these groups were recorded close to the edges of adjacent nuclear track plates so that the track counts are uncertain. The nearest candidate in our (d, p) experiment for the state observed in the pick-up 5ZCr(d,p)53Cr

-Ed =7.5MeV

Level No. 24 E x = 5.715

&

~,

MeV

= 4

E J

too

i

i

i

I

90

I

180

~ c.rn. - degrees

Fig. 1 l. Angular distribution o f p r o t o n group no. 24 assigned In = 4 angular m o m e n t u m transfer. The solid curve is the D W B A prediction calculated from parameter set 2 of table 4.

reaction is our level at 4.435 or 4.489 MeV (nos. 37 or 38) excitation. There is also evidence from the proton spectra analyses at larger angles that there are unresolved components (see table 3 and 5) probably of the order of 10-12 keV associated with each of these groups. The angular distributions for each doublet are displayed in fig. 12 with the distribution of the In = 0, 3s transition (no. 44). It is clear that an 1, = 0 assignment for the 2s transition can only be made tentatively from the present (d, p) angular distribution. The deduced 2s strength for each transition is shown in table 5. 2.6.6. Non-stripping and In unassigned distributions. Besides those levels dealt with in the foregoing discussion, 16 additional levels have been observed in the (d, p) reaction below an excitation of 4.5 MeV. The angular distributions of eight of these are displayed in fig. 13. The remaining eight have cross sections less than 0.01 mb/sr. All, as a rule, have a low cross section and may be classified as predominantly due to non-stripping processes. Many of these experimental angular distributions tend to

Cr

NUCLEAR

29

STRUCTURE

be isotropic, while in the case of others, no particular pattern appears prominent. A few of these weak levels have shapes with suggest that the stripping process may, at least in part, be the reaction mechanism; but experimental data which reasonable accuracy at critical angles were not available to permit a more complete analysis. ~'2Cr" ( d , p )

~3Cr -

E d =7.SMeV

Edge of P1ete L_ower Lim:t Count i I

Level No, 37

| Level No. 38

~

E×= 4.435 MeV

Ex = 4.489 MeV

r

,o°L_

b

!

I

'

t t

o

I

I

I

I

I 180

90

I

0

I~

I 90

I

I 180

Level No. 44 Ex = 4.696 MeV jn:O

3". io°

I°-~

I

0

I

I

90

180

go.,,,. ( d e g )

Fig. 12. A n g u l a r distribution o f p r o t o n groups with probable In = 0 a n g u l a r - m o m e n t u m transfer. The solid curve is the D W B A prediction calculated f r o m p a r a m e t e r set 2 of table 4. Either group nos. 37 or 38 may correspond to the In = 0 (d, p) transition identified in n e u t r o n pick-up experiments with 2s character (see text). Level no. 44 m o s t likely corresponds to excitation t h r o u g h a simple stripping process to a 3s state.

It may be of interest to note here that the cross sections of the levels designated with n.s. (non-stripping character) and n.a. (no assignment) in table 5 are from one to two orders of magnitude less than those observed in the excitation of these same states

0

"0

,.Q 0

Jill

z

I i

I

t

i.---o----i

i

Jill

i

i

i

Iiiii

~

i

i

I

Ii

i

i

i

o

~

0

~E Ln

"o ILl

I* I I I

I

I

~ i I I I

I

I

i

I

i

i

Ill

i

i i i

i

i

Ir

t

#,

E

Q. "0

I-

z~ ~'~

0

LIIll

I

I

i'

~

'llttll

t

.%

i

o

Illl

I i

f

I

I

l,lf

i i

i

o

>

z

c~

~

.o Im

~4 I,,,, '_o

, ,

,

a

li,,,~'~,

~'_o

~

Jlfll

~ (..islq uJ ) 'w'~(.~p I..,.0p )

f

I

I

tl"-O'---IIlll

~o

I I

I

I

I

o

Cr NUCLEAR STRUCTURE

31

via the (p, p') reactions. Compare level no. 5 in figs. 5 and 13, for example, and note the comparative yields of other n.s. and n.a. levels in fig. 2. Level nos. 21, 23 and 26 have not been observed in the (d, p) work yet exhibit strong excitation via the (p, p') reactions. In addition: 58 other levels in 53Cr have been measured between 4.7 and 6.7 MeV excitation. No attempt was made to obtain the angular distributions of the proton groups from these levels because of the difficulties encountered particularly at the forward angles in identifying the 53Cr levels in the presence of intense contaminant proton groups. The excitation energies of these levels have been included in table 3.

