Polarization effects in the 2H(3He, tp)p reaction at E = 33 MeV

Nuclear Physics North-Holland

A526 (1991) 45-58

POLARIZATION

EFFECTS

IN THE ‘Ht3He, tp)p REACTION E =33MeV SE.

Uniuersity 0.

KARBAN,

AT

DARDEN

of Notre Dame, Notre Dame IN 46556, USA

C. BLYTH,

J.B.A.

ENGLAND.

J.M.

NELSON

and

S. ROMAN

Scl~ool of Physics and Space Research, Universit_vof Birmingham, UK Received (Revised

17 September 16 November

1990 1990)

Triple-differential cross sections and vector analyzing powers have been measured for the for ten pairs of lab angles in the ‘H(-‘He, tp)p reaction at E,, = 32.5 MeV. Data are presented range 6, = 15”-30”, 6, = 20”-55”. most of which correspond to the kinematic region in which the quasi-free ‘He+n+ t+p reaction with the unobserved proton as spectator is expected to be the dominant mechanism. In addition to the usual QFR maximum, most of the energy-sharing distributions of cross section exhibit a smaller maximum at lower energy along the kinematic locus in the E,, E, plane. The analyzing power is generally negative in the vicinity of the QFR peak, but exhibits a maximum in the region between the two peaks in the cross section. This behavior is reproduced by distorted-wave ~mpuise-approximation calculations which include coherently amplitudes corresponding to the cases in which each of the two protons in the final state are the spectator. The best agreement with the data is obtained when the radial integrals are cut off at a maximum radius of - I5 fm. The predicted analyzing powers show little sensitivity to the parameters of the two-body reaction, but rather depend almost entirely on the spin-orbit terms in the distorting potentials, a behavior which is similar to that observed in nucleon-transfer reactions involving a transferred orbital angular momentum of zero.

Abstract:

E

NUCLEAR

REACTION ‘H(polarized ‘He, pt) E = 32.5 MeV; measured a(@,, 8,), vector analyzing power vs arc length. CD, target. PWIA, DWIA analysis. __

1. Introduction In a previous paper ‘) we reported on measurements of the breakup reaction 2H(3He, 3He p)n induced by a 33 MeV polarized 3He beam, and on the analysis of the results using both the PWIA and the DWIA. Most of the measurements were taken for kinematic conditions favorable to the quasi-free-scattering (QFS) mechanism, and the energy-sharing distributions of cross section in the vicinity of the QFS peak were, in most cases, reproduced reasonably well by the DWIA calculations. The vector analyzing powers were found to be small in the vicinity of the QFS peak, and in general agreement with both the PWIA and DWIA predictions. Away from the QFS peak, both the measured and the DWIA-calculated analyzing powers usually have larger values, although no systematic agreement between the data and the calculations was apparent in the analysis. In some instances, the larger analyzing powers occur in kinematic regions where the 3He and the spectator neutron have 037%9474/91/$03.50

@ 1991 - Eisevier

Science

Publishers

B.V. (North-Holland)

46

relative

S.E. Da&n

energies

corresponding

22 MeV. Although

the DWIA

ef al. / Polarization

eflects

to the O- and 2- resonant calculations

states of 4He near E,-

give substantially

better

fits than

the

PWIA to both the shapes and magnitudes of the cross-section data for most of the fifteen pairs of angles for which data were presented in ref. ‘), the analyzing-power data are better reproduced by the DWIA calculations for only a third of the data, and for some of these the improvement over the PWIA calculations is marginal. A clear demonstration of the extent to which the DWIA approach can adequately reproduce the polarization effects thus remains to be made. The present paper contains an extension of the analysis carried out in ref. ‘) to the charge-exchange breakup reaction ‘H(3He, tp)p in kinematic regions where the quasi-free reaction (QFR) 3He + n + t + p is expected to be the dominant mechanism. The charge-exchange breakup reaction differs from the QFS reaction in that Iinafstate effects associated with resonances in 4He may be expected to play a more prominent role since both protons in the final state may interact with the triton. Previous work on the ‘H(3He, tp)p reaction has been confined to cross-section measurements 7m5.7-9),with the exception of the measurements of Meyer et al. “), who measured both vector and tensor analyzing powers for “He(d, tp)p at Ed= 15 MeV. The observed values of A, were relatively small (iA,.\
here were obtained in the same experiment described in ref. ‘), details are the same as those reported there and in ref. 14) of

