A study of the 54Cr(d, p)55Cr and 53Cr(t, p)55Cr reactions

Nuclear Physics A198 (1972) 237--256; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

A S T U D Y O F T H E S4Cr(d, p)SSCr A N D SaCr(t~ p)SSCr R E A C T I O N S A. E. MACGREGOR t and G. BROWN University of Bradford, Bradford BD7 1DP Received 9 June 1972 (Revised 27 September 1972) Abstract: Differential cross sections have been measured for (d, p) and (t, p) reactions leading to levels of s 5Cr" Some spin assignments have been made using thevaluesofthe angular momentum transfer obtained from the angular distributions for both reactions; spin assignments for levels observed by l. = 1 and In = 3 transitions in the (d, p) reaction have been made using empirical J-dependence. One level of J = ½-, possible two, has been located and it is suggested that it has been observed in the (d, p) reaction as a result of higher-order processes and not via particle-hole admixtures in the wave function of the target nucleus. It is shown that substantial admixtures of 2p.t. and If.I. neutron pairs exist in the 54Cr ground state wave function and that these data are compatible with that of the (p, d) reaction. The level structure of 55Cr is discussed and shown to be similar to that of 59Ni. NUCLEAR REACTIONS 54Cr(d,p)S~Cr, Ed = 8, 10 MeV; 5aCr(t,t)sacr and 5aCr(t' p)55Cr ' Et = 12 MeV; measured cr(0); deduced triton optical model parameters. SSCr deduced levels J, z~, S. Enriched targets.

1. Introduction L i m i t e d i n f o r m a t i o n is available o n the structure o f the 55Cr nucleus. T h e (d, p ) r e a c t i o n has been used to m e a s u r e level positions by Bjerregaard et al. 1), a n d o u r selves 2), a n d to o b t a i n spectroscopic i n f o r m a t i o n by B o c k et al. 3) a n d R o s a l k y et al. 4). N o theoretical calculations are available for 55 Cr; calculations have only been m a d e for the simpler nuclei which c o n t a i n only one or two particles, o r holes, in a nucleon shell. W h i l s t these calculations are generally successful in p r e d i c t i n g the p o s i t i o n s o f energy levels, they are n o t always successful in predicting the t r a n s i t i o n strengths of stripping a n d p i c k - u p reactions. Refinements to the simple calculations which increase the configuration space a n d include core-excitation a n d particle-hole c o m p o n e n t s i m p r o v e , as might be expected, the a g r e e m e n t with experiment, e.g. the calculations for 51Ti b y D i v a d e e n u m a n d Beres 5). It is difficult, however, to decide h o w g o o d the a g r e e m e n t is, since discrepancies m a y be due to deficiencies in the calculated wave functions o r in the u n d e r s t a n d i n g o f the n a t u r e o f r e a c t i o n mechanisms. O f significance in this c o n t e x t is the c o m p a r i s o n o f e x p e r i m e n t a l a n d theoretical d a t a for a lowlying level o f J = 3 - o b s e r v e d in the N = 29 nuclei. Theoretical calculations 5.6) * Present address: Newcastle upon Tyne Polytechnic. 237

238

A.E. MACGREGOR

A N D G. B R O W N

predict that the wave functions of these levels are primarily based upon core excitation and this is supported by experimental data from proton inelastic scattering from 53Cr [ref. 7)]. Angular distributions for the (d, p) reaction to these levels in 51Ti [ref. 8)] and 53Cr [ref. 3)] show stripping patterns associated with In = 3 transitions but these cannot be accounted for by stripping via particle-hole components of the wave function of the target nucleus 8). Such observations suggest that higher-order (d, p) processes may be responsible for transitions to levels based on core excitation and that some discrepancies between experimental and theoretical spectroscopic factors may be due in part to this effect. Additional information on the importance of these processes and thus the importance of core-excitation components of nuclear wave functions is desirable. This information is most readily obtained from measurements of the transition strengths of the (d, p) reaction to levels which cannot contain single-particle components accessible by this reaction. Since it might be anticipated that the 54Cr wave function should not contain lf~ neutron holes and since a J = ½level based on core components is known to exist in the neighbouring 53Cr nucleus, we consider that it is desirable to locate 3 - levels in 55Cr and measure the transition strength of these in the 54Cr(d, p) reaction. To provide experimental data on the structure of 55Cr we have studied the (d, p) and (t, p) reactions leading to this nucleus for incident energies of i0 and 12 MeV respectively. These experiments form a part of a systematic survey of these reactions for nuclei with A ~ 50 and A ~ 90. So that comparisons of the spectroscopic information deduced for different nuclei are facilitated, the same experimental techniques have been used consistently and a high accuracy of relative measurements has been sought. Some experimental information for calcium and chromium nuclei have been used 9) to compare summed spectroscopic factors with the sum-rule limits. In this paper spin assignments and detailed information on the level scheme of 55Cr are presented.

2. Experimental procedure The experiments were performed using the Aldermaston multigap spectrograph so that relative differential cross sections for the angular range 0 L = 5 ° to 0 L = 175 ° were obtained simultaneously. The targets used were nominally 100/~g" c m - 2 thick on a carbon film approximately 10 pg • cm -1 thick and were made in the manner described previously z). A mass analysis of the samples used for target preparation is given in table 1. The relative differential cross sections for the (d, p) and (t, p) reactions were obtained from separate single exposures in the multigap using incident energies of 10.0 and 12.0 MeV respectively. A typical spectrum is shown in fig. 1. Relative differential cross sections for levels observed in the (d, p) reaction at Ed = 10 MeV have been obtained up to an excitation energy of 5 MeV. So that the spins of levels observed by In = 3 transitions could be obtained from the J-dependence

54Cr(d, p) AND SaCr(t, o) REACTIONS

239

o f the angular distributions 1o), a separate experiment was performed to obtain these angular distributions at Ea = 8 MeV. All measurements indicate that the level density of 55Cr is rather high for excitation energies above 3 MeV. Since the energy resolution and accuracy of energy measurement for the (t, p) reaction was not sufficient to allow detailed comparisons with the data of the (d, p) reaction, analysis of this reaction above an excitation energy of 3 MeV has been restricted to the location of L = 0 transitions. TABLE 1 Percentage isotopic composition of the samples used for preparation of targets Mass

Target

50 52 53 54

SaCr

54Cr

0.3 14.8 83.5 1.4

0.06 1.43 0.59 97.98

160

xk E E

120

9

11 5¢Cr

23

i00

-I,,,4' 80

'Cr

(/) ¢.)