3. Comparison with other experiment and theory The spectroscopic strengths shown in fig. 14 for the 54Cr(p, d) transitions to the ground state and first two excited states in 53Cr ( j , = ½-, ½- and ~-, respectively) give evidence of appreciable admixture of Pt, P~r and f~ particles in the ground-state configuration of S4Cr. Four additional states (at 2.324, 2.664, 2.715 and 3.625 MeV) are reported in the (p, d) experiment although with much reduced intensities. These also give indication of higher orbital admixture in 54Cr when compared to the strengths of the corresponding excitations in the present (d, p) experiments. Six of the remaining seven states shown in fig. 14 are populated with appreciable strength in the (p, d) experiment and are assumed to arise from excitation of particles in the filled lf~, ld~ and ls~ shells. Each of these levels is also identified in the 52Cr(d, p) reactions but with much less strength. Thus it appears that S2Cr also contains some admixture of lf~, ld~ and 2s~ holes. Of particular interest are the four states at 1.285, 1.537, 3.354 and 3.438 MeV identified by Whitten 26) as having l f t character. He further notes a J-dependence effect in the angular distributions of the deuteron groups corresponding to these levels when compared to the angular distribution of the 1.008 MeV, In = 3, -~- state. In the present (d, p) data, an anomalous behaviour is also suggested at the most forward angles (below 45 °) for our l. = 3 angular distributions. The differential cross section decreases much less rapidly at small angles for the ~- states (fig. 9b) than for the other In = 3 distributions (fig. 9a), assumed ~-, and corresponding to singleparticle levels. In an earlier study of the (d, p) transition to the 1.285 MeV states using 10 MeV incident deuterons, Bock et al. 45) noted a similar anomaly at the forward angles. They interpreted the data to result from a superposition of an In = 1 and In = 3 transition and suggested the population of the state takes place through a two-step process of stripping plus inelastic excitation. The low-lying levels in s 3Cr have been theoretically interpreted as single neutron shell-model states outside a closed f~ neutron shell. Comparison with experimental evidence is made from the (d, p), (p, d) as well as other, single neutron-transfer reactions. According to the theoretical calculations, the 1.285 MeV level has essential-

32

M . N . R A O e t al.

LEVEL

STRUCTURE

OF

53

240r29

5.0 o

3 (5/2)z I

V2+-~ + _

, / - - o.12 0.68

(~/2) ~ - - ~ ' - o .

-

-

"

~--

2 (5/2) + ~ 2 (5/2) + - (I)----~--------(I) /

4.0

2

( 5/2)*-

4

91Z +

I

(7/z-) - (~Z) + - -

o.15 O. 03

(2)

(5/2*)/--x~

O. OI

(3)

(5/2-)

o. 3

- -

I - - ' . (I) I

Z

I/2+

0

(5IS) -J

0.12 ~

0.30 - 1.2

3/2-

I

(7/2-) 712 "

3

3

0.04

-

3I

.7

5.2 0.77

-

2 -

1.40-

(3/;'+)

O. 08 -

(3) ( I)

3.0

O. 18

0.85

0.21 0.54 0.03 ~o.oi

3/Z- - -

(3,1~

17

/-" 0.04 ~ - 0.580Jt

1

0.006 0.96

3/Z-

< 0.01 - <0.08-

I/25/2

< 0 . 0 2 -

3/2-

2.0

1.0

0.0

53Cr

(3)

(7/2-) ~

0.13

3 . 2 -

7/2-

3

(3)

(7/2-)-

0.43

0 . 7 -

7/2-

3

3

5/2-

0.51-

5/2-

3

I

I/~

0.71

0.31 ~

V2-

I

I

3/2-

2.22

0 . 8 3 -

.In

jTr

(2J+I)S

1.50

5ZCr (d,p) 53Cr Stripping

S

3/2jTr

I ,In

54Cr (p,d)53Cr (ref. 26)

Anolysis

Fig. 14. Comparison of level positions in 5~Cr and spectroscopic transition strengths from the present (d, p) experiment with the experimental (p, d) data o f ref. 26).

