Scattering and charge-exchange reactions with polarized 3He on lithium isotopes

Nuclear Physics A3@ f 1981) ?&92 @ North-Holland Publishing Company

SCATTERING AND CHARGE-EXCHANGE WITH POLARIZED ‘He QN L~HIU~~

REACTIONS ISOTOPES

A. K. BASAK *. 0. KARBAN, S. ROMAN, G. C. MORRISON, C. 0. BLYTH and J. M. NELSON Department qf‘ Physics. University of‘ Birminyhum, England Received 19 February I981 (Revised 13 May 1981) Abstract: Angular distributions of different% cross sections and anatysing powers have been measured for elastic and inelastic scattering as well as the charge-exchange reactions induced by 33.3 MeV 3He on ‘?‘Li. The elastic data have been analysed to deduce the optical-model parameters. The inelastic scattering and charge-exchange reactions have been analysed in terms of both macroscopic and microscopic models. A combination of direct and multi-step processes was required to tit the data. The experimental analysing powers were used to distinguish between various reaction mechanisms.

E

NUCLEAR REACTIONS 6.7Li(3Re, 3He), (%e. ‘He’). [‘He, t)%E = 33.3 MeV; measured G(B), A&@>;deduced optical-modei parameters, reaction mechanism. Enriched 6Li target.

1. Introduction

For the last two decades, ineIastic scattering and charge-exchange reactions have been used extensively to study the properties of nuclei. On the theoretical side, the earliest description of the inelastic scattering was in terms of the collective (macroscopic) model ‘3“) w h’rch a ssumed a non-spherical optical-model potential and led to the solution of a set of coupled equations. In order to apply this model to chargeexchange reactions ‘3 3)1 the optical model was further generalized by including an isospin term 4). The macroscopic model has been successful in the interpretation of inelastic cross-section and polarization data 5- I) as well as cross-section data for isobaric-groundstate (ICS) transitions in charge-exchange reactions 3*8- “1. HOWever, the model has failed to provide a consistent description *) of the isobaricexcited-state (IES) transitions and is unsuitable For transitions to non-anaiogue states, which are also populated in charge-exchange reactions 9V12), To deal with inelastic scattering and charge-exchange reactions consistently, a more comprehensive model, the so-called microscopic model 13*14) has been developed. In the microscopic description, inelastic scattering and charge-exchange * On leave from Rajshabi University, Bangladesh. 74

.4. K. Bad

et d. // Scut/rri~q

und charge t~.vchun~c~

15

reaction data are complementary in extracting the strengths of various terms of the microscopic interaction r4). While the isospin independent terms are expected to dominate in the inelastic scattering, the weaker isospin dependent strengths can be unfolded from the charge-exchange reactions 9. “). From the theoretical point of view, both (p, n) and (3He, t) reactions are expected to provide identical information about the nuclear states; experimentally the (3He, t) reactions have the obvious advantage over the (p, n) reactions in the easier detection of the outgoing particles. On the other hand, the (3He, t) reaction is more difficult to interpret in the microscopic model, as both the projectile and ejectile are composite. The (3He, t) reaction may also proceed via sequential processes as reported in refs. 16-18). Neglect of the possibility of competing sequential processes may seriously affect the extraction of the microscopic strengths. There is also evidence 19) of two-step process via pick-up channels contributing to the (proton) inelastic scattering. With the availability of a polarized 3He beam, it was of considerable interest to investigate the polarization effects in 3He induced inelastic scattering and chargeexchange reactions. In analogy with the one-nucleon transfer reactions, the analysing powers are expected to be sensitive to the total angular momentum transfer J which in the case of spin transfer S = 1 can have generally three values J = L and L + 1, where L is the transferred orbital angular momentum. Furthermore, a simultaneous analysis of the experimental cross-section and AP data might lead to a more reliable extraction of the microscopic strengths. The analysing powers may also provide information on the importance of multi-step processes, particularly in the chargeexchange reactions. Most of the charge-exchange reactions, (p, n) or (3He, t) on lithium isotopes reported earlier 20.21) involved 1ow bombarding energies (5 10 MeV) where the contributions from compound and heavy-particle stripping processes are expected to be substantial 21). The differential cross sections for the 6Li(p, no), ‘Li(p, no) and ‘Li(p, n,) reactions at l&20 MeV were reported by Anderson et al. 22). Assuming the reaction to proceed via a one-step direct process only, the authors deduced the relative strength of the spin-isospin and isospin intereactions 3*r5) without considering any tensor interaction 23). Recent work by Austin et ul. 24) on the 7Li(p, n) reaction at 25, 35 and 45 MeV indicates a substantial role of the tensor interaction. However, Austin et al. did not consider the possibility of a sequential reaction mechanism in the reaction. The 3He induced inelastic scattering and charge-exchange reactions were reported only by Rogers and Wegner 25) at 31.5 MeV and by Givens et al. “j) at 24.6 and 27.0 MeV, but no theoretical analysis was attempted in these studies. The present work reports on measurements of the differential cross sections and analysing powers of the elastic and inelastic scattering as well as charge-exchange reactions induced by 33.3 MeV 3He particles on 6Li and ‘Li targets. The inelastic data have been analysed using the collective and microscopic model coupled-channels (CC) formalism. The charge-exchange reaction data have been treated by the direct and two-step calculations. Exchange effects 27) in the microscopic calculations are