S.E. Darden et al. / Polarization effects I

I

-QFR-

60 I50 (0 : 40!? ” 30a? 20 -

4

I

I

I

20

30

I

IO 8,

I

40

(degrees)

Fig. 1. Combinations of angles 0, and 8, for which measurements and analysis were made. The solid circles show the pairs of angles for which data are presented in figs. 2-4. The continuous curve shows the locus of angle pairs for which the unobserved proton can be left with zero energy in the laboratory system.

that paper. Although measurements were carried out for more than 20 combinations of triton and proton observation angles, and the data were analyzed for most of these, the statistical accuracy of the data in a few cases was too poor to warrant further analysis. The DWIA analysis was carried out on the data for eighteen angle combinations, ten representative cases of which are presented here. As was done in ref. ‘), the energy-sharing distributions were projected onto the kinematics locus in the E,, E, plane, with the events being summed into bins of energy width equal to 1 MeV. Both cross-section and analyzing-power data are presented as a function of energy, S, measured along the locus in a clockwise direction. Fig. 1 shows the angle pairs for which the DWIA analysis was carried out. The solid circles represent those angle pairs for which data are presented here. The locus of angle pairs for which the quasi-free reaction 3He+ n + t + p can occur with the proton in the target deuteron being left with zero energy in the laboratory system is given by the solid curve. Figs. 2-4 show the results of the measurements. The uncertainties shown are statistical only. The estimated uncertainty in the absolute normalization of the cross sections is about a factor of two. Analyzing power is defined as in the Madison convention lo), with the positive y-axis along the direction of k,x k,, where k. and k, correspond to the incident 3He and the outgoing triton, respectively.

3. Impulse-approximation

calculations

Both PWIA and DWIA calculations were carried out using the program THREEDEE of Chant and Roos ‘I). Modifications were required to permit the use of complex reaction amplitudes for the 3He+n+ t +p reaction in the computation of the two-body t-matrices. Since limited experimental data for the polarization

48

el al. / PolarizaGon

SE. Darden

effects

J

AY

_

0.8

DW2AMP.,-

0.4

c

*

0

.0.4 0.4

ll0

,0.4

0.4

0

,0.4

0.4

I0

0.4

I

IO

I

I

I

20

30

0

S (MeV)

II

I

IO

20

I

30

1&O

Fig. 2. Triple-differential cross sections and vector analyzing powers as a function of energy measured along the kinematics locus for o1 = 15” and f?,,= 20”, 35”, 40”, and 45”. The indicated uncertainties are statistical. The dashed and continuous curves are the predictions of the PWIA and DWIA QFR calculations, respectively. In these calculations, a coherent combination of two amplitudes was used, corresponding to each of the protons in the final state being the spectator. The dotted curves show the results of a DWIA calculation in which only the amplitude corresponding to the unobserved proton being the spectator has been used. For each set of angles, the number, R, by which the two-amplitude DWIA calculation has been multiplied is given. The small arrows indicate where the cm relative energy of the triton and the unobserved proton in the final state has a value corresponding to the O- or 2resonances in 4He at E, - 22 MeV.

observables of this reaction are available, a modified set of the reaction amplitudes calculated by Furutani 12) in his study of the excited states of 4He were used. In his calculations, Furutani used the generator coordinate method with a tri-nucleon-plusone-nucleon cluster model employing realistic effective potentials between the clusters. His phase shifts reproduce most of the experimental data on both 3H(p, P)~H and 3He(n, n)3He to high accuracy for c.m. energies up to 15.0 MeV, but the data on the 3H(p, n)3He reaction are less well reproduced by these calculations. A

SE.