Cr NUCLEAR STRUCTURE

33

ly the configuration [2 +, p~]~- and, therefore, the transition strength predicted in the neutron stripping reaction is zero. However, this state is observed in both the neutron pick-up and transfer reactions, and in the present (d, p) experiment a strength ( 2 J + 1)S = 0.43 is deduced assuming a If neutron transfer. Whitten 16) and Bock et al. 27) have investigated this discrepancy by examining the collective properties of the low-lying states in 53Cr by using the (p, p') [refs. 26,27)] and (d, d') [ref. 27)] reactions. It has been proposed 46) that excitations of levels in odd-mass nuclei may be described in terms of weak coupling of the odd particle with the collective excitations of the doubly even core. In this weak-coupling model, a quadruplet of states is predicted in 53Cr by the coupling of the p~ neutron to the 2 +, 5ZCr core, thus generating states with J~ = ½-, k - , 3 - and ½-. The inelastic cross sections are proportional to 2Je + 1 and related to the core inelastic cross section through the expression ff(S3Cr)Jf _ a(52Cr)Jc

2Jr+ I (2Jc+ 1)(2j+ 1)

The J~ = ½-, {t- and ~z- states are probably mixed with the p½, p~ and f~ singleparticle states, and it is also likely that the 1.285 MeV ~- state has some f~ neutron hole component even though the excitation of the 1.537 MeV ~- level in the (p, d) experiment 26) is observed to contain the major portion of the lf~ neutron shell component (43 ~ of the shell-model prediction). Assuming that the 1.285 MeV state in s 3Cr is fully described by the weak-coupling model, Whitten 26) and Bock et al. 27) have analysed the inelastic scattering cross sections and compared their results to the predictions of this model. Table 7 presents a summary of this comparison and also incorporates the present results obtained with 7.5 MeV bombarding energies• The data have been normalized so that the 1.285 MeV level is assumed to contain the full strength, 8.0, predicted by the simple weakcoupling model. It is interesting to note that even when the shapes of the inelastic angular distributions of these low-lying levels in 53Cr using 7.5 MeV incident protons (fig. 5) are different from the 17.5 MeV distributions of Whitten 26), the magnitude of the peak (01a b = 35 °) remains practically the same. However, in the case of the 52Cr(p, p') excitation of the 1.433 MeV 2 + state, the differential cross section at 0 -- 35 ° is 5.1 mb/sr at 17.5 MeV, while it is 17.0 mb/sr with 7.5 MeV incident protons. The difference in shape for the 53Cr(p ' p,) angular distributions can be accounted for by the fact that at lower bombarding energies the compound-nucleus contributions are larger, and the difference in strength observed at the two energies for the 5ZCr(p, p') first excited 2 + state indicates that compound-nucleus contributions are more important in 52Cr than in S3Cr at 7.5 MeV proton energy. This is consistent with the fact that the (p, n) threshold is 5.491 MeV for 52Cr and only 1.380 MeV for 53Cr and, therefore, at 7.5 MeV proton energy compound-nucleus effects are more relevant in 52Cr [ref. a a)].

M.N. RAOet al.