A. K. Basak et al. / Scattering and charge e.vchange

16

not considered and the possible contribution from the sequential process via the intermediate unbound deuteron channels ‘*) is also ignored. 2. Experiment and results The analysing powers were measured using the 33.3 MeV polarized 3He beam 28) from the Birmingham University Radial Ridge Cyclotron while the cross-section data were obtained in a separate run with an unpolarized beam under the same experimental conditions. The details of the experimental set-up and the data reduction method have been given in ref. 29). Self-supporting w 2.4 mg/cm2 thick targets were prepared by mechanical processing of metallic lithium under an argon atmosphere. The 7Li target was made from natural lithium (93 %) while the 6Li target was enriched to 95 %. The target thicknesses were determined from energy losses of 241Am cc-particles and checked by weighing at the end of the run allowing for thin oxygen layers at the surfaces. The corresponding cross-section uncertainties were estimated as not exceeding 15 %. The /

I

6Li136,3He)6Li

I

10

I

30

E ~33.3 MeV

I

50

70

7Li(3$,3He)7Li

I

90

II 10

Ez33.3

MeV

I

30

50

70

90 8c.m.

I

Fig. 1. Differential cross sections and analysing powers of the elastic scattering of 3He by 6Li and ‘Li at 33.3 MeV compared with the optical-model predictions. (a) Predictions for the scattering on 6Li with the potential sets (table I) A (broken curves) and B (solid curves); (b) Same for the scattering on ‘Li with the potential sets E (broken curves) and F (solid curves).

m

6Li[3t% 3He’16Li

E:33.3

MN

60

30

8 c.m.

Fig. 2. Differential cross sections and analysing powers of the inelastic scattering of 3He leading to the 2.185 MeV (3+ ; 0) state in ‘Li and the 0.478 MeV (i- ; f) state in ‘Li. (a) Predictions from the macroscopic CC calculations using pz = -0.75 (solid curves) and the microscopic CC calculations without tensor term (broken curves) and with tensor term (dash-dot curves); (b) Predictions from the macroscopic CC calculations using pz = 0.70 with spin-orbit deformation (solid curves) and without (dash-dot curve), and the CRC calculations using /I’~ = 0.48 and the coupling scheme in fig. 7a (broken curve).

I

I

7L~i!&3H~)7L,

I

/

I

I

E =33.3MeV

1.63 MeV. 7/2-

30

STATE

60

90 9c.m

Fig. 3. Differential cross section and analysing 4.633 MeV (I- ; $) state. Broken curves are the and the coupling scheme in fig. 3b, solid curves bz = 0.50 and the

power for the inelastic scattering of ‘He leading to the predictions from the CC calculations using /?* = 0.70 are the predictions from the CCBA calculations using coupling scheme in fig. 7f.

78

A. K. Basak et nl. / Scatteriny

anti charge e.uchangr

overall energy resolution of about 250 keV was sufficient to achieve reasonable separation of all final states studied. The beam polarization was monitored con30) based on the 3He-d scattering. tinuously in a down-stream polarimeter

2.1. THE

ELASTIC

AND

INELASTIC

SCATTERING

The measured differential cross sections and analysing powers for the elastic scattering of 3He on 6*7Li are shown in fig. 1. Only the strongly populated 0.478 (J”; T = fp ; t) and 4.633 MeV ($- ; +) states in 7Li and the 2.185 MeV (3+ ; 0) state in 6Li were analysed and the results are shown in figs. 2 and 3. There is a striking difference in analysing powers of the elastic scattering and also of the inelastic scattering to the excited states for the two lithium isotopes. On the other hand, the differential cross section data for the ground states are similar and the cross section data of the 2.18 MeV state in 6Li resembles that of the 4.63 MeV state in ‘Li.

2.2. THE (jHe, t) REACTIONS

Only the ground

($- ; 3 ) state transition I

was clearly observed

I

6Li(3%,t)6Be

I

g.s.

T

in the 6Li(3He. t)6Be

/

E = 33.3 MeV

O.L-

30

60 9 c.rn.

Fig. 4. Differential direct, microscopic

cross section and analysing power of the 6Li(3He, t)6Be,,,, reaction compared with model predictions (dashed curves), indirect transition calculations (dash;dot curves) and a combination of both (solid curves).