60

N' p,..

~0

6

.,¢ 2O

l

3

I 0.5

J~

, A 1.0

i' 1.5

2.0

I 2'5

3"0

EXCITATION ENERGY (MeV] Fig. 1. Typical spectrum for the 5aCr(t, p)SSCr reaction. The method employed to obtain absolute (d, p) cross sections has been described previously 9). First the relative differential cross sections for elastic deuteron scattering, for 0L = 35 ° to 0 L = 175 °, and those for some strong levels of the (d, p) reaction, for 0 L < 35 °, were obtained using the Aldermaston multigap spectrograph by placing two exposures of 50 pC and 500 pC on one set of plates with slightly different magnetic field settings. The absolute cross sections for deuteron elastic scattering were measured using position sensitive detectors in the Harwell single-channel spectrograph. Suitable normalizations gave absolute values of the (d, d) and (d, p) cross sections over the full angular range 9). The differential cross sections of the (t, p) reaction have been linked, in the manner described above, to those for the (t, t) reaction in the range 0L = 35 ° to 0L = 175 °. It has not been possible however to measure absolute cross sections for the (t, t) reaction and as a result it has been necessary to

240

A.E. MACGREGOR

A N D G. B R O W N

establish an absolute scale from an optical-model analysis which will be described later. The accuracy of the relative cross sections of the (d, p) reaction is 5 ~o for cross sections > 0.15 m b . sr - t and 10 ~o for values ~ 0.04 m b . sr-1; for the (t, p) reaction it is 5 ~ for values > 0.04 m b - s r -~ and 107/o for values of 0.01 m b . s r - l ; a suitable interpolation can be made for other cross sections. The accuracy of absolute 1.0-

cr o-R

0.1

t

:I

I

I

t

0,01

,

30

60

9'0

,

120

'

150

180

Oc.M..(deg.) Fig. 2. Relative differential cross sections for triton elastic scattering by 53Cr. TABLE 2 Triton parameters deduced from the optical-model fit to elastic scattering and other parameters used in D W B A calculations

triton proton neutron

deuteron b) proton neutron

V(MeV)

ro (fin)

a (fm)

W (MeV)

151 50.0

1.24 1.25 1.25

(t, p) calculations 0.66 21.5 0.65 13.3 0.65

85.5 50.0 a)

1.175 1.25 1.20

(d, p) calculations 0.821 0.65 0.65

2) Adjusted to give a binding energy o f Q + 2 . 2 6 MeV. b) Ref. 9).

W" (MeV)

17.84 13.3

r'o (fro)

a" (fm)

1.47 1.25

0.79 0.47

1.366 1.25

0.688 0.47

S4Cr(d, p) AND 5aCr(t, p) REACTIONS

241

cross sections is believed to be generally _ 10 % for the (d, p) r e a c t i o n 9) a n d ___20 % for the (t, p ) r e a c t i o n (subsect. 3.1). I

]

i

i

'

j

f[

b,

0,000

/~

0,21,5

0.573

t

0.1

t

f t

l.O B't

M0 t ! (t,

~Lr

C] ILl

2 \I-4~


2'905

V

,\

,

]

1.487

>

\

f

'

t

¢ ~.o ?~'l

a.212

Z I.C

~"

4 059

~t\t

\,\

2

/.-181

'~

/,'881

\ •

I

I

I

90

I

I

I

I

I go ,

, ecM

t

,

9'0

'

'

I

l l ~ , , I

[degrees)

Fig. 3. Angular distributions for l. ~ 1 transitions of the ~4Cr(d, p)SSCr reaction at Ed = 10 MeV. 3.

Results

3.1. T H E 53Cr(t, t)53Cr R E A C T I O N A N D T H E D E T E R M I N A T I O N O F A B S O L U T E V A L U E S O F T H E (t, t) A N D (t, p) CROSS SECTIONS

Relative differential cross sections for elastic scattering o f tritons in the angular range 0L = 35 ° to 0 L = 87.5 ° a n d 0 L = 7 2 . 5 ° to 0L = 175 ° were o b t a i n e d f r o m the

242

A . E . MACGREGOR A N D G. BROWN

exposures o f 50 ILC and 500/zC respectively, together with relative cross sections for the (t, p) reaction to the g r o u n d state and 2.098 MeV level o f 55Cr at 0c = 5 ° and 12.5 ° f r o m the 500/~C exposure. By normalizing the two sets o f elastic scattering measurements at angles Of0L = 72.5 °, 80 ° and 87.5 ° all data were placed on the same relative scale. By normalizing these (t, p) data to the appropriate measurements from the main (t, p) experiment all data for the (t, p) reaction were also placed on a relative scale.

/~\ 2.03~

1,0

I

/\

/•

2.283

/'

2.87~

o

\

0,1 !

i

i

e

i

i

J

A

i

f

i

I

,

,

/t~ 3.95~

,\ ~

0'!

!

/,'399

1.0

-3

it/°l~t

4

0"1

J

J

i 90

f

!

