Final-state spins of 49Sc from the 48Ca(7Li, 6He) reaction

Nuclear

Physics

A348 (1980) 339 - 349; @ North-Holland

Publishing

Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

FINAL-STATE SPINS OF 49Sc FROM THE ‘*Ca(‘Li, 6He) REACTION K. W. KEMPER Department

of Physics, Florida State Universityt, Tallahassee, Florida 32306 and Department of Nuclear Physics, IAS, The Australian National University Canberra, Australia

A. F. ZELLERft

and T. R. OPHEL

Department of Nuclear Physics, IAS, The Australian National University, Canberra, Australia

Received 5 May 1980 (Revised 7 July 1980) Abstract: The forward-anglej-dependence of the 48Ca(7Li, 6He) reaction has been used to determine the spins of the states populated. Spectroscopic factors are in good agreement with previous (3He, d) values when the new spin values are used. The centroid energies obtained show that the If,,, and 2P 1,2 states are nearly degenerate in @‘SC.The value obtained for the If,,, strength shows that the calculated magnitude of the (‘Li, 6He) reaction is correct to within 10 y0 when Cohen and Kurath spectroscopic factors are used in the exact finite-range DWBA calculations.

E

NUCLEAR REACTIONS 48C(7Li, 6He), E = 34 MeV; measured a(0). 49Sc levels deduced J, S, and single-particle centroid energies.

1. Introduction

Recent compilations ‘32, of the level structure of 4gSc show that the spins of many of the predominantly single-proton states are not determined even though this nucleus is an important testing ground for nuclear structure models because it contains only a single proton outside the doubly magic 48Ca core. Earlier (3He, d) studies have determined the transferred orbital angular momenta to these states.

+ Work supported in part by the National Science Foundation. ++Present address: Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA. 339

340

K. W. Kernper et al. 1 48Caj 7Li, ‘He) 49Sc

Final-state spins were inferred from systematic and sum rules. In several important cases, these assignments are in disagreement with recent 48Ca(p, rf measurements. The present work was undertaken to determine the spin of these states through the use of forward-angle heavy-ionj-dependence 3*4). We have chosen the (‘Li, ‘jHe) reaction for these studies because it is possible to get sufficiently good energy resolution with this reaction to extract data for all of the single-particle states observed in the (3He, d) studies. ,A recent limited study 5, of the 48Ca(7Li, 6He) reaction was able to resolve a long-standing discrepancy between (3He, d) and (p, y) studies giving further impetus to the present detailed reaction study. In addition to the final-state spin determinations, proton spectroscopic factors are extracted by compa~ng the data to exact finite-range DWBA CalcuIations.

2. Experimental procedure The ‘Li ions were extracted from a lithium charge-exchange ion source and accelerated to 34 MeV by the ANU 14UD Pelletron Tandem Van de Graaff. The target was prepared by evaporating CaCO, enriched to 97 % in 48Ca onto a carbon backing. Target and detector efficiency changes were monitored by repeating the IO0 data after every three points in the angular distribution. The reaction products were momentum analyzed by an Enge spectrograph and detected in a heavy-ion gas proportional counter 6*7, operated in the light-ion mode. In this mode, the position and energy-loss signals from the detector are sufficient to distinguish the 6He products from the prolific LXand ‘Li reaction products. Because of the need for detailed angular distributions, the polar acceptance angle of the spectrograph was limited to 0.7”. Data were taken from 3.7.Y to 12.75O lab in lo angle increments and from 14°-380 with de = 3”. The product of spectrograph solid angle times target thickness, used to determine the absolute reaction cross sections, was obtained by measuring ‘Li elastic scattering and comparing it to previously measured data *). The relative errors shown in the figufes contain both errors derived from the number of counts and those arising from the need to peak fit the high excitation energy portion of the spectra. The absolute error in the cross sections was + 12 o! and arose from angle setting and charge integration errors. Typical spectra are shown in fig. 1. The energies of the states identified are taken from refs. ” 2). The contaminant r4N and 19F reaction peaks arise from the 13C and la0 content of the target and backing materials. The contaminant peaks obscured the weakly excited 2.23 and 2.37 MeV states at most angles so that angular distributions were not obtained for these states. The peak corresponding to the 14N 2.31 MeV state provided difficulties in extracting yields to states in 49Sc around 5 MeV excitation at a few angles. Whenever reliable peak areas could not be extracted because of this peak, the data were not included in the analysis.