79

30

60

90

30

60

8c.m. Ftg. 5. Differential cross section and analysing power of the 7Li(3He. t)‘Be reaction for transitions leading to the ground (i- ; f) state and the 0.429 MeV (f- : i) excited state. Solid curves are the predictions from macroscopic calculations without the isospin spin-orbit potential r’:., The AP predictions for the groundstate transition with C’J., = - 14.0 and + 14.0 MeV are also shown as broken and dash-dot curves, respectively. 7L~13i&17Be. I

I

h57MeV(7/2-1 I

I

STATE I

I

Fig. 6. Differential cross section and analysing power of the 7Li(3He. t)‘Be reaction leading to the 4.57 MeV (i- ; f) state. Broken curves are predictions of the microscopic, direct reaction calculations, dash-dot curves for the (3He-a-t) sequential process and solid curves for the CCBA (coupling scheme in fig. 7f) calculations.

80

A. K. Basal

et ~1. / Scarwring and champ rxchange

reaction and the data are shown in fig. 4. In the 32.5-52.5 (lab) angular range the total yield was corrected for contributions from the 4.57 MeV transition to 7Be due to the 4.7 Y0 7Li contamination in the 6Li target. The shape and magnitude of the differential cross section was found to agree with the results of Rogers and Wegner 25). The measured AP for this non-analogue transition exhibit a distinct oscillatory structure. The ground (3- ; t), 0.429 (+- ; 3) and 4.57 MeV (f- ; $) states of ‘Be were found to be strongly populated in the (3He, t) reaction. The cross-section magnitudes for these analogue states of 7Li were substantially smaller than those for the corresponding inelastic scattering. This suggests that the off-diagonal coupling strength 2, in the charge-exchange reaction is much weaker compared to the corresponding strength in the inelastic scattering. The measured cross sections and analysing powers of the reaction to the three states are shown in figs. 5 and 6. It should be pointed out that the polarization effects in the (3He, t) reactions are quite large and the angular distribution pattern differs substantially for different transitions.

3. Formalism applied in the analysis 3.1. THE MACROSCOPIC FORM FACTOR

Details of the formalism involving the form-factor calculations in the macroscopic model are described in refs. 2*3). Only the salient features of the calculations when applied to the (3He, t) reactions are discussed here. The form factor can be written as

Here C#and ilf are the wave functions, labelled appropriately, A is the target mass and t and Toare the isospins of the projectile and target, respectively. The potential U’(v) is the isospin-dependent part 4, of the optical-model potential, which may be complex 3, and include a spin-orbit term 3’). To describe both the IGS and IES transitions, it is necessary to consider deformation of the target nucleus. To first order this leads to

where X = (r-&)/a, R, = r,A* and a is the diffuseness. The first term in (2) contributes to the IGS transition, where L-transfer is zero in this model. The second term is responsible for the IES transition with an angular momentum transfer Z. It is possible to write (1) in terms of raising and lowering isospin operators as

with t+_ = t, + it,. The operator T, can only connect initial and final states of the same isospin with the To= values differing by unity. Thus the macroscopic model is unable to account for the transitions to non-analogue states. 3.3. THE MICROSCOPIC

FORM FACTOR

The detailed formalism involving the microscopic calculations is discussed in refs i6, i7). An effective interaction between 3He and a target nucleon is assumed to be of the form i3. 14,23)

with S = 3F2(a, . v) (aI . Y)-(cT~ . cl) and r = R, - rl. The subscript p refers to a point projectile and 1 to a target nucleon, R, is the space vector of the projectile c.m. and u and z are the spin and isospin operators, respectively. The interaction strength is denoted by V,, where S and Tare the spin and isospin transfers respectively. The corresponding tensor interaction strengths are denoted V’,,,. and V,,,. No spin-orbit interaction is included in eq. (4). In the (3He, t) reactions the terms containing Vol, V, 1 and V,,, strengths contribute, while for inelastic scattering all strengths may be involved with V,, dominant. The tensor term gives a dominant contribution 23, 25) through L = .I+ 1 for transitions involving an unnatural parity transfer (J = L) 1). The Yukawa type of the radial dependence g(r) = exp( -~I-)/PT was applied to natural parity transfers (J = L), while for unnatural parity transfers the OPEP 23, 25) form of interaction was used, 1+ L + ~

h(r) =

[

pr

3

W2

1

g(r),

with V,, = V,,, and p = 0.7 fm-‘. In general the parametrization of the Yukawa and OPEP radial dependence may differ and can lead to different values of V, 1. In what follows the strength of unnatural parity transfers is denoted by V’, 1. The spectroscopic amplitudes were obtained from the shell-model wave functions calculated 47) from the (616)2BME two-body matrix elements of Cohen and Kurath 32). The relevant expression is given in eq. (A.6) of ref. 14). Single-particle radial wave functions were calculated using the standard procedure 48). 3.3. CCBA AND CRC CALCULATIONS

