The 54Cr(3He, d)55Mn reaction

2.G

I

Nuclear Physics A123 (1969) 627--640; (~) North-Holland Publishing Co., Amsterdam N o t t o b e reproduced by photoprint or microfilm without written permission from the publisher

T H E S4Cr(SHe, d)SSMn R E A C T I O N J. RAPAPORT, T. A. BELOTE, W. E. DORENBUSCH and R. R. DOERING Physics Department and Laboratory for Nuclear Science t, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA Received 17 September 1968 Abstract: The proton states m ~SMn have been studied by means of the 5~Cr(SHe,d) reaction with

10.0 MeV 3He ions. Deuteron angular distributions for stripping transmons to states below 5.5 MeV excitation were measured using the MIT multiple-angle spectrograph. A DWBA analysis was carried out to determine lp values and transition strengths. The observed level structure of 55Mn is compared with those from (8I-Ie,d) reacUons leading to S3Mnand ~IMn. E [

I

NUCLEAR REACTIONS 64Cr(SHe,d), s4Cr(3He, SHe), E = 10.0 MeV; measured o(Ea, 0), Q. BSMndeduced levels, ~, lp, transition strengths. Enriched target.

1. Introduction

The results that are reported here are part of a continuation of investigations of (aHe, d) reactions on the Cr isotopes 1,2). Levels in 55Mn up to an excitation energy o f 3.86 MeV have been studied previously in this laboratory a) by magnetic analysis o f inelastically scattered protons. More recently, Katsanos et al. 4) measured the levels o f 5SMn in a similar manner up to 3.915 MeV excitation. The 54Cr(3He, d) 55Mn reaction has also been reported by Cujec et al. 5). The radiative capture of protons by ~4Cr has been studied by Abuzeid et al. 6), wherein 7-rays up to 2.20 MeV were observed. Nath et al. 7) have measured inelastic neutron scattering from 55Mn and give tentative spin assignments for levels below 1.884 MeV excitation. Possible spin assignments for levels below 2.56 MeV excitation energy using nuclear resonance fluorescence have been reported a,9). In the present work, the 54Cr(aHe, d)SSMn reaction at 10.0 MeV incident energy was carried out using the M I T multiple-gap spectrograph. Data were obtained for 35 excited states below 5.5 MeV. The experimental procedure and results are described in sect. 2. Spectroscopic factors were extracted for the 55Mn stripping transitions using a distorted-wave Born approximation (DWBA) analysis (see sect. 3). A discussion of the level scheme of 5SMn ' sum-rule analysis and comparison with calculated level schemes to, 11) is given in sect. 4. The results for 55Mn are compared with those obtained from the 5o, 52Cr(3He ' d)S 1, 53Mn reactions reported previously 1,2). t This w o r k has been s u p p o r t e d m part t h r o u g h funds provided by the U.S. Atomic Energy Commission under A E C C o n t r a c t AT(30-1)-2098.

627

628

j. RAPAPORT e t al.

2. Experimental procedure and results 2.1. T A R G E T

The 47 #g/cm 2 thick 5*Cr target was prepared by vacuum evaporation of chromium oxide onto a thin formvar foil. The chromium isotopic composition was 1.43 ~ 52Cr, 0.59 ~o 53Cr and 97.98 ~o S*Cr. 2.2. E L A S T I C S C A T T E R I N G

Elastic scattering of 3He from 5*Cr was measured at 10.0 and 5.0 MeV bombarding energies. The 5.0 MeV scattering was used to determine an absolute cross-section scale assu~-aing Rutherford scattering. The 10.0 MeV results are shown in fig. 1 along with 101

54Cr ( 3He 3 He) EnHe =10.0 MeV

m

b

t

10-~

I 30

r 60

[ 90 8LQb

I 120

I 150

Fig. 1. Angular distribution o f a H e elastically scattered by 54Cr at 10.0 MeV. The data are presented as the ratio to the R u t h e r f o r d elastic-scattering value. The error flags indicate statistical uncertainties. T h e solid curve is an optical-model fit to the data using the SHe parameters given in table 2.

the optical-model calculated curve. The error on the absolute cross-section scale is estimated to be -t-20 ~ . Relative errors are represented by error flags on the data points. 2.3. THE (aHe, d) REACTIONS The aHe beam was obtained by accelerating 3He + + ions in the M I T - O N R electrostatic generator. The reaction particles were analysed with the MIT multiple-gap

I00

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15C

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DISTANCE ALONG PLATE (cm)

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EXCITATION ENERGY (MeV) 50 45 I

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LAB ANGLE-45 ° INCIDENT ENERGY- I 0 0 0 MeV SPECTROGRAPH FIELD - 12 675 G EXPOSURE • 4 000 )JC

54Cr (3He,d)SSMn

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EXCITATION ENERGY (MeV) 15 I0

18• "4N (I)

I

55

3O

Lf.