I g~O

90

'

ec,

/." 867

2.

t

I

90

(degrees)

Fig. 4. Angular distributions for I. = 0,2 and 4 transitions of the 54Cr(d, p)SSCr reactions at E a ~ 10 MeV. Optical-model parameters were derived from the triton elastic scattering distributions for 0 r < 139 ° using volume absorption and a real well radius o f r o = 1.24 fm; the absolute normalization o f the data was allowed to vary to give the best fit. The fit to the experimental data is shown in fig. 2 and the optical-model parameters given in table 2. The choice o f volume term for the imaginary potential and a radius parameter o f 1.24 fm for the real well, were made on the basis that these gave acceptable fits to data for m a n y nuclei o f different mass ~1). Only data out to angles o f 0 L < 139 ° was

S4Cr(d, p) A N D S3Cr(t, p) R E A C T I O N S

243

used since it has been observed 9) that, for the (d, d) reaction, the use of data at larger angles produced anomalies in the optical-model parameters for different nuclei. The absolute cross-sections obtained for elastic triton scattering from the optical-model fitting were then used to calculate absolute cross sections for the (t, p) reaction. The same procedure has been used for the (d, d) and (d, p) reactions and found 9, t ~) to give cross sections within 7 ~ of the measured values for 16 nuclei near A ~ 50 or A ~ 90. Thus it seems probable that the systematic error in measurement of (t, p) cross sections will not be greater than 15 ~o. 1.0

0'52~

j'\

0'893

1'229

2'570

,'

\'~i,

uJ ffl ~

-J

v \ ,0 ,

,

0.1

t o

n

z

J

i

I

i

•

I

2,622

t,(t't~,t

,

A

. . . .

It

I

3.168

t,.78/,

90

90

Z, Ft {.tt

0'1

t

t

9'o

n

t

I

I

90

GeM ( d e g r e e s )

Fig. 5. Angular distributions for In = 3 transitions o f th.e 54Cr(d, p)SSCr reaction at Ea = 10 MeV.

3.2. T H E S~Cr(d, p)SSCr R E A C T I O N

The experimental angular distributions for this reaction are compared in figs. 3-6 with those predicted by DWBA calculations; to facilitate the comparison the angular distributions have been normalized to unity at the first maximum. The theoretical angular distributions were obtained with zero-range local calculations without spinorbit terms and using the parameters of table 2. The values of angular momentum transfer, maximum differential cross section and spectroscopic factor are compared in table 3 with the data of Bocket al. 3), Rosalky et al. 4) and the experimental data for the S3Cr(t, p)55Cr reaction. Spectroscopic factors were obtained from the present data using a normalization constant of 1.5. The data reported here were obtained using a more highly enriched target than that previously used 2) and there are some differences in level assignments. The levels previously reported 2) at 0.920 MeV and 1.418 MeV have not been observed in the present work and are thought therefore to have been due to the 52Cr impurity in the target

244

A.E. MACGREGOR AND G. BROWN

'°/f

°L°°o°~°v] ,o A

o2,~ev

'~

A

os2,~ov1

MeV L=o.2

~

l0

0-573

5

•

5

~-

"

oq

c

t

"/I

I

,

o

0'

io

5

1 1 $

o.

i

,o.

oo.

÷ $

°~ * ' ~'o.' "o:'

'

'o.'

' ~o.'

' ~'o.'

'

o.

~o.

°o.'

'

O (c.m.) Fig. 6. Angular distributions for transitions of the SSCr(t, p)SSCr reaction at Et = 12 MeV.

used previously. However new levels at 2.355, 2.723, 2.895, 3.009, 3.714 and 3.810 MeV have been observed in the present experiment. It can be seen from table 3 that our measurements of cross sections are generally in good agreement with those of Bock et al. 3) but that there are a few discrepancies. The difference in the spectro-

54Cr(d, p) AND S3Cr(t, p) REACTIONS

245

scopic factors derived by Rosalky et al. 4) and ourselves is due to the use in the former work of cross sections at angles away from the main stripping peak and the use of m a x i m u m differential cross sections and a normalization constant of 1.5 in the present work. The levels to which In = 1 assignments have been made are shown in fig. 3. As a result of the rather low Q-value for the (d, p) reaction (4.033 MeV), these distributions become rather structureless at high excitation energies and it becomes necessary to rely on D W B A predictions for these assignments. We have assigned several more levels with In = 1 than either Bock et aL 3) or Rosalky et al. 4) and differ from the former work in preferring the assignment of I, = 1 rather than 1, = 2 for the level at 4.881 MeV. We consider our assignment to the 3.714 MeV level as particularly tentative since it can be equally well fitted by either In = 1 or 2. Some difficulty was experienced in resolving the 2.710 MeV level from the nearby states and as a result the data are considered accurate to only 20 ~o. The difficulty in resolving the 2.905 MeV level from the 2.895 MeV level was equally severe but this is not important since the latter level contributes less than 10 Y/ooto the observed cross section. The levels for which In = 0, 2, 4 and In = 3 assignments have been made are shown in figs. 4 and 5. All of the levels for which In = 2 is assigned exhibit a first maximum at slightly smaller angles than is predicted by the D W B A calculations for which it was assumed that the neutron is captured into the 2d orbitals. In contrast to Bock et al. 3) we obtain a satisfactory fit with ln = 2 rather than with l n = 3 for the 4.162 MeV level. The angular distributions calculated for In = 3 transitions give a p o o r fit to the experimental data for the 1.229 MeV level away from the main stripping peak and a particularly bad fit everywhere for the 2.570 MeV level; thus an In = 4 distribution is also shown for the latter level. However the observation o f L = 2 in the (t, p) reaction to a level at 2.570__+0.015 MeV precludes any assignment other than In = 3 unless there is a closely spaced doublet at this energy. Only one In = 4 and four 1, = 0 assignments have been made (fig. 4); for the calculation of spectroscopic factors for the latter transitions capture into the 3s~r orbital was assumed. There are many levels for which it has not been possible to assign a value of the angular m o m e n t u m transfer. For weak levels this may be due to reaction mechanisms other than simple stripping. However there are many levels with a maximum differential cross section greater than 0.1 mb • s r - ~ for which a stripping pattern would be expected. Since most of these occur at an excitation energy of approximately 3 MeV where the level spacing is observed to be only 55 keV, the probable explanation of the difficulties experienced is likely to be the presence of unresolved levels. 3.3. THE 53Cr(t, p)SSCr REACTION The angular distributions for levels below an excitation energy of 3.33 MeV are shown in fig. 6; the angular m o m e n t u m transfers and maximum cross sections are given in table 3. In general L-values have been obtained by comparing the shapes of the experimental distributions with those obtained from D W calculations. The cal-

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Level no.