In the coupled channels Born approximation (CCBA) and coupled reaction channels (CRC) calculations, the relative phases of various paths are important. A mixing of collective and microscopic paths often leads to a phase ambiguity. The relative phase has a dominant effect on the analysing powers of the various channels

82

A. K. Busuk et al. i Scartrrinq

und charge r.vchanye

coupled in the calculations and, therefore, fitting of the measured APs was used to resolve this ambiguity. However. this may still leave an overall phase ambiguity with the consequence that the sign of the deformation parameter /l applied in the calculations need not give the correct shape of the nucleus. In the calculations the optical potential parameters were adjusted 19) to compensate for feedback effects to the elastic channel. All the CCBA and CRC calculations were performed with the zerorange code 33) CHUCK3, which was modified to predict the reaction analysing powers. For sequential calculations involving intermediate CI- and d-channels, the spectroscopic amplitudes were again obtained 47) from the two-body matrix elements of Cohen and Kurath 32). In transitions involving the deuteron channels, the tiniterange corrections based on the local energy approximation ‘“) were made. In the (3He, a) channels no such correction was applied, since it is known 35) that this procedure may lead to singularities in the bound-state wave function. The zero-range normalization amplitudes for the ( 3He, d) and (3He, ~1)reactions 225 and 479 MeV . fm*, respectively 34. 46).

4. Analysis 4.1. THE ELASTIC

of the elastic and inelastic

were chosen as D, =

scattering

SCATTERING

The standard optical model was applied to analyse the 3He elastic scattering on 6*‘Li. The search code 37) RAROMP was used to obtain the phenomenological 3He potentials parametrized in the usual way 36) by fitting simultaneously the crosssection and AP data. Two discrete sets of parameters characterized by a different volume integral 36) JR were obtained and they are listed in table 1 (A and B for 6Li, E and F for 7Li). For both targets the spin-orbit potential has been found to be sharply localized at the nuclear surface, as was previously observed for other targets 29, 38). The difference between the ‘jLi and 7Li‘spin-orbit strengths probably reflects differences in other terms of the two optical potentials, although the effect of the target spin, which has not been investigated in the present analysis, cannot be ruled out. The tit to the ‘Li data including the analysing powers is good for both parameter sets E and F (fig. 1). In the case of 6Li, however, the optical-model predictions fail to reproduce the AP data in detail, although the cross-section data are reasonably described as can be seen in fig. 1.

4.2. THE MACROSCOPIC

ANALYSIS

OF INELASTIC

SCATTERING

Inelastic scattering angular distributions to the 2.185 MeV state in 6Li and 0.478 MeV state in ‘Li were first analysed in terms of the collective rotational model using the code 39) ECIS. The deformation parameter BZ and some of the optical-model parameters, in particular the absorption strength, were adjusted to lit simultaneously

x3 TABLE 1 Optical-model parameters Channel

Potential set

C’,

r0

q,

Wv

“He+“Li

A B c D

100.1

I.14 1.11 1.11

0.810 0.685 0.685 0.685

171.0 171.0

3He+7Li

E F G

176.6 146.9 146.9

I.11 1.39 1.39

t+&Be t+‘Be

H I J

130.0 130.0 130.0

1.30 1.30

3He+7Li t+‘Be cc+hLi

Cl c2 c3

a+‘Li

“)

I+‘,,

rw

c(,,.

Lb,,.

16.2 35.4 17.0 25.0

1.12 1.31 1.39 1.39

0.854 0.710 0.591 0.591

1.15 1.44 1.72 1.72

1.36 1.36

0.178 0.178

0.707 0.684 0.684

51.7 29.1 20.0

0.96 1.91 1.91

0.801 0.407 0.407

2.45 5.20 5.20

1.23 I .43 I .43

0.249 present 0.211 work 0.21 I

32.0 34.0 33.0

1.28 t 28

1.30

0.416 0.416 0.416

I .2s

0.952 0.952 0.952

6.25 9.00 5.00

1.62 1.62

0.448 0.448

156.0 149.0 205.0

1.35 1.35 I .42

0.691 0.691 0.650

8.0 20.0 7.0

1.81 1.81 I .85

0.490 0.490 0.600

2.34 2.34

1.44 I.44

0.175 0.175

K

190.0

1.10

0.600

25.0

1.39

0.600

5”

a+“Li

L

190.0

1.42 0.650

6.0

1.39

0.600

ii& )

cc+‘Be

M

90.0

1.34

0.873

“) All depths

175.3 I.11

1.15

7.5

0.810

in MeV and lengths

1.05 0.384 present 1.35 0.292 work

1.62 0.448

51)