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o

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3.O

35

7O

Fig. 2. Deuteron spectrum from B4Cr(SH¢, d)SSMn observed at a lab angle of 45% Deuteron groups corresponding to states in SSMn are labelled with the numbers used to identify the states in table I. Several contaminant groups are identified.

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o

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J. RAPAPORT et al. TABLE, 1 S u m m a r y o f results for the 54Cr(SHe, d)65Mn r e a c h o n at E3ne -----10.0 M e V

Level no. 0 1 2 3 4 5 6 7 8 9 10 I1 12 13 14 15 16 17 18 19 20 (21) 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Q a) (MeV)

Ex b) (MeV)

Ex c) (MeV)

2.568 2.441

0 0.127

0 0.127 0.983 1.289 1.527 1.884 2.197 2.252 2 426 2.564 2.751 2.991 3.037 3.081 3.156 3.263 3.424 3 529 3 607

1.041 0.687 0.370 0.318 0.142 0.008 --0.174 --0.416 --0.460 --0.502 --0.579 --0.692 --0.861 --0.956 --1.040 -- 1.343 -- 1.430 --1.605 --1.650 -- 1.925 --2.018 --2.070 --2.174 --2.236 --2.328 --2.429 - - 2 458 --2.490 --2..¢ 17 --2.614 --2.798 --2.930

1.527 1.881 2.198 2.250 2.426 2.560 2.742 2.984 3.028 3 070 3.147 3.260 3.429 3.524 3.608 3.911 3.998 4.173 4 218 4.493 4.586 4.638 4.742 4 804 4 896 4 997 5.026 / 5.058 5 085 5.182 5.366 5.498

(dtr/dO)ma x d) (mb/sr) 0.002 0.32 0.002 0.004 0 38 0.038 0.006 1.4 0.067 0.36 0.008 0.039 0.31 0.010 0.085 0.027 0 29 0 42 0.30 0.043 0.30 0.020 0.050 0.13 0.082 0.28 0.12 0.032 0 051 0.62

0.15 0.50 0.27

lp

(2Jq-I)C2S

j s e)

3

3.22

½3-

1 3

0.51 0.28

(½)-

1 (0) 1

1.35 0.05(2s) 0.30

(~) (½÷)

2 1

0.10(ld) 0.24

(])+

3

0.42

1 1 3 1 1

0.20 0.29 1.53 0.02 0.18

1 1 1 1 l 3

0.06 0.05 0.14 0.06 0.02 0.20

1

0.30 r)

1 1 3

0.07 0.24 1.05

(~)-

a) T h e estimated uncertainty is 18 keV for level nos. 0 t h r o u g h 20; 25 keV for the other levels. b) T h e estimated uncertainty is 10 keV for level no. 1; 15 keV for the other levels. e) Ref. 3). Only those levels c o r r e s p o n d i n g to transttions observed in this experiment are listed in this c o l u m n . M a n y other levels were seen in the (!0, p') reaction. d) T h e estimated error in the absolute m e a s u r e d cross sections ~s -t-20 percent. T h e cross section at 0~ab = 7.5 ° is g~ven for the lp = 0 transition. e) Tentative spin assignments are indicated in parentheses. t) This quartet o f levels was d e c o m p o s e d using a h n e - s h a p e peeling technique at an angle h a v i n g g o o d resolution, a n d strengths o f a b o u t 0 05, 0 06, 0.07 a n d 0.12 for levels 29 to 32, respectively, were obtained.

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, 910 120 i 150 , 180 ,SO

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Fig. 3. A n g u l a r distributions o f deuterons f r o m s4Cr(SHe, d)56Mn. T h e dtstrlbutlons are labelled with the n u m b e r s used to identify the corresponding states in table 1. Statistical uncertainties are indicated by error flags on the data points. T h e solid curves are the D W B A predictions calculated with the code T A N Y A u s i n g the p a r a m e t e r s given in table 2.

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Fig. 4. See caption for fig, 3.

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Fig. 5. See caption for fig. 3.

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J. RAPAPORT et al.