K. W. Kemper et al. / 48Ca( ‘Li, 6He) 49Sc

3oor---

1

I

1 , 1

250 -

341 I

I

48Ca(7Li,6He) E = 34MeV e,= 3.75O

It

250

-

CHANNEL

NUMBER

Fig. 1. Spectra for the %Za(‘Li, 6He) reaction taken at two different laboratory angles.

K. W. Kemper et al. / 48Ca(7Li,

342

6He)

@SC

3. Analysis and results 3.1. FINAL-STATE

SPINS

The angular distributions for the excited states for f3_ 5 20” are shown in fig. 2. It has been shown 3, that forward-angle (‘Li, 6He) data are a strong function of the final-state spin. For the p+ states, an I = 0 contribution occurs which leads to a rise in cross section close to zero degrees relative to p3 states. For f-states, f+ transitions are dominated at small angles by an I = 2 component. The I = 2 component is 10 times stronger for an f3 transition when compared to an f3 transition.

5.38

4.07

IO0-

.

0.. . .

.

3.81

11’ t

5/2-

t”

b-

L

7

L

L

4.49 .

.

.

l

1

. . .

.

l

\

.

l/2 -

IO’ -

I

Fig. 2. Forward-angle data for the 48Ca(7Li, 6He) reaction. The solid curve for the f-states in the upper portion of the figure is the data for the 4.07 MeV +- state. In the lower portion, the solid curve is the data states, for the 3.08 MeV +- state. Note that the data for B,., < 10’ are different from those of neighboring showing very blear j-dependence.

K. W. Kemper et al. / @Ca(‘Li,

6He) 49Sc

343

To determine the final-state spins, forward-angle data to states whose spins are well determined ” ‘) h ave been used to provide a characteristic shape with which the data for other states can be compared. For the f-states, the 4.07 MeV, $- data have been chosen and for the p-states, the 3.08 MeV, 3- data were used. The solid curves in fig. 2 are the data for the characteristic angular distributions. Note that the angular distributions for the 3.81 and 4.49 MeV states are quite different from those of neighboring states for angles smaller than 10” c.m. and that they display a clearj-dependence. It is possible that changes in the shape of the angular distributions IO'

I

I

I

p3/2

--E,

I

.

PI12

-.-

E, i3.08 Me” =5.68 MeV

8

cm

MeV Ex=5.30MeV E,= 0.0 MeV

E,=3.81 -

(deg.)

Fig. 3. The forward-angle portion of the DWBA calculations. These curves show the expected dependence of the data for different excited states. TABLE

1

Summary of experimental results

-WJeV)

1”)

0.0

3 1 3 3 3 1 3 1 3 3 1 1

3.08 3.81 4.01 4.35 4.49 4.14 5.03 5.09 5.38 5.68 5.82

J” ‘)

“) Taken from refs. ‘-rr). b, Average of values taken from refs. 9-11). “) Previous values taken from refs. rs2). d, From the present work.