4.4

)

6.00

1.15

0.810

)

49)

in fm; I, = 1.3 fm.

bl

3/2%a

3/2 7LI

7Li

7L,

Fig. 7. Coupling schemes used in different calculations: (a) CRC calculations for the inelastic scattering to the 0.429 MeV state in 7Li (subsect. 4.4); (b) CC calculations for the inelastic scattering to-the 0.429 and 4.633 MeV states in ‘Li (subsect. 4.2); calculations involving the multi-step processes for the (3He, t) reactions leading to (c) ‘Be,.,_; (d) ‘Be,,,.: (e) 7Be0.429 Mev and (f) ‘Be,,,, Mev transitions (subsect. 5.3).

A. K. Basak et al. i Scattering

84

and charge, r.rchanqr

the cross-section and AP data. For the 2.185 MeV in 6Li the best fit (solid lines in fig. 2a) was achieved with B = - 0.75 and the parameter set C (table 1). In the calculations for the 0.478 MeV state in ‘Li, the absorption strength in the set F was reduced to 20 MeV (set G in table 1). A value of p2 = 0.70 was necessary to lit the magnitude of the cross-section data. The effect of deformation of the spinorbit term on the AP can be seen in fig. 2b by comparing the solid (no deformation) and dash-dot (deformation included) curves. Although the effect is large (sign reversal at forward angles) the data is poorly fitted in both cases. CC calculations, assuming that the three ‘Li states are members of the K = frotational band, were carried out using the coupling scheme in fig. 7b. The additional coupling has only a small effect on the 0.478 MeV state and the model fails to describe the 4.633 MeV (I-) state data. as is apparent from fig. 3 (dashed curves).

4.3. THE MICROSCOPIC

ANALYSIS

OF INELASTIC

SCATTERING

Assuming an inert a-particle core, the inelastic scattering can be described in terms of recoupling of the valence nucleons in 6Li and ‘Li due to the effective 3He-nucleon interaction. The corresponding CC calculations were performed with the code CHUCK3 and with the parametrization as defined in eq. (4).

TABLE

The 3He-nucleon Reaction

6Li(3He,

‘He’)

6Li(3He, t) ‘Li(‘He,

t)

7Li(3He. t)

interaction Final state

2.185 MeV

strengths Type of calculation coupledchannels

deduced

from

2

the (jHe,

‘He’) scattering

and (3He, t) reactions

Section referred to

Parity transfer

Form of interaction

4.3

natural

Yukawa

unnatural

OPEP

V,, = -120: V ,. = 40 I’,;. = 8.0 v;i = v,,,

Range 11in fm-i

Strengths WeV)

1.0 0.7 = 7.6

0.7

g.s.

direct

5.2

unnatural

OPEP

g.s. and 0.429 MeV

direct

5.2

natural unnatural

Yukawa OPEP

V,, c;,

= V,, = 27.0 = I’,,, = 8.0

0.7

4.57 MeV

direct

5.2

natural unnatural

Yukawa OPEP

V,,, = V,, = 40.0 v;i = V,,” = 10.0

I .o 0.7

1.o

6Li(3He, t)

g.s.

direct + multi-step

5.3

unnatural

OPEP

Vi1 = I’,,, = 7.0

0.7

7Li(3He, t)

g.s. and 0.429 MeV

direct + multi-step

5.3

natural unnatural

Yukawa OPEP

V,,, = V,, = 40.0 v;, = v,,, = 4.5

I.0 0.7

7Li(3He, t)

4.57 MeV

direct + multi-step

5.3

natural unnatural

Yukawa OPEP

Vol = V,, = 40.0 V;, = V,.. = 9.5

I.0 0.7

A.

K. Busak et

a/.

: Sratteriny

and charyr r.t-change

85

The 2.185 MeV state in 6Li can be excited by the S = 0, 1 and T = 0 transitions and therefore only terms containing the I/&, I’,, and r/;L,,strenghts can contribute. These strengths were adjusted to reproduce the cross-section magnitude and the resulting values are listed in table 2. The predictions. which are shown in fig. 2a as broken curves (without I&) and dash-dot curves (with I&), lit the cross-section shape well but the AP is out of phase with the experiment. It is clear from fig. 2a that although the effect of the tensor term is small on cross sections, it can contribute significantly to the analysing powers. The isospin of 7Li being non-zero, all the terms in eq. (4) may contribute to the inelastic scattering to the 0.478 MeV state. Microscopic calculations with the same strengths as used in the 6Li case and assuming Vi, = Vol predicted cross sections an order of magnitude smaller than the experimental data. An unrealistic value is) of k’,, = 450 MeV is required to produce the magnitude of the experimental cross sections. Analysis of the inelastic data to the 4.633 MeV state was not attempted in view of the complexities involved in the calculations and the observed failure of the model in describing the 0.478 MeV transition data. 4.4. EFFECT

