Charge exchange study with the 40Ca(7Li, 7Be)40K reaction

2.B: 2.N I

Nuclear Physics A313 (1979) 477-484; ~)North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

CHARGE EXCHANGE STUDY WITH THE 4°Ca(~Li, 7Be)4°K REACTION M. E. WILLIAMS-NORTON t, F. PETROVICH, K. W. KEMPER, R. J. PUIGH it, D. STANLEY and A. F. ZELLER t,t

Department of Physics, Florida State University, Tallahassee, Florida 32306, USA Received 24 July 1978 (Revised 20 September 1978) Abstract: Angular distributions have been measured for the (4-, 3-) and (2-, 5-) doublets at ~ 0.0 and 0.85 MeV excitation in 4°K with the reaction 4°Ca(TLi, 7Be)for 7Be in both its ground and first

excited states at ETLI = 35 MeV. Microscopic distorted wave approximation calculations including only a central force do not reproduce the cross sections. Inclusion of a tensor force may resolve this disagreement. E

NUCLEAR REACTION 4°Ca(*Li, 7Be), E = 35 MeV; measured tr(0); compared data with microscopic DWA analysis.

1. Introduction In a recent study of the 2sSi(7Li, 7Be) reaction 1) microscopic distorted wave approximation calculations seemed to indicate that a one-step interpretation of some of the (TLi, 7Be) transitions was possible. To study the (7Li, 7Be) reaction mechanism further, results for the 4°Ca(TLi, 7Be)4°K reaction at 35 MeV are presented here. Microscopic distorted wave approximation (DWA) calculations employing a central force are compared to the data for the first two doublet of states at 0.0 and 0.85 MeV in *°K for 7Be in its ground and first excited states.

2. Experimental procedure Beams of 7Li-, obtained from an inverted sputter source, were accelerated to 35 MeV by the Florida State University Super FN Tandem Van de Graaff Accelerator. Typical beam currents on target were 400 nA. The targets were made of natural CaF2 evaporated onto 10 #g/era2 carbon backings. Reaction products were detected with two A E x E Si surface barrier detector telescopes with A E detector thicknesses t Present address: Physics Department, Ripen College, Ripen, Wiseonin 54971. ,t Present address: Physics Department, University of Washington, Seattle, Washington 98195. t** Present address: Department of Nuclear Physics, The Australian National University, Canberra, Australia. 477

478

M.E. WILLIAMS-NORTON

et al.

of 22 and 15 #m and E-thicknesses of 700 #m. Conventional electronics were used to process the AE and E signals which were then stored pairwise in an on-line computer. The AE and E sigfials were displayed on a storage scope and gates were drawn around the particle groups of interest with an interactive light pen. Because 8Be is not stable enough to reach the detectors, good separation between 7Be and 9Be is possible. The gated events were then sorted into linear energy spectra. The data were taken in a conventional scattering chamber in 2.5 ° steps in the angular range from 15° to 30°. A polar angle of 0.3 ° lab was subtended in these measurements. In the 7Be spectra each peak corresponding to states in 4°K is a doublet because 7Be is detected in its ground and first excited states. Earlier measurements of the 63Cu(6Li, 7Be)62Ni reaction 2) showed differences in the shape of the angular distributions at forward angles for 7Be detected in its ground and first excited states which could be explained by the difference in structure of the two states. The results provided the motivation to extend the (7Li, 7Be) measurements to the angular range 7.5°-15 °. Again, 2.5 ° step sizes were taken. The data were taken in the FSU quadrupole spectrometer. A polar angle of 0.5 ° was subtended, and the efficiency of the spectrometer was determined by normalizing the spectrometer data to the scattering chamber data at 15°. The product of target thickness times solid angle, necessary to obtain absolute cross sections, was found by measuring 20 MeV 7Li elastic scattering in the angular range from 12.5° to 25°. This scattering was within + 770 of Rutherford as found earlier by Bethge, Fou and Zurmiihle 3). The absolute cross sections for the reaction data are + 17 ?/oand arise almost totally from the low yields in the (7Li, TBe) reaction. To calibrate the (7Li, 7Be) spectra, 63Cu(6Li, 7Be)62Ni spectra were measured at several angles, at a bombarding energy of 33.4 MeV. This energy was chosen 4OCa(7Li,rBe) 4OK E 7Li = 35 MeV eLA B =