Darden et al. / Pohization

2

0

IO

20

* * bI \

\n

49

effects

i-o.4 2o”/ 50

30

S (MeV) Fig. 3. Measured

and calculated cross sections and analyzing powers for 0, = 15”, tip = 50”, 55” and 0, = 20”, 8,, = 40”. 50”. See the caption to fig. 2.

modified set of Furutani’s complex amplitudes was obtained by fitting the ccosssection 13) and analyzing-power data ‘“1 for this reaction at three energies, using the spin-&on-spin-i phase-shift search program SHOSH I’). For c.m. energies up to 15 MeV, the data can be fitted using only orbital angular momentum values of zero, one, and two. Moreover, no channel-spin mixing parameters are required to fit the data, so the 3H(p, n)3He phase shifts can be used to describe the analyzing power for the m3He, t)p reaction. For use in the calculation of the two-body f-matrices in the DWIA calculations, complex phases for cm energies up to about 40 MeV are required, so a smooth extrapolation of the phases up to this energy was made. There

SE. Darden et al. / Polarization effects

50

DW I AMP. DW2AMP.-

.....

0

20

IO

300

IO

20

30

S (MeV) Fig. 4. Measured

and calculated

is a large uncertainty

cross sections and analyzing powers 0,=45’. See the caption to fig. 2.

in such a procedure,

for 8, = 25”, eP = 45” and 0, = 30”,

but it has little effect on our results

as

is discussed below. In the DWIA program, calcuations are made using two-body f-matrix elements corresponding to 3He+n energies obtained from both the initial-energy and the final-energy prescriptions. The c.m. two-body energy obtained using the initialenergy prescription is larger than that resulting from the final-energy prescription, and it is for the calculations employing the initial-energy prescription that the values of the two-body phase shifts at higher energies are required. However, the results of the initial-energy-prescription calculations are generally poorer than those obtained using the final-energy prescription, and only the latter results are used in the calculations presented here. The optical-model potentials used in the present analysis are very similar to those used in ref. ‘) and are given in table 1. A large number of calculations were made employing considerable variations in all the potential parameters. The parameters given in table 1 are those which provided the best overall fit to the data for those angle pairs where the QFR mechanism appears to be the dominant process. The most pronounced feature of the cross-section data of figs. 2 and 3 is the peak at S -22-25 MeV, which corresponds to a QFR with the unobserved proton as spectator. Also evident in the data are a shoulder on the low-energy side of the QFR peak as well as a secondary maximum at S - 8-9 MeV. Both of these features occur in regions

where the relative

energy

of the triton

and the unobserved

proton

SE. Darden er al. / Polarization effects TABLE

Optical-model Channel

V,

‘He+d t+p

220.0 47.4

parameters

51

1

“) used in the DWIA calculations

a,-

1.45 1.86

“) Notation for the parameters parameters in fm. The imaginary

0.424 0.67

3.0 4.23

1.69 1.76

0.84 0.20

3.0 2.42

1.02 0.94

0.18 0.20

is standard, see ref. “). Well depths are in MeV; radius and diffuseness potential form factor is a derivative Woods-Saxon type.