OF REACTION

CHANNELS

ON INELASTIC

SCATTERING

Measurements of the 7Li(3He, cr)6Li reactions reported in the following paper 41) indicate the importance of the pick-up channels in the 3He-7Li interaction. To investigate the effect of the a-channels on the inelastic scattering to the 0.478 MeV state in 7Li, CRC calculations were performed using the coupling scheme shown in fig. 7a. The ground (1 ‘) and the 2.185 MeV (3+) states in 6Li were coupled microscopically. The inclusion of the ‘Be states in this scheme is discussed in subsect. 5.3. The modified optical parameter sets used in the calculations are Cl, C2 and C3 for the 3He, tl- and t-channels, respectively (table 1). The deformation parameter was reduced to /3* = 0.48 to reproduce the cross-section magnitude in the inelastic data. The predictions (broken curves in fig. 2b) failed to describe the oscillations in the cross section and the positive analysing powers of the data. However, the AP data are in phase with the CRC calculations. Since the collective model failed to describe the inelastic scattering data for the 4.633 MeV state in 7Li, an exploratory calculation was performed in which the reaction mechanism was extended to include coupling to the $- analogue state in ‘Be (see subsect. 5.3). The ground (3-) and 4.633 MeV ($-) states in 7Li were coupled on the basis of the collective rotational model with no spin-orbit deformation. The deformation parameter value and the absorption strength in the parameter set E were adjusted for a better fit to the cross-section data of both final states. It was found that p2 = 0.5 and WV = 20 MeV were required by the cross-section data. The predictions (solid curves) are compared with the data in fig. 3. Although the CCBA calculationsreproduced the slope of the differential cross section, the fit to the AP data remains poor.

5. The charge-exchange 5.1. THE MACROSCOPIC

reactions

ANALYSIS

The macroscopic model is the simplest way of describing the (3He, t) reactions but it is not suitable for the 6Li(3He, t)6Be,,,, non-analogue transition requiring a T = 1 transfer. The model has been applied to the quasi-elastic (IGS) and quasi-inelastic (IES) transitions in the 7Li(3He, t)7Be reaction. Since the off-diagonal coupling strength 2. 3, is much weaker compared to the diagonal part, the standard DWBA formalism was used in the analysis employing the code 40) DWUCK4. The isospin-dependent part U’(r) of the optical-model potential was parametrized in the same ways as the isospin-independent part. For the latter, the sets F and I (table 1) were used in the entrance and exit channels respectively. The isospin strengths I/’ and Wb were varied to fit the magnitude of the ground-state transition cross section. The prediction shown in fig. 5 for the ground state was obtained with V’ = 180 MeV and Wb = 65 MeV. The large oscillations, which contradict both crosssection and AP data, reflect the L = 0 transfer required by the model. Inclusion of the isospin spin-orbit term Vt.O,= f 14 MeV (dashed and dash-dot curves) did not improve the fit to the AP data. Only L = 2 is allowed in the transition to the 0.429 MeV state in ‘Be and with other parameters fixed by the ground-state transition the magnitude of the cross section was adjusted by varying the deformation parameter BZ. The value b2 = 1.O was used in the calculations, shown in fig. 5. The fit to the cross-section data is poor but the sign and position of the AP minimum are reproduced correctly. The 4.57 MeV state in 7Be can be populated in the reaction via L = 2 and 4 transfers. With all other parameters (including b2 = 1.0) fixed, the deformation parameter p4 was varied in the macroscopic DWBA calculations for the transition to the 4.57 MeV state. The predictions were far off the data both in magnitude and shape and as such are not shown. 5.2. THE MICROSCOPIC

ANALYSIS

In the microscopic one-step calculations using the effective 3He interaction (4), contributions from various (LSJ) triads allowed by the selection rules, were added coherently using the code CHUCK3. The 6Beg.s, is populated by transferring the (011) and (211) combinations of angular momenta, allowing contributions from the V, 1 and V,,, terms only. Since the OPEP form requires I/‘, 1 = V,,,, there is only one variable parameter which can be determined by fitting the magnitude of the experimental cross sections. The error on the resulting value (7.6k2.5 MeV) reflects the uncertainty in the optical-model parameters. The predictions (broken curve in fig. 4) using the potential sets D and H (table 1) reproduced the main features of the data. However, the fine structure in the cross-section data around 40” (c.m.) has not been fitted and there is also disagreement with the AP data at forward angles.

87

0.1

..-iLo

-0.1

I

I

I

I

30

60

:

I

6c.m Fig. 8. Differential cross sections and analysing powers of the 7Li(3He, t)‘Be reaction leading to the ground and 0.429 MeV states, compared with the predictions from the direct microscopic (dashed curves) and indirect multi-step (dash-dot curves) calculations. The coherent sum of the direct and multi-step contributions is represented by solid curves.