634

magnetic spectrograph and were detected in 50 pm Eastman Kodak NTB nuclear emulsions. Aluminium absorber foils were placed in front of the emulsions to stop the scattered 3He and reaction a-particles. A 4000 #C exposure was taken for the reaction data, and the deuteron spectrum observed at 0~ab = 45 ° is shown in fig. 2. The energy resolution was 30 keV. The deuteron groups corresponding to a residual mass of 55 were identified from their kinematic energy shift with angle. In table I, the Q-values and excitation energies for the levels observed in s 5Mn are given. Because of the weakness of the ground-state transition, its Q-value was calculated from the measured first excited state Q-value assuming an excitation energy of 0.127 MeV for this level. The measured Q for the first excited state 2.441 +0.015 MeV was determined by reference to known contaminant Q-values and is the average of the results obtained at three angles of observation. Using this value, we obtained a groundstate Q of 2.568 +0.018 MeV; this result is in excellent agreement with the Q-value of 2.570+__0.005 MeV obtained from the mass table t2). Because of the larger uncertainties in the calibration of the spectrograph at high fields, a correction to the calibration used in extracting Q-values was made by observing deuteron groups from known contaminants along the plates. The excitation energies reported here are in good agreement with those previously reported 3,~). Many of the levels reported in 5 SMn were not observed in this experiment because of the selectivity of the (3He, d) reaction. In ref. 4), 62 levels were reported below 3.92 MeV of excitation, whereas we observe only 20 levels below the same excitation energy. The angular distributions are shown in figs. 3-5 in comparison with DWBA calculations.

3. Optical-model and DWBA analysis The 10 MeV elastic 3He scattering data were measured to obtain the optical-model parameters to be used in the DWBA analysis. The parameter search was made using the code ABACUS 13)starting with the parameters obtained from 11.0 MeV 3He elastic scattering on S2Cr reported in ref. 2). The resulting best-fit parameters, as well as the deuteron and proton parameters used in the present analysis, are given in table 2. A Woods-Saxon potential was used for both the proton bound state and the 3He and deuteron potentials. Volume absorption was used for the 3He potential. All calculations were performed with a zero-range interaction, local optical-model potentials and no spin-orbit interaction. No lower cut-off was used in these calculations. The DWBA calculations were carried out using the code T A N Y A developed at MIT. The transition strengths ( 2 J + 1)C2S were determined by relating the DWBA calculated cross section to the experimental cross sections summed over angles through the relation (d~)

= 4.42(2J+ exp

1)C2Saca~c(O),

54Cr(aHe, d)5~Mn REACTION

635

where J is the final nuclear spin, C the isospin Clebsch-Gordan coupling coefficient, S the spectroscopic factor and 4.42 a normalizing factor resulting from the use of a Hulth6n wave function for the deuteron and an Irving-Gunn wave function for the 3He ion t4). The values of the orbital angular momenta of the captured proton lp were deduced by comparing the predicted and observed angular-distribution shapeS. TABLE 2 Optical-model p a r a m e t e r s Particle

V (MeV)

W (MeV)

ro (fm)

16.84

a (fm)

3He

165.36

1.07

0.757

d

112.0

1.00

0.90

p

a)

1.20

0.65

W' (MeV)

18.0

r'0 (fm)

a" (fro)

roe (fm)

1.59

0.586

1.40

1.55

0.47

1.30 1.25

T h e optical potential used was o f the f o r m V (r) = -- V(ex + l ) - l - - i ( W - - 4 W ' d ~ ) (ex" + l )-~ + V¢(r, re), with x--

r--roAt~ , a

x'

r--r'°A~ - - a ,r

r e : roeA~.

V¢ 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 o. a) A d j u s t e d to give the transferred p r o t o n a b i n d i n g energy o f Q(3He, d)-F5.49 MeV.

4. Discussion 4.1. S T R E N G T H

FUNCTION

AND SUM-RULE ANALYSIS

The level structure of s SMn is presented in fig. 6 in the form of a strength function. In its ground state, 55Mn has 25 protons and 30 neutrons coupled to J~ = ~- [ref. is)]. Therefore, the ground state should not be excited by the transfer o f a lf~ proton to the 0 + ground state of S4Cr. The measured cross section is about 2/~b/sr as compared with a 320 #b/sr maximum cross section for the transition to the first excited state (J~ = 27--). This latter transition shows a typical lp = 3 angular distribution and carries alinost the full If~ single-particle strength. It is interesting that the cross section for the ) - transition is about an order of magnitude less than for similar (aHe, d) transitions to ~2 states observed with Ti and Cr targets 1). In the case of S4Cr, the neutrons occupy orbitals above the lf~ shell, whereas in the cases reported in ref. 1), the neutrons were presumably all of lf~ character. The transitions to states 2 and 3 at 0.983 and 1.289 MeV excitation are also seen with small cross sections. They are presumably of the (lf~)-3 configuration and have been given J~ assignments 7,8) of 9 - and ~ - - , respectively. Five other lp = 3 transitions are observed in this experiment below 5.5 MeV excitation. Besides the transition to the first excited state, it is probable that level no. 5 at