J” “) 1::::-

iI :;It: :2

cz Sexp b,

0.963 0.636 086 0.179 0.077 0.573 0.121 0.060 0.341 0.134 0.125 0.075

C%,,

7

1.055 0.54 0.050 0.224 0.080 0.470 0.143 0.040 0.383 0.098 0.056 0.041

344

K.. W. Kemper et al. / 48Ca(7Li,

6He) @SC

will occur for excitation energies of states different from those of the state used for the characteristic shape. To explore the shape dependence for different final states, use can be made of DWBA calculations. The calculations will be described in detail in the next section. Here all that is needed is the state dependence of the first 20“ of the angular distributions. The calculations for different final-state excitations are shown in fig. 3. For the p and f* states, very little change occurs between the shape for a state at 3 MeV and one at 5.7 MeV. For f+ transitions, the angular distribution rises at forward angles as the excitation energy increases. Table 1 lists the spins obtained from this work along with the previous values 9-11). As shown earlier 5, our assignment of *- to the 4.49 MeV state resolves a long-standing discrepancy between spins inferred from (3He, d) systematics and a 48Ca(p, y) study 12). This work also showed that the 3.81 MeV state has J” = s- rather than $- as previously inferred. This state was previously assigned to be $- because of the assumption that the ground-state transition exhausted all of the f%strength. Our result for the 3.81 MeV state agrees with a previous 48Ca(p, y) work ’ 3). Our work confirms the 3 assignment for the ground state of 49Sc and also shows that all of the I = 3 transitions above 3.81 MeV are to states with spins of 3. The present work also shows that the p+ and p+ states are fragmented with separation between components of these states of at least 2.5 MeV. 3.2. SPECTROSCOPIC

STRENGTHS

To obtain the spectroscopic factors for the observed transitions, exact fmiterange DWBA calculations have been performed with the code 14) DWUCKS and compared to the data. The values are extracted from the relationship 2J,+l C%, c2s2(Tnw5, (T = ex* 2Ji+1 where C’S, is the spectroscopic factor for ‘Li + 6He+p and C2S2 that for 49Sc + 48Ca+p. The ‘Li value (0.888) was taken from Cohen and Kurath 15). The results from the present study are shown in table 1 along with those from previous studies. The data for the full angular range measured along with the DWBA calculations are shown in figs. 4 and 5. To generate the entrance and exit channel distorted waves, optical parameters from previously 8, measured ‘Li+ 48Ca and 6Li+48Ca scattering were used in the entrance channel and exit channels, respectively. Since Li elastic scattering does not determine these parameters unambiguously, but instead determines sets of parameters that are related to each other through continuous ambiguities 16), a great deal of freedom exists in the choice of the parameters used in the calculations. Our initial choice of parameters was based on an earlier (6Li, ‘Be) study “) which showed a considerable sensitivity to the particular choice of parameters. The (6Li, ‘Be) study was the basis for the choice of parameters presented in ref. 8). The param-

K. W. Kemper et al. / 48Ca(7Li, IO ’

I

I

I

I

I

I

I

345

6He) 49Sc I

I E ,:4.07.5W

E,=3.81,7/2-

--f

0

IO

20

30

40

20

IO

50

0 Fig. 4. Angular

IO0

I

30

40

,

50

IO

20

30

40

50

(dw)

for the first three If states in %c.

distributions

,

Cm

70

Both If,,,

and If,,, calculations

are shown.

,

E y, = 5 38,5/2-

0

IO

20

39

40

50

IO

20

30

40

50

8 c.m.(

Fig. 5. Angular

distributions

for other

If states

in %k.

IO

20

30

40

50

IO

20

30

40

50

deg.)

Both

If,,,

and

If,,,

calculations

are shown.

eters from ref. 8, are given in table 2. The 6Li parameters which best fit the 34 MeV 6Li+ 48Ca data were used for the ground-state transition. For the transitions to the excited states, parameters that best described 28 MeV scattering were used. The calculations done with these parameters provide a reasonable description of the data. However, they do not give a good description of the rate of decrease in cross section for larger angles for the f-states. Many other parameter sets were

K. W. Kemper et al. / 48Ca(7Li,

346

Optical System

6He) @SC

TABLE 2 parameters used in the DWBA

and bound-state

calculations

Energy (MeV)

7Li+48Ca 6Li+48Ca

34 34 28

1.22 1.20

b.s.

- 165.4 - 165.4 - 190.9 “1

Woods-Saxon real and imaginary “) The potential depth was varied

volume potentials were used with R, = rxAi’3. to give the proper proton separation energy.

0.83 0.83 0.83 0.65

1.20 1.25

,I

17.93 17.93 23.75 = 25

1.78 1.75 1.75

0.83 0.83 0.83

h""+""t""

,I\

--

PI/?