in the final state corresponds to the resonances in 4He having J” = O- and 2 with resonance energies of 1.3 and 2.3 MeV, respectively. These two resonances contribute strongly to the structure in the cross section and analyzing-power of the ‘H(p, n)3He reaction for cm energies below -3 MeV, and they may contribute in the present reaction by way of a QFR process in which the observed proton is the spectator. At most of the angles for which data are shown in figs. 2-4, the energy of the unobserved spectator proton at the position of the main QFR peak is typically in the range 0.05-0.40 MeV. In comparison, the energy of the observed proton at the position of the smaller peak in the cross section near S - 8.5 MeV is typically in the range 11-16 MeV. Using a Hulthen wave function for the deuteron, one would expect on the basis of the momentum distribution that the peak height in the latter case would be reduced by at least two orders of magnitude below the height of the main QFR peak. However, two effects combine to significantly enhance the peak near S - 8.5 MeV in a DWIA calculation. One is the effect of the distortions, and the other is the fact that the rather low cm relative energy of the ‘He+ n system calculated using the final-energy prescription results in a rather large cross section for the 3He+n+t+p reaction. On the basis of these considerations, we decided to use in the impulse-approximation calculations a coherent combination of two amplitudes, corresponding to each of the two protons in the final state being regarded as the spectator. This was accomplished by including in the coherent sum on the right-hand side of eq. (16) in the 1983 paper of ref. ‘I) the amplitudes calculated for both the case in which the unobserved is the spectator.

proton

is the spectator

and the case in which the observed

proton

4. Results and discussion The data presented in figs. 2 and 3 correspond to angle combinations for which the QFR process with the unobserved proton as spectator is the dominant feature of the cross section. Most of the analyzing-power data in these figures show a characteristic behavior which consists of small negative values of A? in the region of the strong QFR peak in the cross section, together with a positive maximum in

52

SE. Darden et al. / Polarization effects

A, centered around S - 14-15 MeV, below which it becomes negative again. In fig. 4, data are shown for two angle combintations for which the strongest peak in

the cross section proton

as spectator.

appears

to correspond

Three different

to a QFR

mechanism

types of calculations

with the observed

are shown in these figures.

The solid curves show the results of the DWIA calculations employing a coherent combination of the two amplitudes corresponding to each of the two protons being the spectator. For a few representative sets of angles, DWIA calculations in which only the amplitude corresponding to the unobserved proton being the spectator are shown (dotted curves) for comparison. Two-amplitude PWIA calculations (dashed curves) are also shown for a few cases. In the event that the calculated values of the observables exhibit narrow maxima or minima, they have been averaged over the 1 MeV bin width used in projecting the coincidence data onto the kinematic locus. The effect of the finite angular resolution of the detectors was investigated by carrying out calculations for angles differing from the nominal values by amounts comparable to the angular resolution. The differences in the predictions were found to be generally less than the uncertainties in the measurements. The number denoted by R for each set of angles are the numbers by which the two-amplitude DWIA cross sections have been multiplied in making the figures. For all of the DWIA calculations shown, the set of optical-model parameters given in table 1 were used. The radial integrals in the DWIA calculations were evaluated from r = 0 to rmax = 14.0 fm in order to produce a better fit to the crosssection data. The effect of extending the radial integrals out to - 30 fm is to increase the magnitude of the peak cross section by about a factor of two, and to decrease the width of the QFR peak by 25-30%. The main effect on the calculated analyzing power is to shift the maximum in A, to higher values of S by an amount of O-l MeV, depending on the values of Bt and er,. In carrying out the two-amplitude DWIA calculations

the magnitude

of the amplitude

corresponding

to the observed

proton

being the spectator was reduced by a factor of two. Without this reduction, the cross sections for the smaller peaks occurring near S - 8 MeV are overpredicted by about a factor of five. This is not particularly surprising, as the contribution of this amplitude is sensitive to both the shape of the momentum distribution of the neutron in the deuteron and to the distorting potentials used in the calculations. All of the calculations shown in figs. 2-4 were made using the final-energy prescription for determining the energy at which the two-body I-matrices were to be evaluated. When the initial-energy prescription is used, the predictions for the shapes of both the cross section and the analyzing power in the vicinity of the main QFR peak are about the same as when the final-energy prescription is used. In the energy region of the cross-section maximum near S - 8 MeV, however, use of the initial-energy prescription leads to predicted cross sections which are too low by at least an order of magnitude and to analyzing powers which are in most cases more negative than those shown in figs. 2-4. The reasons for these differences are to be found in the kinematics and the off-shell nature of the reaction. In the region of

S. E. Darden

the principal

QFR maximum,

comes

the

from

spectator, typically

amplitude

the cm ‘He+n

where

ef al. / Polarization

most of the contribution

corresponding relative

effects

energies

53

to the cross section

to the unobserved using

the final-energy

in the range 5-10 MeV, with the initial-energy

proton

being

prescription

the are

values being 2-5 MeV larger.