2.341 2.355 2.570 2.622 2.695 2.710 2.723 2.874 2.88 2.895 2.905 3.009 3.043 3.114 3.168 3,196

0.000 0.245 0.524 0.573 0.893 1.229 1.447 1.487 2.031 2.098

& (MeV)

0.04 (0.04 ~:0.03) 0.08 0.87+(0.01)

4 (0~ 2)

1.00

0.13 0.04+0.04 (0.03+)0.01 0.14

0.08 0.06 0.08 0.06

0

2 (0+2) 1+4 0

2

4

2 3

o~+(3)

1.21 0.16 O. 16 + (0.02) 0.06+0.07 0.04

0 2 2+(4) O+2 2

L

s 3Cr(t ' p) 5 SCr

TABLE 3

~-

(,~)-

(3)-

6.89 4.14 1.37 5.6 0.15 0.07 0.22 0.28 0.06 0.65 0.3 0.1

14.1 2.09 0.7 2.9 0.37 0.13

0.66

0.03

0.39

0.01

0.07

0.30 0.37

0.92 0.87 5.82 0.09 0.02

2.35 0.34 1.38 0.45 0.67 0.23

present data

< 0.4 4.0 0.16 1 0.34 0.05 3 0.57 0.04 1

2

1

~(~, .~)+

3 3

1 2 4 0 1

1 I 3 1 3 3

•~.~- + ( ~ ) -

~(~)+ ~+ + , ~ ½+ ~-

~-~(~)-

-

Present data

Experimental data for the levels o f SSCr

3

1

1

I

3 3

1 2 4 0

1 1 3 1 3 3

0.8

0.41

5.5

1.3

0.42

7.5 5.0 1.3 8.0

12.0 2.5 0.8 3.1 0.55 0.18

0.8

0.04

0.43

0.1

0.4 0.48

0.97 1.35 6.7 0.23

2.06 0.39 1.40 0.47 0.94 0.29

Bock et al. a)

54Cr(d ' p) s 5Cr

I

1

I

1

1

1 1

0.04

0.37

0.10

0.61

0.35

1.86 0.22

(~)-

(½)-

(½)-

½-

]-

:~-

R o s a l k y et aL 4~

Z

O

> Z ~7

O

.~

to

27 28 29 3O 31 32 33 34 35 36 37 38 39 4O 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.212 3.312 3.371 3.534 3.574 3.650 3.714 3.800 3.810 3.847 3.871 3.902 3.955 4.001 4.046 4.059 4.162 4.181 4.276 4.399 4.433 4.479 4.517 4.545 4.571 4.631 4.646 4.677 4.734 4.753 4.784 4.807 4.867 4.881 2 2

(L D + (L D +

0 2

(½)-

(~, D +

0 (3) 2 1

(D(3, 3) + (½)-

½+

½+

(L D +

(½)-

0 (1) 2 1

½+

(1)

1 (I)

1

(½)-

(½)-

(½)-

(½)-

0.9 1.46

(0.09)

0.55 0.15 1.41 0.41

(0.08)

0.16 0.23 0.42 0.18 0.04 0.10 0.12 0.07 0.07 0.78 0.35 0.08 0.17 0.07 0.85 0.73 1.78 0.73 0.04 5.7 0.3 0.33 0.05 0.2 0.15 (0.17)

0.10 0.08

0.03 0.25

0.12 0.04

0.02 0.06 0.24 0.05

0.02

0.06

0.01

0.04 0.02

0.02

2 2

0 2

2

0 2 l

3

2

1

0.09 0.2

2.5 0.7

0.O9

7.0 0.4 0.6

3.0

0.2

0.2

0.14 0.3

0.13 0.11

0.14

0.33 0.67 0.05

0.47

0.04

0.02

I

0.02

(½)-

t~

z

>

>. Z

248

A.E. MACGREGOR AND G. BROWN

culations were performed using a two-nucleon calculation written mainly by Yates and based on the theory of Rook and Mitra 25); the parameters used were those given in table 2. Difficulty is experienced in obtaining a good fit to the data for the 1.447 and 2.905 MeV levels but the experimental angular distributions are closely similar to those o f L = 4 transitions observed in the 52Cr(t, p)54Cr reaction ~2) and as a result this assignment is favoured. For the level at 0.524 MeV an L = 2 assignment does not produce a good fit and it appears that the data points near 0 = 45 ° suggest the presence of an L = 4 component. There is evidence of either an L = 2 or L = 3 component in addition to an L = 0 component for the 2.098 MeV level; L = 3 is preferred since this is compatible with the observation via the (d, p) reaction of a level with J = -~+ at this excitation energy. The angular distribution for the 2.695 MeV level indicates the presence of an L = 4 transition in addition to at least one another (possibly L = 1). Difficulty was experienced in deciding whether the angular distribution for the level at 2.905 MeV had an L = 0 component since the Q-value for this level is within 10 keV of that of a level of 54Cr for which an L = 0 transition has been observed. The original analysis of the present data showed that after correction for the 54Cr level, an L = 0 component remained. However further comparisons of transition strengths of 5aCr levels observed in the present work with published data x2) indicated that this correction was not very reliable and as a result we cannot be sure of the presence of an L = 0 component in the transition to the 2.905 MeV level. It can be seen from fig. 6 that in general good fits to the experimental data can he obtained but that evidence is obtained of mixed L-values to some levels. Since the ground state spin of 53Cr is ~ - the seIection rule for the (t, p) reaction, viz.:

J,+ L >=Jr >=,It-L, (where t and f refer to the target and final nucleus) permit mixed L-values to a level of a given spin. Thus the observation of such mixtures may not indicate the presence of closely spaced doublets. Below an excitation energy of 2.05 MeV these L-values and the/-value of the (d, p) reaction are consistent with the excitation of a single level (table 3). Above this energy the angular momentum assignments from the (t, p) and (d, p) reaction are not compatible with the excitation of a single level and evidence for unresolved doublets is obtained. This makes it particularly difficult to identify corresponding states in the (t, p) and (d, p) reaction and in view of this and the difficulty in allowing for levels arising from 52Cr impurity in the target we have confined the analysis of data to levels at an excitation energy greater than 3 MeV to only the location of L ~ 0 transitions. The latter, which are not listed in table 3, have been observed at excitation energies of 3.53 MeV, 3,57 MeV and 4.16±0.02 MeV with differential cross sections at 0 L = 5 ° of 0.08, 0.13 and 0.21 mb" sr -~ respectively. In view of the high level density indicated for ~5Cr by data from both reactions, it is unlikely that these L = 0 transitions of the (t, p) reaction correspond with ln = 1 transitions of the (d, p) reaction.

5*Cr(d, p) AND ~aCr(t, p) REACTIONS

249

3.4. SPIN ASSIGNMENTS TO THE LEVELS OF 5SCr Since the (t, p) and (d, p) reactions excite different final state configurations, some caution must be exercised in concluding that an L = 0 transition of the (t, p) reaction and an In = 1 transition of the (d, p) reaction proceed to the same level. Additional information, from for example the J-dependence of the angular distributions of the (d, p) reaction, can be useful in showing when the same level is excited in the two reactions. Since the strength of the 2p~ and 2p~r single-particle level is split over many levels of 55Cr ' the J-dependence criteria of Lee and Schiffer 13) which can be used reliably only when S > 0.1 is of limited use in spin assignments. The deep minimum at 0L m 145 ° in the angular distributions for the levels at 0.245 and 1.487 MeV (fig. 3) strongly suggests J = ½-; the absence of this minimum for the ground state transition gives the expected J = ~2- assignment. However it has been predicted theoretically 14) and observed experimentally 4,15, ~6) that more structure exists in the angular distributions for In = 1 transitions to J = ½- levels than to J = ~z- levels and that in particular the minima at forward angles are deeper for the J = ½- levels. Thus it is possible to examine data at forward angles to obtain spin assignments, though the levels selected for comparison must be at similar excitation energy so that the small effect observed is not obscured by the Q-dependence of the angular distributions. It can be seen from fig. 2 that the minima at 0 g 40 ° and 0 ~ 80 ° are deeper in the angular distribution to the level at 0.245 MeV than they are for the ground state and the level at 0.573 MeV. This suggests J = ½- for the 0.245 MeV level and J = k - for the other levels. They are also deeper for the 1.487 MeV level than for the 2.341, 2.710 and 2.905 MeV levels, suggesting J = 1- for the former level and J = ~- for the latter levels. These observations show that the (t, p) and (d, p) reactions lead to consistent spin assignments for the ground state and 0.245, 0.573, 2.341 and 2.710 MeV levels; thus it is considered that the same state is being excited by the two reactions. An assignment of J = ½- is preferred for the level at 2.905 MeV from the similarity of the angular distributions to this level and that at 2.710 MeV; thus the suspicion of an L = 0 transition of the (t, p) reaction to this level, which we have not been able to justify fully, may be correct. The assignment of the angular momentum transfer for the (t, p) reaction to levels observed via In = 3 transitions of the (d, p) reaction does not permit differentiation between J = ½- or J = ~-, since an L = 2 transition is permitted to levels of each spin. In order to obtain spin assignments for these levels we have compared angular distributions of the In = 3 transitions at incident energies of 8 and 10 MeV and used the empirical criterion for the J-dependence of these distributions at forward angles [ref. 1o)]. It has been shown i 0) that for lf2p shell nuclei significant differences exist in the angular distribution at 0 < 80 ° for levels of J = ½- and J = 3 - and that the height of the second maximum relative to the first maximum is 0.33 at both energies for J = ~ - levels, but has the values of 0.33 and 0.23 at E~ = 8 MeV and 10 MeV respectively for J = ~- levels.

250

A. E. M A C G R E G O R 1

1

I

o° ~ ' ~

06

i

i

I

I

i

i

i

i

J

i

J

i

i

o.~

%

o"414!

I

i

A N D G. B R O W N

i "tl,--,-<~

/

0'2 ~-

~, "i,

/

\

,4

"'.~.~.,-t,

\,

~p'j

+,+ + '

~Lt

O Lt.I t,0 0.4I f ' J ,< E 0Z

'~",

m

\

i, .~

~t~

r X;,%~,

..... -~+

,~i, j."~" '~,,r ~ "~-*'",~

\{

•

3

I

d [ r*/

k \

.L

L ~t'("i'i,

0-4 t L

~"~-..% ~

0"2

'~

*k

,~.¥i

\'t, 0-6 0.4

t'J"'(;4

%<

EI=SMeV I

,

40

I

8'0

1

EI=IOMeV i

120

,

I

I

160 4 eC.M.(degrees)

80

10

10

Fig. 7. A c o m p a r i s o n o f the a n g u l a r distributions o f l, = 3 transitions o f the 5*Cr(d, p)55Cr reaction at Ed -- 8 a n d 10 MeV.