1

E,=4.49,1/2-

E x =3.00,3/ZI

E,=5.025.3/2-

1

--

\

p3/2

Ex=5.82,1/2-

48Ca(7L~,6He)4gS~ E= 34

MeV

L

0

Fig. 6. Angular

IO

20

30

distributions

40

50

IO

20

30

40

50

for the 2p states in @SC. Both 2p,,,

IO

and 2p,,,

calculations

are shown.

1.75 1.75 1.75

K. W. Kemper et al. / 48Ca(7Li,

6He) @SC

347

tried, but it was not possible to describe the larger-angle data and at the same time describe the elastic scattering data. The magnitude of the calculated cross sections did not change by more than f20 % for all of the calculations performed. The difficulties encountered in describing the data over the entire angular range found in the present work have been reported earlier I*) for heavier projectiles like (160, r5N). For these heavier-ion reactions, dynamic distortion effects have been recently shown lg) to provide one possible explanation for the inability of the standard DWBA to describe these reactions. A different explanation 20) has been suggested by a double-folding model analysis of existing 7Li + fp-shell target scattering data. In this latter analysis, it was shown that the 7Li projectile is sensitive to the interior of the interaction potential and that the normal assumption of WoodsSaxon potential shape for the real and imaginary potentials is perhaps incorrect. Until more is understood about the detailed form of the interaction potential between two heavy ions one should probably not expect to get detailed fits to the smaller cross section portion of the angular distributions. 3.3. WEAK TRANSITIONS

The cross sections for the 2.23 MeV (+‘) and 2.35 MeV (3’) states were both about 0.040 mb/sr at 10” c.m. These states have a structure ‘) that is predominately one particle one hole with respect to the 48Ca core and are populated by mechanisms that are not single-particle transitions. No analysis of these data was carried out in the present work. The population of the 3.51 MeV state was too weak to extract an angular distribution. It was not possible to extract reliable data for the peak labelled 6.41 MeV in the spectra of fig. 1. At some angles, this region appeared to be characterized by a doublet. 3.4. TOTAL STRENGTHS

The summed single-particle strengths and the average single-particle energies are given in table 3. The p+ strength for the present work, in parentheses, includes a contribution of 0.28 assumed for the higher-lying states observed by Erskine et al. lo), but not seen in the present work. The summed strengths for the f-states are in good agreement with previous (3He, d) work. The strength of the f%transition shows that the Cohen and Kurath r5) 7Li --t 6He+p spectroscopic strength is correct to better than 10 %. The p-state strengths from the present work are lower than those found with the (3He, d) reaction. However, there is some uncertainty in the (3He, d) work because of the lack of extreme forward angle data. The data in refs. ‘*11) do not extend in to small enough angles to observe the first stripping peak. Consequently a slight shift in angle between the data and calculations makes as much as a 20 y0 difference

K. W. Kemper et al. / 48Ca(7Li, 6He) 49Sc

348

TABLE3 Total observed strengths and average energies

f712 Pa/z f 512 P1,2

c*s3

E(MeV)

1.10 0.65 0.93 0.51 (0.79)

0.17 3.46 4.76 4.84

*)

c2s “)

1.02 0.81 0.96 0.92

E(MeV)

1.08 0.86 0.86 0.91

‘)

0.266

1.05

3.57 4.96 4.85

0.80 0.72 0.90

‘) Present work. “) Ref. ‘). “) Ref. lo) (includes 0.06 addition for the 4.35 MeV state) d, Ref. II).