In this energy range, the two-body phase shifts used change relatively slowly with energy, so the f-matrices for the two cases are not very different. In the region of the smaller maximum in the cross section near S - 8 MeV, the dominant contribution comes from the amplitude corresponding to the observed proton being the spectator, and in this case the effect of the off-shell nature of the reaction is particularly pronounced. The cm two-body energies calculated using the final-energy prescription are quite small, of the order of -2 MeV or less, while the energies for the initialenergy prescription are much larger, typically 25 MeV or greater. As a result, the difference between the two prescriptions for calculating the two-body f-matrices in this energy region are large. In fact, the relative cm final energy between the triton and the unobserved proton in this region generally becomes less than the cm threshold energy of the 3H(p, n)‘He reaction (0.764 MeV) over a region of S which is typically - 4 MeV wide and is centered around S - 12 MeV. Since this corresponds to a situation in which the two-body reaction cannot occur, the calculation is aborted in the subroutine which calculates the two-body t-matrices when this happens. The problem can be circumvented by gradually increasing, as this energy region is approached, the calculated two-body relative energy in the final state by an amount sufficient to keep it above threshold at all times. Since the energy dependence of the two-body f-matrix is especially strong in this energy region because of the presence of the O’, O-, and 2- r esonances in “He, the dependence of the predicted cross section and analyzing power on the energy S will depend on the algorithm used to keep the final tp relative energy above threshold. Three different procedures were tried for doing this and the results differ mainly in the predicted values of the cross section in the range S- lo-14 MeV. The effect on the predicted analyzing power is much less than on the cross section and the general trend of A,. is not affected. In view of the somewhat arbitrary way in which the t + punobs relative energy is adjusted to keep it above the threshold energy for the t + p -+ ‘He + n reaction, the detailed cross-section predictions of the two-amplitude DWIA calculations in this energy region cannot be taken too seriously. It is clear from the data and calculations shown in figs. 2-4 that the PWIA calculations (dashed curves) fail completely to reproduce the energy dependence of the analyzing-power data. The predictions of the single-amplitude DWIA calculations are almost the same as those using the combination of two amplitudes for values of S greater than about 18 MeV, but they show no maximum in the cross section near S = 8 MeV and their predictions for A,. differ somewhat from those of the two-amplitude calculations where S is less than about 18 MeV. The cross-section data for the angle pairs Ot/O, = 25”/45” and 30’/45’ shown in fig. 4 are only qualitatively reproduced by the DWIA calculations, particularly in the region where

XE. Dar&n

54

S > 12 MeV. The general two-amplitude

The analyzing-powers

effects

trend of the A, data for these angles is reproduced

calculations,

dent of the two-body

et al. / Polalizutio~

predicted reaction

by the

but only down to S - 8 MeV. by the DWIA calculations

amplitudes

used to describe

are relatively the quasi-free

indepen3He + n -+

t tp reaction. This is illustrated in fig. 5, which shows the effect of using different sets of two-body reaction amplitudes on the predictions of the DWIA for 8,/8r,= 15”/50”, using a one-amplitude calculation in which the observed proton is the spectator. The solid curve is for a normal calculation, i.e., one in which the two-body phases are those used for the calculations of figs. 2-4. When all three triplet P phases are taken to be equal, i.e., no spin-orbit splitting of the P-waves, the results are as shown by the dashed curves. The dotted curve corresponds to all phase shifts being set equal to zero except those for the S-wave. In this case, the analyzing power for the two-body reaction vanishes, as does the plane-wave prediction for A,.. While the cross sections of fig. 5 show considerable dependence on the two-body phases used in the calculation, the analyzing power is relatively insensitive to these parameters, particularly in the region around S- 3 MeV where A, is largest. This insensitivity of A,. to the two-body t-matrix explains why the DWIA calculations are able to reproduce the general trend of the analyzing-power data reasonably well while at the same time providing only a qualitative fit to the cross section over much of the energy region covered by the measurements. I