The calculations

for the 7Li(3He,

t)‘Be reactions

are more complicated

as both

natural and unnatural parity transfers are allowed involving a large number of (LSJ) triads. Having determined the strengths for the unnatural parity transfers from the 6Li(3He, t)6Be,,,, reaction, the remaining strengths V,,, and V, 1 for the natural parity transfers were varied as above. The range parameter was fixed at p = 1.O fm- ’ and since the calculations were insensitive to the relative strengths of V,, and V, 1, the two values were kept equal. The strengths V,,r = V, 1 = 27.0 MeV deduced from the tits to both ground and 0.429 MeV transition data are within the range of values obtained from other (‘He, t) works lo- 12-’ 5, 18.24.42). However, to reproduce the cross-section magnitudes of the 4.57 MeV transition, both P’,, and V,,,, strengths have to be increased by a factor of 3: The predictions using the potential sets E and J (table 1) are shown as broken curves in figs. 6 and 8 and the corresponding strengths are listed in table 2. Comparing the results of the macroscopic and the microscopic analyses it is evident that the latter provides much better overall fits to the data for the ground and 0.429 MeV states. The failure of both models to tit the 4.57 MeV transition data points either to the spectroscopic amplitudes being incorrectly predicted by the shell model or to a more complicated reaction mechanism.

88 5.3.

A. K. Basak PI al.

MULTISTEP

ANALYSIS

i

Scattering

and c,harqe e.\-chanqr

OF THE CHARGE-EXCHANGE

REACTIONS

In order to investigate the importance of multistep processes in the (3He. t) reactions, calculations were performed involving c1- and d-channels, as well as inelastic scattering. Because of the inherent complexity of such calculations, the initial analysis assumed that the reaction proceeds by sequential processes only. The optical potentials used for CI- and d-channels are listed as the sets K, L and M in table 1. For all four transitions the (3He, c() (CI,t) process was found to be more important than the (3He, d) (d, t) process and, at the same time, comparable to, or stronger than the direct process. This is demonstrated in fig. 6 where the sequential calculations via the intermediate 3+ state in 6Li (dash-dot curves) reproduced the cross section of the 7Li(3He, t)7Be,,,7 Mev reaction. Similarly, the sequential process can account for the strength of the (3He, t) reaction populating the 0.429 MeV state in ‘Be (dash-dot curves in fig. 8) and also improves the fit to the AP data. In the case of the 6Li(3He, t)6Be,.,. reaction the sequential process via the c(channels generates too large cross sections. It was found that this discrepancy can be removed by including the 6Li 3+ state in the calculations. Moreover, this reaction is also significantly affected by the sequential process via the d-channels. The coherent sum of the deuteron and u-channels contributions are shown as dash-dot curves in fig. 4. Similar calculations, involving the first excited states of both ‘Li and 6Li were performed for the 7Li(3He, t)‘Be ground-state transition (dash-dot curves in fig. 8). The predictions reproduce the second maximum in the cross section and the AP behaviour at forward angles. Finally, the direct microscopic transitions (subsect. 5.2) were combined with the above indirect processes in a single calculation using the coupling schemes in figs. 7c-7f. Some adjustment of the microscopic strengths (table 2) as well as optical-model parameters, particularly in the incident channel, was necessary. The coupling between the elastic and inelastic channels was discussed in subsect. 4.4. The spectroscopic amplitudes used in the reaction channels were again kept at the theoretical values (subsect. 3.2). The corresponding predictions are shown as solid curves in figs. 4, 6 and 8. It is evident that the coherent sum of direct and indirect processes results in a superior lit to the data, particularly to the analysing powers for all the (jHe, t) transitions studied.

6. Discussion It was pointed out in subsect. 2.1 that the AP data for the elastic scattering of 3He on 6Li and ‘Li have different patterns, although the two differential cross sections are very similar. It is, therefore, not surprising that the optical model cannot describe the AP data on 6Li and ‘Li simultaneously. Although scattering on light nuclei is not in general expected to be well described by the optical model, the present analysis of the ‘Li data was successful. This is perhaps related to the fact