in (3He, d) p-state strength. The limited number of angIes taken in ref. lo) make a detailed comparison between the data and calculations difficult. It would be extremely useful to have a higher energy detailed (3He, d) study carried out so that an accurate assessment of the p-state strength can be made. When the spin assigments made in the present work are combined with the spectroscopic factors, the average level energies can be dete~ined. These values are given for this work and for the (3He, d) study of Erskine et al. lo) in table 3. The (3He, d) study of the ref. lo) was used because it contains spectroscopic strengths for levels up to 7 MeV in 4gSc. The (3He, d) values for the levels above 6 MeV were used to get the p1 (7Li, 6He) energy. The principle change in the average level energies between thezpresent work and that of ref. lo) is that the 2p+ energy is shifted down from 6.04 MeV to 4.84 MeV. This shift occurs because the 4.49 MeV state is j- rather than $- as assumed in ref. lo). With the present spin assignments, the f+ and p3 levels become almost degenerate whereas in 41Ca, they are separated by 1.4 MeV. Existing theoretical calculations I’) do not reproduce the single-particle level spectrum of 4gSc. 4. Conclusions The forward-anglej-dependence of the (7Li, 6He) reaction has been used to determine the spins of the single-particle states in 4gSc. Previous spin assignments had been made from systematics and sum rules after the I-transfers were determined from (3He, d) reaction studies. The results from this work show that there is a slight splitting of the lfi strength and that the 2p, strength is not as fragmented as previously thought. In 4gSc, the 2p, and If+, centroid energies are nearly degenerate. From a reaction study viewpoint, the present results show that the forward-angle portion of the data is well described by finite-range calculations, but the rate of decrease with increasing angle is underestimated by the DWBA calculations. The strength of the f% transition shows that the DWBA calculations have the correct

K. W. Kemper et al. / 48Ca17Li, ‘He) 49Sc

349

normalization to within 10 y0 when the Cohen and Kurath spectroscopic factors are used to describe the projectile-ejectile system. The present work has demonstrated the need for more forward angle (3He, d) data so that reliable p-state strengths can be obtained. It is hoped that the present results will stimulate additional theoretical calculations of 4QSc. The authors wish to acknowledge M. Stephens.

helpful discussions with C. W. Clover and

References I) M. L. Halbert, Nucl. Data Sheets 24 (1978) 175 2) C. M. Lederer and V. S. Shirley, Table of isotopes, 7th ed., (Wiley, New York, 1978) 3) R. L. White, K. W. Kemper, L. A. Charlton and G. D. Gunn, Phys. Rev. Lett. 32 (1974) 892; K. W. Kemper, R. L. White, L. A. Charlton, G. D. Gunn and G. E. Moore, Phys. Lett. 52B (1974) 179 4) W. Henning, D. G. Kovar, J. R. Erskine and L. R. Greenwood, Phys. Lett. 5JB (1975) 49 5) K. W. Kemper, A. F. Zeller and T. R. Ophel, J. of Phys. 64 (1978) L17 6) D. Shapira, R. M. DeVries, H. W. Fulbright, J. Toke and M. R. Clover, Nucl. In&r. 129 (1975) 123; J. R. Erskine, T. H. Braid and J. C. Stoltzfus, Nucl. Instr. 135 (1976) 67 7) T. R. Ophel and A. Johnston, Nucl. Instr. 157 (1978) 461 8) R. I. Cutler, M. J. Nadwo~y and K. W. Kemper, Phys. Rev. Cl5 (1977) 1318; (E) 16 (1977) 1692 9) D. D. Armstrong and A. G. Blair, Phys. Rev. 140 (1965) B1226 10) J. R. Erskine, A. Marinov and J. P. Schiffer, Phys. Rev. 142 (1966) 633 11) R. M. Britton and D. L. Watson, Nucl. Phys. A272 (1976) 91 12) H. Struve, H. G. Thomas, M. J. Bennett and D. D. Armstrong, Phys. Rev. C7 (1973) 1418 13) M. Adachi and H. Taketani, J. Phys. Sot. Jap. 35 (1973) 325 14) P. D. Kunz, University of Colorado (unpublished); L. A. Charlton, Phys. Rev. C8 (1973) 146 15) S. Cohen and D. Kurath, Nucl. Phys. Al01 (1967) 1 16) G. Igo, Phys. Rev. Lett. l(l958) 72 17) G. M. Hudson, K. W. Kemper, G. E. Moore and M. E. Williams, Phys. Rev. Cl2 (1975) 474 18) W. Henning, Y. Eisen, J. R. Erskine, D. G. Kovar and B. Zeidman, Phys. Rev. Cl5 (1977) 292 19) E. A. Seglie, J. F. Petersen and R. J. Ascuitto, Phys. Rev. Lett. 42 (1979) 956 20) C. W. Glover, R. I. Cutler and K. W. Kemper, Nucl. Phys. A341 (1980) 137