I

EFFECT

OF

OBSERVED

I

Z-BODY

PROTON

-

NORMAL

- --

ALL 3PJ PHASES

.....

ONLY

PHASES

IS

SPECTATOR

-

CALCULATION

S-WAVE

EQUAL PHASES

f 0

S(MeV) Fig. 5. DWIA calculations showing the effect of using different phases for the n(“He, t)p reaction. The calculations arc for 8, : 20”, 0, = 40” with the observed proton as spectator. The solid curve is for a normal calculation, i.e., the phases are as in the calculations for figs. 2-4. The dashed curve is for the case in which all three triplet P-phases are equal, and the dotted curve is for a calculation in which only the L = 0 phases are non-zero.

55

S.E. Darden et al. / Polarization effects

The measured if spin-orbit

analyzing

powers

terms are included

are reproduced

by the DWIA

calculations

only

in the optical

potentials used to represent the 3He-d in the final state. If these interaction in the initial state and the tpqpec interaction spin-dependent terms are absent, the analyzing powers predicted by both the DWIA

and the PWIA are just those for the quasi-free ‘He+n+ t + p reaction, which, for the kinematic regions involved in the present measurements, are in most cases small in magnitude and show little dependence on S. Fig. 6 shows the effect on the calculated A,. of the spin-orbit terms in the ‘He-d and tp optical potentials. The calculation is for 0,/ ep = 1Y/40” with the unobserved proton as spectator. The solid curve shows the predicted A? when spin-orbit terms are present in both the “He-d and tp potentials, and the dashed curve results when only the tp potential contains a spin-orbit term. When no spin-orbit terms at all are present, A, is given by the dotted curve, which is identical to the plane-wave prediction. The cross section is virtually unaffected by the spin-orbit terms. It is clear from fig. 6 that the observed analyzing power is almost entirely a consequence of spin-dependent distortions, principally in the ‘He+d channel. This dependence of Ay on the L.S terms in the optical potentials is very similar to what occurs in single-nucleon transfer reactions when the transferred orbital angular momentum is equal to zero. In the DWBA theory lh) of transfer reactions, the vector polarization effects in such cases arise entirely from the spin-dependent terms in the optical potentials, unlike the case of non-zero transferred orbital angular momentum, for which spin-independent distortions alone can give rise to vector-polarization effects. In the breakup reaction, it is the difference between the plane-wave and the distorted-wave predictions for A) which arises from the spin-dependent part of the distorting potentials. This result

‘He+d -V,,=3 V,,=O . . . . . . Vso’ 0

---

‘Ht3He,t

t+P 2.4

p)

p

B+ =15O 8,:40°

2.4 0

AY

0.4 0.2 0 -0.2 -0.4

30 IO S (MeV)

20

30

Fig. 6. DWIA calculations showing the dependence of the cross section and analyzing power on the spin-orbit terms in the ‘He-d and tp optical model potentials. The calculations are for 0, = 15”, 0,, = 40”. The depths of the spin-orbit potentials are in MeV.