TABLE 4 Ratio o f cross sections at the second m a x i m u m relative to that at the first m a x i m u m , for 1. = 3 transitions o f the (d, p) reaction Ex (MeV)

Incident energy 8 MeV

10 MeV

0.524 0.893

0.4 0.33

0.22 0.32

1.229 2.560 2.622

0.55 0.50 0.55

0.50 0.25 0.29

3.168

0.45

0.26

54Cr(d,p) AND S3Cr(t, p) REACTIONS

251

The angular distributions for the I, = 3 transitions at E a = 8 MeV and E a = 10 MeV are displayed in fig. 7 and the ratios of cross sections at the second and first maxima are quoted in table 4. It can be seen that only the 0.524 and 0.893 MeV levels have ratios which are in agreement with those of the J-dependence criterion 1o). The 0.524 MeV level must be assigned J = ~- on the basis of its strength or this criterion and we assign J = ½- to the level at 0.893 MeV from the J-dependence criterion. The other levels have ratios which are higher than that found in previous work and this may be the result of the Q-value being lower for these levels than for any others considered in J-dependence studies. Since a theoretical description of the J-dependence phenomenon is not available and since the magnitude of changes with Q-value and A (or Z ) have not been established experimentally, the use of the empirical criterion must be considered to be an extrapolation. Assuming smooth changes with Q-values, etc., it seems reasonable to expect the magnitude of the change in the ratio of the maxima between E d = 8 MeV and Ed = 10 MeV to give an indication of the spin. It can be seen from fig. 7 and table 4 that between these energies there are very large changes in the angular distributions and this ratio for the 2.570, 2.622 and 3.168 MeV levels; thus one can be reasonably confident in assigning J = ) - to these levels. It is very ditficult to make any assignment for the 1.229 MeV level since between E a = 8 MeV and E d = 10 MeV the angular distribution (fig. 7) does not change near the second maximum but does change near the first and second minima. However at E a = 10 MeV the cross sections in the region of the first minimum and second maximum are higher than for the other levels and on this basis we suggest tentatively a j = z - assignment. 4. Discussion

It has been suggested by Rosalky et al. 4) that an assignment of J = g2- to the 2.905 MeV level gives a spacing between the single-particle energies of the 2p~ and 2p~ states of 0.84 MeV; since this does not agree with the value of 1.66 MeV for neighbouring nuclei 16), they preferred to assign a spin of J = ½-. However the present work gives J = 3 - for the levels at 2.710 and 2.905 MeV and locates several other l, = I transitions to levels of 55Cr at excitation energies greater than 3 MeV. Assuming as seems probable that the states above 3 MeV are of J = ½-, we calculate the single-particle energies of the 2p~, 2p~ and lf~ states to be 0.55, 1.78 and 1.95 MeV respectively. These values and the energy difference derived for the 2p~ and 2p4 states (1.23 MeV) are compatible with other data in this region of the periodic table. It has been shown by Whitten 17) from an investigation of the 54Cr(p, d)53Cr reaction that there are substantial (2p4) 2 and (lf~) 2 admixtures in the ground state wave function of 54Cr. Assuming the values of Je given in table 4, the summed values of ( 2 J + 1)S obtained from the present work are 3.28, 1.57, and 2.97 for the 2p~, 2p~r and lf~ transitions respectively, whereas the shell-model expectations are 2.0, 2.0 and 6.0. As pointed out previously 9) the large value of the 2p strength of 4.85 indicates

252

A . E . M A C G R E G O R AND G. BROWN

s u b s t a n t i a l ( l f ~ ) 2 admixture in the 54Cr ground state wave function; the present division between 2p~ and 2p~ transitions shows also (2p~) 2 admixtures. These measurements on the extent of the admixtures can be compared with those of Whitten 17). Using these data to derive the values of the occupancy, Vf, of a nuclear shell 18) and the present (d, p) data to give the vacancy, U2, we find the sum of these values to be 1.05, 0.95 and 0.59 for the 2p~, 2p~ and lf~_ transitions respectively. The values for the 2p, and 2p~ transitions are within the errors of measurement equal to the expected value of unity, but that for the lf~ transitions is too low and probably indicates that too low a value of ( 2 J + 1)S has been obtained for the (d, p) reaction. It has been suggested 9) that the low values of the lf,r strength observed for the (d, p) reaction with lf~_shell nuclei is due to the difficulty of locating all the levels over which the strength is split rather than being due to the use of DWBA calculations which do not give the correct ratio of If to 2p strengths. We believe this to be the case here. A comparison of the differential cross sections for the (t, p) and (d, p) reaction to a particular level should give information on the wave function of the levels involved in the transition. However the (t, p) reaction data can only be used to test detailed calculations of wave functions and not to produce these since there can be interference from transitions to different components of the wave function. Thus in the absence of such calculations for 5 SCr the present data can be discussed in only a qualitative manner. Including the ground state transition, ten L = 0 transitions are observed in the (t, p) reaction at excitation energies of less than 4.2 MeV. These appear in groupings at different excitation energies; to the ground state and the level at 0.573 MeV; to 5 levels between 1.4 and 2.7 MeV; to three levels between 3.5 and 4.2 MeV. Three of these transitions are much stronger than the remainder, namely, the ground state transition, that to the level at 2.098 MeV and that to the 2.341 MeV level. Only the transitions to the ground state and the 0.573 MeV level are observed with any significant strength in the (d, p) reaction. The L = 0 transitions occur by the addition of neutron pairs coupled to zero spin, such as (2p~) z (2p~)02(lf~)~ etc. to the components of the 53Cr ground state wave function. The latter has been calculated 6) to be