34

Bock et al. 27) report that at 10.0 a n d 12.0 MeV the ratio of the inelastic d e u t e r o n cross sections for the 1.285 MeV ~ - state in 53Cr to the 1.433 M e V 2 + state in SZCr is 0.41 ___0.04 as c o m p a r e d to the value 0.4 o b t a i n e d f r o m the weak-coupling predictions using the above formula. The present deuteron inelastic results o b t a i n e d at 7.5 MeV indicate a ratio of 0.69_+0.1 for the same transitions. The relative yields from our 7.5 MeV data are indicated in table 7, a n d the results are seen to be in agreem e n t with those reported by Bock et al. 27). TABLE 7 Proton and deuteron inelastic scattering cross sections to low-lying states in ssCr compared to the weak-coupling model predictions and normalized to 8.0 for the 1.285 MeV transition

Weak-coupling model ~3Cr(p, p') ref. ~6) Ep = 17.5 MeV c) ref. zT) Ep = 11.0 MeV this work Ep = 7.5 MeV a) ~3Cr(d, d') ref. 27) Ea = 12.0 MeV ref. zT) Ea = 11.0 MeV ref. 37) Ea = 10.0 MeV ref. 27) Ea = 9.0 MeV ref. ~) Ea = 8.0 MeV ref. z~) Ea = 7.0 MeV this work Ea = 7.5 MeV d)

Ex (MeV) (jn) 1.285({-) 1.537(5-) a)

0.565 (]-)

1.008(~-)

2.0

6.0

8.0

4.0 b)

4.4 3.5 5.3

3.1 3.4 3.9

8.0 8.0 8.0

2.1 2.4 3.5

3.4 3.4 3.8 4.9 4.6 6.4 4.6

2.4 2.5 2.7 2.7 3.2 2.6 2.9

8.0 8.0 8.0 8.0 8.0 8.0 8.0

1.5

1.971(?)

1.7 1.2 1.0 weak

0.35

0.87

a) Mainly shell-model f] neutron hole state. b) The spin of this level is not known; the value of 4.0 applies if this level is assumed to be the missing 3- component of the multiplet. c) a(O)ma~measurements at 0 = 35°. d) tr(0) measurements at 0 = 37.5°. F r o m all these results, it is clear that the low-lying states in 5 3Cr c a n n o t be simply described, a n d that a n exact form of their wave functions should c o n t a i n c o n t r i b u t i o n s of single-particle shell-model states as indicated by the n e u t r o n - t r a n s f e r experiments as well as of collective properties indicated by the inelastic scattering data. T h a n k a p p a n a n d True 47) have performed a theoretical calculation using the coreto-particle coupling model of de-Shalit 46) a n d i n c o r p o r a t e d b o t h the collective a n d single-particle properties to describe the low-lying states in 63Cu, where the odd particle is the 29th p r o t o n outside the lf÷ shell. These calculations have been fairly successful in predicting the energy levels a n d single-particle admixtures of the g r o u n d state a n d several low-lying states in 6,3Cu. m similar calculation where the odd particle is the 29th n e u t r o n outside the lf~ shell would be of interest here for the N = 29 nuclei.

35

Cr NUCLEAR STRUCTURE

The energy levels of nuclei with 20 < Z < 28, N = 29 (viz., 51Ti, 53Cr and 55Fe) and the spectroscopic factors for the (d, p) reactions exciting these nuclei have been extensively calculated by coupling the 29th neutron in the vp~, vp~ and vf~ orbits 25~Cr LEVEL SCHEME 5.0

--

3 I

( 5/2)--x

/--0.68 ~0.18

~

5/Z " ~

0.89

V2 - -

(I) 4.0

--

.-"-0.03

(I)

" - - ' ~ ' - - -

3/2-

I

0.77 V2"

(7/2-)

~

--

0.04

(3)

I

(5/2-)

~

I

3

-

,/---0.04

\

3/2-

2.0

1.0

0.05 o. 63

5/2 - - 3/2 - - V2 ~ - -

0.12

5/2-

0.09

0.10 0.21

0.27

5/2-

t/2-

I.,39

-

-

0.33

k---0.58

-

-

3/2 - -

-

-

-

I/2

-

O.

5/2

-

-

0.006

5/2-

-

-

1.22

0.96

3/23/2 -

-

-

0.89 O. 0 5

3/2

"

-

5/2-

-

-

o.

17

5/2

-

-

7/2-

-

-

0.0

-

66

0.23 1.54

-

-

0.51

13.0.