J. RAPAPORT et al.

636

1.881 MeV excitation may also belong to the lf~ configuration, while the remainder are probably of lf~ character. The simple shell model 16) predicts a total strength of 4.0 for the lf~ transitions, all having T< = }, since the neutron lf~ shell is full. 55

LEVEL STRUCTURE OF 25Mn~3 60-

L

50

40 =

m

20--

I0

O0

~4Ct(3He,d)

l p =0

/p= I 001

i

OI

,i

./p=2 IO

,I

Jp=3

I00

tl

(2 J,,- I)CzS

F i g . 6. Strength function for 56Mn. The excitation energy scale is given on the left. The values of (2Jrq-1)CaS from table 1 are plotted on a logarithmic scale in the last four columns.

The two neutrons outside the lf$ shell in the target S4Cr ground state are expected to be distributed in the 2pt, 2p, and lft orbits. An estimate of the neutron occupation in these shells can be obtained from the neutron pick-up data of Whitten 17). He reports the results of the S4Cr(p, d)S3Cr reaction and obtains spectroscopic factors of 0.83, 0.31 and 0.51 for the transitions to the ½-, ½- and ~- states, respectively. As-

UCr(aHe, d)55Mn REACTION

637

suming the occupancy of these shells to be in the ratio of the observed (p, d) spectroscopic factors and that the protons occupy no shells higher than lft, one would expect a (3He, d) strength of 5.24 for the T< = { lf~ transitions and 0.76 for the T> = ~ lf~ transitions. We observe a summed strength of 3.2 (level nos. 14, 18, 28 and 35) which probably indicates that part of the lf÷T< strengths lies above 5.5 MeV excitation. The T> transitions lie above the region studied in this experiment. In table 3, the predicted sum-rule strengths are compared with the observed values. TABLE 3 Summed strengths (2J+1)C2S for T< states 2s,

ld~

theory a)

0

0

9.24

4.0

experiment

0.05

0.10

6.7

3.5 b)

~) See discussion in subsect. 4.1. a) All observed lp = I transitions.

If

lq

b) State nos. 1 and 5.

lq 5.24 3.2 e)

2p 5.32 4.1 d)

c) State nos. 14, 18, 28 and 35.

Ex(MeV)

30

I ~2-II-72

(o) I 20

';'~-

9/2-

,~~/~-

9/2-

I0

3

55Mn(p,p')

h-

54Cr(~He,d) ~p J"

- - 5 / z -

MCGRORY

VERVIER

Fig. 7. Comparison with calculated level schemes. The ~SMn(p, p') level scheme 4) and the (aHe, d) results are compared with the calculated level schemes of McGrory n ) and Vervier 10).

638

J. RAPAPORT et al.

The lp = 1 strength is distributed in the region above 1.527 MeV among T< = states. Since in this experiment we do not distinguish between p~ and p , transitions, the over-all strength for p-state transitions is compared in table 3 with the sum-rule limit of 5.32, again calculated assuming the neutron occupancy measured in the (p, d) experiment 17). Level no. 4 at 1.527 MeV excitation may correspond to the (lf~)-a J~ = ~- level. If this is the case, it has a large 2p~ admixture. This may be due to the fact that it is only 0.72 MeV from the strongest lp = 1 level (E x = 2.252 MeV) which is probably the major component of the 2p~ single-particle state. It is likely that other lp = 1 and lp = 3 transitions lie above 5.5 MeV, pointing to the reason why the full sum rule is not fulfilled (see table 3). The only lp = 2 transition is observed at an excitation energy of 2.984 MeV. This is a rather low-lying state and by systematics (see fig. 7) it is assigned as a ld~ proton hole state. Similarly, a tentative lp = 0 transition is observed at Ex = 2.426 MeV and presumably corresponds to a 2s¢ proton hole state. In general, the results reported here are in only fair agreement with those of ref. s). They report 16 levels below an excitation energy of 4.8 MeV. Our strengths are about 25 ~o lower than theirs for lp = 1 transitions and from about 40 % to a factor of 2 lower for the lp = 3 levels. Also, our excitation energies for the higher-lying levels are about 35 keV lower than those reported in ref. s). 4 2. COMPARISON WITH CALCULATED LEVEL SCHEMES The experimental level schemes observed by 55Mn(p ' p,) [ref. 4)] and by 54Cr (3He, d) are compared with the calculated level schemes of McGrory 11) and Vervier [ref. 1o)] in fig. 7. The lower-lying levels are in good agreement with those calculated in ref. it). A 3 - level is predicted near 2.1 MeV in both calculations and probably corresponds to the observed lp = 3 level at E x = 1.881 MeV. The expected strengths of the transitions are not given in either ref. 1o) or ref. 11); therefore a further comparison is impossible. 4.3. T H E (3He, d) R E A C T I O N S I N T H E E V E N Cr I S O T O P E S