~953 = 0.8757r(f~_)~v2p~+ Bn(f÷)4 +v(2p~, 2p~ or l f~) + C,7(f~)v~+ l f~, where rc and v refer to protons and neutrons, respectively. Since there are several pairs that can be added to each component, the large number of transitions is easily understood; differences in the cross sections will occur as a result of phase cancellations and differences in the amplitudes of the configurations in the various wave functions. However since it is observed for 55Cr that there is an energy gap of at least 1 MeV between the 2p~: and the 2p~ or lf~_ single-particle levels, an energy difference is expected between levels produced by (2p~) 2 transfers and those produced by (2p~) 2 or (lf~) 2 transfers. This suggests that the wave functions of the ground state and 0.573 MeV levels consist primarily of a 2p~ neutron pair added to the 53Cr ground state wave function. This is qualitatively in agreement with the results of the (d, p) reaction since the addition of a 2p~_ neutron to the ground state wave function of 5*Cr

54Cr(d, p) AND 53Cr(t, p) REACTIONS

253

given by 6) ~54 = 0.93~r(f~)~v(2p~, 2p~ or lf~)+0.a8~z(f~)24.v(2p~ or lf~)2÷, leads to some wave function components which are those reached by the addition of a 2p_~ neutron pair to the 53Cr wave function, i.e. to the ground state and 0.573 MeV level of 55Cr" The observation of the 2.341 MeV level by a weak In = 1 transition of the (d, p) reaction is understood by noting that the addition of (2p~)o2 or (lf~) 2 neutron pairs to major components of the 53Cr ground state wave function can lead to configurations readily produced by adding a 2p~ neutron to a minor component of the S4Cr ground state wave function. It can also be shown that there are several ways in which the observation of an L = 0 + 2 transition to the 0.573 MeV level can be explained since there are several ways in which the appropriate particles can be added to components of the 53Cr wave function and lead to the same final state. These comments illustrate the complexity of any analysis of the data of the (t, p) reaction. The L = 2 transitions of the (t, p) reaction occur by the addition of (p~, p~), (p~, f÷), etc., neutron pairs. As expected from the proximity of the 2p~ and lf~ singleparticle levels in 55Cr no energy groupings are observed. However three of the L = 2 transitions are much stronger than the remainder, and the states so formed (0.16, 0.524 and 2.570 MeV) are observed in the (d, p)reaction. Thus it seems probable that these transitions occur by the addition of neutron pairs to the predominant configuration of the ground state wave function of 53Cr. At least one level, and possibly two, of J = ½- are excited in the (d, p) reaction. It seems unlikely that these are excited by the addition of a lf~_ neutron to the 54Cr ground state wave function since the presence of a significant (Ifk) 2 vacancy in the wave function is improbable and since the leveIs are observed at excitation energies of 0.89 and 1.23 MeV, i.e., approximately 1.5 MeV below the expected energy of the (lf~) -1 configuration. Levels of J = ½- excited in the (d, p) reaction but which are not based on a lf~ hole configuration have been observed in the N = 29 nuclei 6-8). Experimental investigations into the structure of these levels has indicated that they are based upon configurations of the form of [rc(f~)4 ÷v2p~]~- and that they may be excited in the (d, p) reaction by a two-step process. The spectroscopic factor for the (d, p) transition to these levels for N = 29 nuclei is very similar to that for the 0.893 MeV level of 5SCr. Thus it seems very likely that a higher-order (d, p) process can account for the observation of these levels in 55Cr. It seems probable also that as a result of the lowering of the f~ single-particle level in s 5Cr relative to the N = 29 nuclei, several levels can be expected arising from the configurations [rc(f~)~÷v{(2p or lf)02(2p~ or lf~)}]~- and hence that more than one level of J = ½- could be observed. The excitation of these via an L = 2 transition of the (t, p) reaction presents little difficulty since appropriate core excitation components exist in the S3Cr ground state wave function. It is interesting to compare (fig. 8) the spectroscopic information for 55Cr with the

254

A.E.

experimental

19,

MACGREGOR

and theoretical

2 0 )

2 1 - 2 3 )

AND

G. B R O W N

data for the 59Ni nucleus which also has

three neutrons outside the N = 28 shell but which has a closed proton shell. The spectroscopic factors used in the comparison of fig. 8 are taken from the present data

5%r

4 -

,J"

59Ni J

n'

In

1

5"

3 -

1

×~

4 1

1

{,

1

2 3-

2

x¼ 4 ¸ 2

2 -

5-(1) g3 1>

3 - -

1 -

7

3

1 q

×! 1-

4 1 -

1

O-

2

x2

3-

3-,

0

.

.

.

.

,

.

.

.

0.5

( 2 J-'-I ) S

.

i

1.0

.

.

,

0

.

.

.

i

0.5

.

,

1-0

.

.

.

.

i

1.5

(2,.T',-1)S

Fig. 8. A c o m p a r i s o n o f the spectroscopic i n f o r m a t i o n for 55Cr with e x p e r i m e n t a l data for 59Ni.

for 54Cr(d, p)S 5Cr reaction and the mean of all available data 19, 2o) for 58Ni(d,'p) 59Ni" Below an excitation energy of 2 MeV, and with the exception of levels with J = ½-, it can be seen that the experimental data for 55Cr and 59Ni are very similar. The same levels appear to be excited in both nuclei with similar spectroscopic factors; the main difference is that the order of the low-lying levels with J = ½- and J = { is reversed. The shell-model calculations for 59Ni in which it was assumed that the N = 28 and P = 28 shells were closed and that the valence neutrons occupied the