.t K. Busuh- er cd. , Scuftwhy./ titd churqr c~.rthumg~~

89

that the pattern of the 7Li analysing power data appears “normal” and is practically identical with that of 3He scattering 29) on “Be. The AP pattern for “Li, however, is quite different which may reflect the cluster structure of the 6Li ground state. This possibility has certainly not been taken into account in the standard optical model and for this reason an application of the folding model may be more appropriate in the analysis of 3He+ 6Li scattering. Because of the small quadrupole moment 43) of the 6Li nucleus (Q = -0.08 mb), a microscopic coupled channel analysis of the 3He inelastic scattering by ‘Li would seem to be more suitable than the collective model description. While the differential cross section is reproduced by both models, the AP data clearly favour the latter. Here again, the cluster effects and also a spin-orbit term in the microscopic effective interaction might be important. In view of the large static deformation of ‘Li (Q = - 58 mb), it is su~rising that the collective model could not give a satisfactory fit to the ‘Li inelastic scattering data. It may be that the model can be improved by taking into account explicitly the reorientation of the ‘Li nucleus, as demonstrated recently by Hnizdo et al. 52) who derived the ground-state “self-coupling” strength directly from the intrinsic electric quadrupole moment. An application of the microscopic model led also to difficulties since it required an unphysically large V,, strength. This might be a result of neglecting anti-symmetrizat~on 27) or some multistep processes involving reaction channels. The CRC calculations for the inelastic scattering to the 0.478 MeV state in 7Li suggest that the state is populated substantially via the sequential (3He-a-3He) path. This is reflected in the reduced value of p2 required in the CRC calculations (p2 = 0.48) which is in better agreement with the electric quadrupole moment of 7Li than that obtained in the collective CC analysis (a, = 0.70). The present finding that pick-up channels are important in the inelastic scattering is also consistent with the analysis by Mackintosh 19) of proton inelastic scattering. For the inelastic transition to the 4.633 MeV state a similar value of the deformation parameter p2 = 0.50 was required when the 7Be 4.57 MeV analogue state was included in the CCBA calculations. All the above-mentioned results suggest that the excited states of ‘Li are substantially populated via reaction channels, although the tits obtained in the above calculations still cannot be considered as satisfactory. On the other hand, the present analysis does not exhaust all possible schemes involving various reaction channels. The present paper reports the first measurements of polarization effects in the (3He, t) reactions and the interpretation of the results. During the analysis (sect. 5) it became apparent that the observed differences in the AP data for the four transitions studied cannot simply be attributed to a J-dependence, mainly because the angular momentum coupling allows several combinations of (KU) transfers-and none of these could be singled out as dominant. The macroscopic model, which could only be applied to the 7Li(3He, t)‘Be reaction

90

.4. K. Basak r*f ni. : S(,~iltflrin~

cind

~~u~~~

~.~i,~i~~z~lf~

successfully predicted the features of the cross-section data for the ground-state transition, but failed to describe the AP data. An application of the isospin spinorbit potential did not improve the situation. The non-oscillatory nature of the AP data of this reaction suggests that it may also proceed via additional non-zero L-transfers which, while not permitted in the macroscopic model, are allowed by the momentum coupling rules. It remains to be seen whether the model can describe the analysing powers of an IGS transition from a spin-zero target. For the IES transitions studied in the present work, the failure of the macroscopic model is even more pronounced, thereby confirming the conclusion of Kunz et al. 8). A microscopic analysis assuming a direct reaction process provides a better description of the data for the 7Li(3He, t)7Be reaction leading to the ground and 0.429 MeV states. In particular, the AP data of the ground-state transition are well fitted. However, the microscopic model fails completely to account for the data for the reaction leading to the 4.57 MeV state. The importance of multistep processes in (3He, t) reaction on heavier nuclei has been previously reported i6-i8). The present analysis has established that the (3He, t) reactions on both ‘jLi and 7Li also include a substantial contribution from sequential processes. Combining the direct and indirect contributions leads to markedly improved fits to the experimental data, particularly to the analysing powers. The remaining discrepancies between the predicted and experimental data could be a consequence of the zero-range approximation used in the present calculations. In this respect it has been shown 18.45) that exact finite-range calculations can affect significantly the contributions from the sequential processes. The sensitivity of the analysing power to the reaction mechanism is most clearly demonstrated by the analysis of the 7Li(3He, t)7Be reaction populating the 4.57 MeV (s-) state. As shown in fig. 8, the predictions from both CCBA calculations (solid curves) and the sequential (3He-cr-t) calculations (dash-dot curves) describe well the cross-section data. However, the corresponding AP predictions are completely different and the data clearly favour a reaction mechanism involving inelastic scattering to the s- state of 7Li. In conclusion the present work demonstrates that despite the extreme lightness of the targets both the 3He inelastic scattering and charge-exchange reactions on 6Li and ‘Li can be explained. It is, however, necessary to depart from a simple picture of direct reactions and to involve multi-step processes explicity. The additional information represented by the analysing powers makes it possible to distinguish between various reaction mechanisms. The authors would like to thank tance during part of the experiment. for making-his version of the code regarding the phase ambiguities in

N. J. Davis and R. P. Middleton for their assisThe authors also wish to thank Dr. J. R. Comfort CHUCK available to us and for his comments CRC calculations.

91

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