(3)

(7/2-)

(3)

(7/2-)

3

5/2-

-

-

I

V2-

I

3/2-

.In

jrr

o. 59

7/2 - -

-

0.0

5/2 - -

-

1.76

0.4:5

-

-

1.50

- -

-

-

-

-

1.66

V2

0.71 I/:,-

-

-

0.55

2,22

3/2-

-

-

2.22

(2j+I)S

dTr

52 CF (d ,p) 5 3 C r F i g . 15. C o m p a r i s o n

-

0.13

5/2-

0.0

~

0.11

(5/2) ---/

I

- ~

0.20

0.13

-

(I)

LE

5/2

~

o.15

(I) 3.0

-

O. Ol

(5,0 (3)

3/2

-

Ramovotarom

- - -

3/2 - -

-

0.88

3.06

d~

Vervier

o f t h e la = 1 a n d 3 t r a n s i t i o n s i n 5aCr w i t h t h e o r e t i c a l c a l c u l a t i o n s p r e d i c t i n g t h e p o s i t i o n s a n d s t r e n g t h s o f t h e o d d - p a r i t y levels.

36

M.N. RAOet

al.

to the even-parity levels of the core. Core states of both vibrational 48) and (nfk)" [refs. 49,5 o)] configurations have been considered. Fig. 15 presents a comparison of the experimentally observed l, = 1 and ln = 3 transitions for the 52Cr(d, p)S 3Cr reaction and the extracted spectroscopic strengths with the calculations of R a m a v a t a r a m 48) and Vervier 50). Only the In = 1 and l n = 3 levels in 53Cr are shown, since neither of the calculations attempts to reproduce the even-parity levels. The spectroscopic strengths of ref. 48) have been normalized to 2.22 for the ground-state transition to agree with the value reported in the present work. As may be clearly seen from the figure, the observed low-lying excitation energies and the fragmentation of the vp~, vp~ and vf~ strengths within these levels in the (d, p) reactions are qualitatively reproduced by the calculations irrespective of the nature of the core states considered. Several discrepancies still exist for the energies and the spectroscopic factors, especially above about 2.0 MeV. The calculations of Vervier s o) have neglected admixtures of configurations involving excitations of the 4SCa core (vf~ hole states) on the assumption that their influence can be absorbed in the effective nucleon-nucleon interactions adopted in the model. Experimentally, however, the In = (3) levels at 1.285 (~-), 1.537 ( k - ) and possibly the levels at 3.354 and 3.438 (fig. 9b) display the influence of such neutron hole-state configurations. More complete calculations including the effects of other configurations neglected in current models especially in the lf~, ld~ and 2s~ neutron hole admixtures may reproduce the experimental data better particularly in the higher-energy parts of the observed level spectra. The authors are indebted to Professor W. W. Buechner for his interest and guidance in these experiments and to Professors H. A. Enge and W. M. Moore for their assistance and helpful discussions in connection with the use of the magnetic quadrupole lens and the (p, p'v) coincidence measurements. We also owe special thanks to Mr. H. Y. Chen for carrying out the D W B A calculations, to Mr. E. Chalbaud for assistance with the (p, p ' ) data reduction, to Mr. A. Luongo for his expert preparation of the target films and to the staff of the plate scanning group for their careful scanning of the nuclear emulsions. Finally, we wish to express our appreciation to Miss Shirley Svenson for her patient and competent preparation of the manuscript. References 1) M. Deutsch and L. G. Eliot, Phys. Rev. 65 (1944) 211 2) H. J. Hausman, A. J. Allen, J. S. Arthur, R. S. Bender and C. J. McDole, Phys. Rev. 88 (1952) 1296 3) B. B. Kinsey and G. A. Bartholomew, Phys. Rev. 89 (1953) 375 4) M. Mazari, W. W. Buechner and A. Sperduto, Phys. Rev. 107 (1957) 1383 5) M. Mazari, W. W. Buechner and A. Sperduto, Phys. Rev. 112 (1958) 1691 6) Nuclear Level Schemes, A = 40, A ~ 92, compiled by Way, King, McGinnis and Van Lieshout, Atomic Energy Commission Report TID-5300 (1955)

Cr NUCLEAR STRUCTURE

37

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