54Cr(d, p) AND 5aCr(t, p) REACTIONS

255

2p or lf~ orbits, give a good description of the 59Ni level structure. The similarity of the experimental data for 55Cr and 59Ni suggests then that similar shell-model calculations might be successful for 55Cr" However the similarity between the two nuclei might be misleading since the comparison is for data obtained with a neutron stripping reaction and as a result differences arising from the different proton configurations are obscured. Levels with J = ½- have not been identified in the 58Ni(d,p)S9Ni reaction. Studies of the (p, d) and (d, t) reactions 24) have shown the existence of levels with J = ½- at 1.96, 2.63 and 3.04 MeV. However the 1.96 MeV level does not show a stripping angular distribution with the (d, p) reaction, the angular distribution for the 2.63 MeV level is assigned as In = 1 at Ed = 7.5 MeV [ref. 19)] and In = 3 at E d = 12 and 15 MeV [ref. 2o)], and the 3.04 MeV level is excited by an In = 1 transition at E d = 7 . 5 and 12 MeV. Thus the only level of J = ½ - which may be observed in the (d, p) reaction appears to be that at 2.63 MeV but the excitation energy of this level is a little higher than the energy of the core-excited configurations located for the N = 29 nuclei and 53Cr. A more likely candidate for these J = 3levels may be the level at 1.685 MeV in S9Ni which is excited by an ln = 3 transition in the (d, p) reaction at all incident energies 19,2o). However no spin assignments have been made. It is worth noting that interference effects from the compoundnucleus reaction might be significant in the 59Ni(d, p)SSNi reaction since there is a large difference in the (d, p) and (d, n) Q-values for 5aNi. Such interference might lead to discrepancies in spin assignments at different energies. Thus it would appear that additional investigations of the 5aNi(d, p) reaction are warranted to determine the magnitude of compound-nucleus effects and to obtain spin assignments for ln = 3 transitions. The observation of levels with J = ~- with configurations based on core excitation would lend support to the observation of Cohen et al. 22) that core excitation is needed to account for the E2 transition rates of the Ni isotopes. 5. Conclusions

The experimental data reported here have (i) Given spin assignments to a large number of levels of 55Cr. (ii) Shown that substantial (p½)2 and (f~)2 admixtures are present in the ground state wave function of 54Cr and that the (p~)Z admixture is compatible with that deduced from the data of the (p, d) reaction 17). (iii) Shown that similarity exists between the level scheme of 5 SCr and 59Ni. This suggests that the influence of proton excitation on the low-lying level structure of 55Cr is less than might otherwise have been supposed. (iv) Revealed the existence of one J = 3- level in 55Cr at 0.893 MeV which may be excited in the (d, p) reaction by a process other than simple stripping. Since similar results have been obtained for two N = 29 nuclei 6-8) it is suggested that similar levels should exist in other nuclei and in particular in 59Ni.

256

A . E . M A C G R E G O R A N D G. BROWN

W e w i s h to t h a n k M r s . Ball, Lees, T i l d e s l e y a n d W a d e f o r their c a r e f u l analysis of the nuclear emulsions and the crew of the Aldermaston and Harwell tandems for t h e i r efficient o p e r a t i o n o f t h e s e m a c h i n e s . W e are g r a t e f u l to the S c i e n c e R e s e a r c h C o u n c i l f o r t h e i r s u p p o r t o f this w o r k .

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

22) 23) 24) 25)

J. H. Bjerregaard, P. F. Dahl, O. Hansen and G. Sidenius, Nucl. Phys. 51 (1964) 641 A. E. Macgregor and G. Brown, Nucl. Phys. 88 (1966) 385 R. Bock, H. H. Duhm, S. Martin, R. Rudel and R. Stock, Nucl. Phys. 72 (1965) 273 D. M. Rosalky, D. J. Baugh, J. Nurzynski and B. A. Robson, Nucl. Phys. A132 (1970) 469 M. Divadeenam and W. P. Beres, Phys. Lett. 30B (1969) 598 J. Vervier, Nucl. Phys. 78 (1966) 497, and private communication R. Bock, H. H. Duhm, R. Rudel and R. Stock, Phys. Lett. 13 (1964) 151 R. N. Glover, A. Denning and G. Brown, Phys. Lett. 27B (1968) 434 G. Brown, A. Denning and A. E. Macgregor, Nucl. Phys. A153 (1970) 145 A. Denning, A. E. Macgregor, A. E. Ball, G. Brown and R. N. Glover, Phys. Lett. 26B (1968) 437; Nucl. Phys. A165 (1971) 641 R. N. Glover, private communication R. Chapman, S. Hinds and A. E. Macgregor, Nucl. Phys. A l l 9 (1968) 305 L. L. Lee and J. P. Schiffer, Phys. Rev. 154 (1967) 1097 C. A. Pearson, J. M. Bang and L. Pocs, Phys. Rev. 179 (1969) 1082 A. E. Macgregor and G. Brown, Nucl. Phys. A190 (1972) 548 G. Delic and B. A. Robson, Nucl. Phys. A134 (1969) 470; J. E. Robertshaw, S. Mecca, A. Sperduto and W. W. Buechner, Phys. Rev. 170 (1968) 1013 C. A. Whitten, Phys. Rev. 156 (1967) 1228 B. L. Cohen, Nuclear spin-parity assignments, ed. N. B. Grove (Academic Press, 1966) E. R. Cosman, C. H. Paris, A. Sperduto and H. A. Enge, Phys. Rev. 142 (1966) 673 B. L. Cohen, R. H. Fulmer and A. L. McCarthy, Phys. Rev. 126 (1962) 698; R. H. Fulmer, A. L. McCarthy, B. L. Cohen and R. Middleton, Phys. Rev. 133 (1964) B955 R. Arvieu, E. Salusti and M. Veneroni, Phys. Lett. 8 (1964) 334; L. S. Hsu and J. B. French, Phys. Lett. 19 (1965) 135; A. Plastino, R. Arvieu and S. A. Moszkowski, Phys. Rev. 145 (1966) 837; N. Auerbach, Phys. Lett. 21 (1966) 57 S. Cohen et al., Phys. Rev. 160 (1967) 903 N. Auerbach, Phys. Rev. 163 (1967) 1203 R. Sherr, B. F. Bayman, E. Rost, M. E. Rickey and C. G. Hoot, Phys. Rev. 139 (1965) B1272; R. H. Fulmer and W. W. Daehnick, Phys. Rev. 139 (1965) B579 J. R. Rook and D. Mitra, Nucl. Phys. 51 (1964) 88