In fig. 8, the experimental strength function for the 50Cr(3He ' d)51Mn reaction 1), SZCr(3He, d)53Mn reaction 2) and the present results for the 54Cr(3He, d)55Mn reaction are compared. The values of ( 2 J + 1)C 2S obtained using similar sets of parameters (same proton bound states and deuteron parameters) are indicated in a linear scale according to the lp value. It is interesting to note the consistency in position as well as magnitude of the ld~ and 2s~ proton hole states in the three cases; the 2s÷ hole state for these isotopes is at about 2.5 MeV with a strength ( 2 J + 1 ) C 2 S = 0.05 and the ld~ hole state at about 3.0 MeV excitation with a strength ( 2 J + 1 ) C 2 S = 0.1. The state carrying the major amount of the 2p~ strength occurs at about 2.0 MeV, but there a r e lp = 1 transitions observed up to 6.0 MeV in all three cases. The ground-state transitions to 5 ~Mn and 55Mn are not allowed in the simple shell

a4Cr(aHe,

d)56Mn

REACTION

639

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J. RAPAPORT et al.

model, because they are J~ = ~ - states. However, in both cases, the transition to the first excited state as well as the transition to the ½- ground state of 5 3 M n carries almost the full lf~ strength. In the case of SlMn, the lfi strength is shared between the first excited state and the IAS state at 4.446 MeV excitation 1). At around 3.5 MeV in all three eases, there is a strong lp = 3 transition probably indicating the onset of the lf~ shell. The authors acknowledge the careful plate scanning of Mrs. Paula Doherty, Mrs. Helen Pelusi and Mrs. Barbara Saccone. The D W calculations were performed at the LNS computation center by H.Y. Chen. The use of the DW code T A N Y A from the MIT cyclotron group is acknowledged. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)

J. Rapaport, T. A. Belote and W. E. Dorenbusch, Nucl. Phys. A100 (1967) 280 B. J. O'Brien, W. E. Dorenbusch, T. A. Belote and J. Rapaport, Nucl. Phys. A104 (1967) 609 M. Mazari, A. Sperduto and W. W. Buechner, Phys. Rev. 108 (1957) 103 A. A. Katsanos and J. R. Huizenga, Phys. Rev. 159 (1967) 931 B. Cujec and I. M. Szoghy, to be published M. A. Abuzeld, M. I. E1 Zalki, N. A. Mansour, A. I. Popov, H. R. Saad and R. E. Stormhko, Z. Phys. 199 (1967) 506 N. Nath, M. A. Rothman, D. M. Van Patter and C. E. Mandeville, Nucl. Phys. 13 (1959) 74 E. C. Booth, B. Chasan and K. A. Wright, Nucl. Phys. 57 (1964) 403 W. J. Alston, H. H. Wilson and E. C. Booth, Nucl. Phys. A l l 6 (1968) 281 J. Vervier, Nucl. Phys. 78 (1966) 497 J. B. McGrory, Phys. Rev. 160 (1967) 915 J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67 (1965) 1 E. H. Auerbach, Brookhaven National Laboratory, BNL 6562 (ABACUS-2) (1962) unpublished R. H. Bassel, Phys. Rev. 149 (1966) 791 H. E. White and R. Ritschl, Phys. Rev. 35 (1930) 1146 J. B. French and M. H. Macfarlane, Nucl. Phys. 26 (1961) 168 C. A. Whitten, Jr., Phys. Rev. 156 (1967) 1228