50 40

15"

'~'11~0 ~1;.'23; ~2~5-Me v Ir -l~ev ]

'

50 m E 3

o 20 I0

500

600 Chonnel

700

Fig. 1. The 7Be spectrum obtained for the 4°Ca(VLi, 7Be)4°K reaction at 35 MeV and 0~.b = 15°.

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479

because the 7Be energies are about the same for these two reactions. A typical 4°Ca(TLi, 7Be)4°K spectrum is shown in fig. 1. The maximum uncertainty in the excitation energies given in fig. 1 is + 30 keV. The two arrows shown for the peaks correspond to 7Be in its ground and first excited states with 4°K in the state or groups of states indicated. The energy resolution was typically 135 keV for this data. 3. Calculations DWA calculations have been carried out for excitation of the 4-, 3- ground state doublet and for the 2-, 5- doublet in 4°K for both (TLi, 7Be0) and (VLi, ;Be1). Form factors for these transitions were calculated using a microscopic, doublefolding model 4) which was used with some success to describe the reaction 28Si(~Li, ~Be)2SA1 at Eta b = 36 MeV [ref. 1)]. In ref. ~) the two-nucleon interaction was chosen to be a Ga~ssian shape. The range and strength of the S = 0, T = 0 part of the interaction was chosen to reproduce the real part of the optical potential for the scattering of 7Li by 28Si. The remaining terms in the two-nucleon interaction were then chosen to be in agreement with the data. In the present calculation the two-nucleon interaction was chosen to be the local representation of the bound state G-matrix obtained by Bertsch et al. 5). This interaction takes the form of a sum of Yukawa potentials which reproduce the even state G-matrix elements of the Reid potential in an oscillator basis 6) and the odd state matrix elements of Elliott et al. 7) taken directly from nucleon-nucleon scattering. Contributions from single-nucleon knockout exchange (SNKE) are approximately included through the introduction of a zero-range term in the interaction which has been shown to be in reasonable agreement with exact calculations of the no-recoil SNKE 8). The interaction takes the explicit forms e-4S e-2.ss Gs=o. T= 1(s) = --4886 4SS + 1175 2~Sss + 310fi(S), e -4s

Gs=I,T=I($) --

-421

4s

e-25s

+480~-

Z.bS

(1)

e-O.Ts

+3.5

0.7~-

- 1456(s).

(2)

This G-matrix interaction along with inclusion of SNKE has been shown to be in general agreement with elastic 9), quadrupole l o), spin-orbit 11), and inelastic 12) scattering. The coordinate s which appears in eqs. (1) and (2) is the nucleon-nucleon coordinate shown in fig. 1 of ref. 4). The 7Li :--, 7Be transitioh densities are the same as those used in ref. 1). The ground state of 4°Ca is assumed to be a pure closed shell. The 4-, 3-, 2-, and 5-, T = 1 levels of 4°K are assumed to be pure lf~ld~ 1 states. Inelastic proton scattering on 4°Ca [refs. ~z, ~)] has found that the effects of configuration mixing in the excitation of T = 1 particle-hole states is generally small. The 4°Ca --. 4°K transition densities were taken to be oscillators given by

M . E . W I L L I A M S - N O R T O N et al.

480

FLtSJ~, l(r ) = ~'~ A/tL~SJ,, 1U lf(r)U la(r), AB AB

(3)

U i f(r) = g - ~-(l~5)½~r3e- ~,2r2,

(4)

4116]~m~.2a.z ~ Uld(r ) = -rr'~ +,15, . . . .. . . .

MLtSJt, 1 AB

~ =

=

r

(5)

4 ( lf~llTL,SS,llld~)

(6)

Jt

41A ~

= 0.536 fm-1.

(7)

The function F~ffJ" l(r) given in eq. (3) is the target radial transition density defined in ref. 4). The geometrical coefficients, ~'~ A~L~SJt. ~, given in eq. (6) are related to singleAB particle reduced matrix elements of the spin-angle tensor T L~s~., which have been tabulated by Bell and Satchler 15). The geometrical coefficients are tabulated in table 1. The value c~ = 0.536 fro- 1 is in close agreement with the value e = 0.53 fro- ~ used by Gillet and Sanderson 16), which was chosen by maximizing the overlap o f the oscillator wave functions with Woods-Saxon wave functions determined from binding energies and elastic proton scattering. TABLE 1 Geometrical coefficients for 4°Ca --~ 4°K transition densities Transition

L~SJt

ML'SJ"IAa

0+__,4 -

314 514

-- 0.318 --0.142

0+--,3

303 313

0.246 0.427

0+--,2

112 312

- 0.724 -0.147

0+~5

505 515

0.439 0.481

The allowed LrJpJ t values for each charge exchange transition under consideration are summarized in table 2. Here L r is the angular momentum transferred to the relative motion of the two nuclei and Jp and Jt are the angular momenta transferred to the projectile and target respectively. The projectile and target transition densities which enter in the construction of the form factor in each case are also shown. The optical potential used (see table 3) was taken from the study of 6Li and 7Li elastic scattering by Cutler et al. iv). As in ref. 1) the same potential was used in both the entrance and exit channels.

~L

©

i

~ m

L

II

O

q~

~Q

~D

r~

482

M.E. WILLIAMS-NORTON i0-1

f

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7

40

et al.

l

4°Co( Li, Be) K Elob: 55 MeV 10-2

7

Total

7

IO o

I

I

I

I

4°Ca(7Li,7Be)4° K Elab: 3 5 MeV 10-3

IO-I

~

N: 6

/

,%._.,, (4-.3-)

L

' ~ ~ . . ~

N=5 x:) 10-2 E

10-2 ~

~ 10-3

E

~ N=5

-o iO- I 7Li '7Be I )

10-2

7~,

10-3~-

I0 -

4

0

~

5-

I0 ' f ~ 2-

~

I0

20

N=2

30

40

50

~

10-31

I

I

i

I

0

I0

20

50

40

50

Oc.m.(deg.)

Fig. 2. Theoretical cross sections for excitations of the ( 3 - , 4 ) a n d ( 2 - , 5 ) doublets in 4°K by the reactions (TLi, VBeo)and (VLi, 7Be0.

Fig. 3. Comparison between theory and experiment for the (3-, 4 ) and (2 , 5 ) doublets in 4°K excited by (TLi, ~Beo) and (TLi, 7Bel). The theoretical angular distributions have been multiplied by the factors shown.

The theoretical cross sections for each of the charge exchange transitions are shown in fig. 2. For the 4 - , 3- ground-state doublet the 3- excitation is slightly dominant for the (7Li, 7Be0) transition. For the (VLi, 7Be1) transition the 3- and 4 excitations are of approximately the same magnitude. Although not shown the (314) transition is at least an order of magnitude larger than the (514) transition for

CHARGE EXCHANGE

483

the 4- excitation in both (TLi, 7Be0) and (7Li, 7Bej. The (303) transition is three times stronger than the (313) transition for the 3- excitation for (TLi, ~Beo). The (303) transition does not contribute to the 3- excitation for (7Li, 7Be1). For both (7Li, 7Beo) and (7Li, 7Be~) the 2-, 5- doublet is dominated by the 2excitation. In both cases the (112) transition dominates the 2- excitation. The total cross sections multiplied by a normalization constant, N, are compared with the data in fig. 3. The agreement with the shape of the data is reasonable for the (4- + 3-)*, (2-, 5-), and (2- + 5-)* excitation. The magnitudes of the calculations differ from the data by as much as a factor of five. For the (4- + 3-) excitation the magnitude of the calculated cross section differs from the data no worse than for the other excitations but there appears to be a definite discrepancy in the shape. The interaction of Bertsch et al. 5) includes tensor terms. Including a tensor term in the nucleon-nucleon interaction may remove the discrepancy in the shape of the (4- + 3-) excitation as well as the magnitude of the cross sections. The magnitude of the cross sections may also be improved by using more correct wave functions. Configuration mixing is not expected to increase the magnitude of the cross sections; it may, however, affect the shape. 4. Conclusions

In this work we have shown that there is no decrease in the magnitude of the (7Li, 7Be) cross section in going from 2sSi to 4°Ca. The major influence on the magnitude of the cross section in this mass region appears to be angular momentum mismatch. The recently measured 4SCa(TLi, 7Be)4SK cross section ~s) is twenty times smaller than that for the 4°Ca(VLi, 7Be)4°K reaction and it has a mismatch of about 5h more than the 4°Ca(TLi, 7Be)4°K reaction. Microscopic DWA calculations with a G-matrix interaction were presented for the excitation of the (4-, 3-) and (2-, 5-) doublets of 4°K by (7Li, 7Be). Although the G-matrix used has been shown to reproduce many aspects of heavy ion scattering, the central components of the interaction do not correctly predict the magnitude of the charge exchange angular distributions considered here. Before any firm conclusion as to the nature of the reaction, microscopic calculations using the tensor components of the interaction used here should be attempted. Such calculations are in progress. References 1) M. E. Williams-Norton, F. Petrovich, K. W. Kemper, G. M. Hudson, R. J. Puigh and A. F. Zeller, Nucl. Phys. A275 (1977) 509 2) G. M. Hudson, K. W. Kemper, G. E. Moore and M. E. Williams, Phys. Rev. C12 (1975) 474 3) K. Bethge, C. M. Fou and R. W. Zurm/ihle, Nucl. Phys. A123 (1969) 521 4) F. Petrovich and D. Stanley, Nucl. Phys. A275 (1977) 487 5) G. Bertsch, J. Borysowicz, H. McManus and W. G. Love, Nucl. Phys. A284 (1977) 399 6) R. Reid, Ann. of Phys. 50(1968) 411

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7) J. D. Elliott, A. D. Jackson, J. A. Mavromatis, E. A. Sanderson and B. Singh, Nucl. Phys. AI21 (1968) 421 8) M. Golin, F. Petrovich and D. Robson, Phys. Lett. 64B (1976) 415 9) W. G. Love, Symp. on heavy-ion elastic scattering, Rochester, New York (1977), and references therein 10) L. A. Parks, K. W. Kemper, A. H. Lumpkin, R. I. Cutler, L. H. Harwood, D. Stanley, P. Nagel and F. Petrovich, Phys. Lett. 70B (1977) 27 11) F. Petrovich, D. Stanley, L. A. Parks and P. Nagel, Phys. Rev. C17 (1978) 1642 12) D. Stanley and F. Petrovich, to be published 13) F. Petrovich, R. Schuffer, H. McManus, C. R. Gruhn, T. Y. T. Kuo, B. M. Preedom and C. J. Maggiore, Phys. Lett. 46B (1973) 141 14) C. R. Gruhn, T. Y. T. Kuo, C. J. Maggiore, H. McManus, F. Petrovich and B. M. Preedom, Phys. Rev. C6 (1972) 915 15) W. K. Bell and G. R. Satchler, Nucl. Data Tables A9 (1971) 147 16) V. Gillet and E. A. Sanderson, Nucl. Phys. A91 (1967) 292 17) R. I. Cutler, M. J. Nadworny and K. W. Kemper, Phys. Rev. CI5 (1977) 1318 18) D. C. Weisser, A. F. Zeller, T. R. Ophel and D. F. Hebbard, Nucl. Phys. A308 (1978) 222 19) D. Stanley, P. Nagel and F. Petrovich, to be published