S.E. LAwden et al. / Polarization

56

effects

can be understood in terms of a simple physical model similar to the Newn’s model “) of polarization effects in transfer reactions. In the QFR picture of the present involved

reaction,

if one ignores

in the two-body

the D-state

reaction

of the deuteron,

is bound

to the target

the fact that the neutron core (the proton

in the

deuteron) in an S-state means there can be no correlation between the neutron’s spin direction and the region of the target nucleus where the QFR takes place. As a consequence, there will be no effective polarization ‘*) of the neutron in the deuteron, and in the absence of spin-dependent distortions the only analyzing power is that which occurs in the two-body reaction. The similarity to the Newn’s model of this simple picture of the polarization effects in breakup reactions was first pointed out by Jacob et al. I’). All of the calculations shown in figs. 2-6 were made assuming the deuteron to be in a pure S-state. An attempt was made to obtain a rough idea of the effect of taking into account the D-state of the deuteron using a single-amplitude (unobserved proton as spectator) calculation for f?,/&iP= lY/40” in which the results of a calculation assuming a pure D-state deuteron were combined coherently with those calculated for a S-state deuteron. The coherent combination was obtained by using amplitudes proportional to the square roots of the cross section and the product of cross section and analyzing power, and combining these amplitudes for the S- and D-wave calculations. The amplitudes for the D-state calculation were multiplied by were carried out 0.224 to provide a D-state probability of - 5%, and calculations for both signs of the D-state amplitudes relative to the S-state values. Aside from a - 2 MeV wide energy region near S = 15 MeV, the general shapes of both the cross section and analyzing power resulting from these calculations is not significantly different from those of a pure S-state calculation. The largest differences between the combined calculations and the pure S-state calculations occur near S = 15 MeV, where the pure D-state cross section is an order of magnitude larger than the pure S-state cross section. Even after taking into account the rather small amount of D-state probability, the cross section in this energy region is appreciably affected when the D-state is included in the calculation, but little can be concluded from this, since this energy region is where the DWIA calculations seriously underpredict the cross-section data in any case. The width and height of the narrow peak in A, near S = 15 MeV are also considerably altered when the D-state is included in the calculations, but the results of such a crude approximation have little or no meaning when the S- and D-amplitudes are of comparable magnitude. Any conclusion as to the effect of the D-state on the peak in Ay will have to wait until a reliable calculation is available. The average value of the normalization factor R for the data of figs. 2 and 3 is about 1.5, which is the order of magnitude expected if the optical potentials are representing realistically the initial- and final-state distortions. The depth of the real central potential for the ‘He-d channel is about 15% greater than that used in ref. ‘), but the radius parameter is about 10% smaller, so that the overall strength is less

S. E. Darden et al. / Polarization effects

than

that

used

in ref. ‘) by about

6%. An obvious

shortcoming

51

of the

DWIA

calculations presented here is that they do not predict the observed shoulder on the main QFR peak in the cross sections, and they predict only qualitatively the smaller peak near S - 8 MeV. It is probably expecting too much of a DWIA calculation at this low an energy and for such light nuclei to quantitatively fit the data in a kinematic region where off-energy-shell effects are so pronounced. A more sophisticated approach will probably be required to reproduce all of the features of the data. The maxima in the cross section near S- 8 MeV appear to be final-state enhancements corresponding to the O- and 2- resonances in 4He. As such, they could probably be incorporated into the calculations in an ad hoc way by using resonance amplitudes similar to those employed by Bruno et al. ‘). However, there are several other 4He resonant states which may be contributing to the cross section in the region of the main QFR peak, and a consistent treatment would have to include these states as well. In any case, it can be argued that the DWIA calculations already take account the 4He resonances through their use of the t-matrices for the n(3He, t)p reaction, so that the inclusion of additional resonance amplitudes would be redundant.

5. Conclusions Data have been presented on the charge-exchange breakup reaction ‘H(3He, tp)p initiated by 32.5 MeV polarized ‘He for ten combinations of triton and proton observation angles in the range 0, = 15”-30”, tip = 20”-55”. For eight of the ten data sets, the energy-sharing cross sections are characterized by a strong peak corresponding to the quasi-free reation n(‘He, t)p with the unobserved proton as spectator. A smaller peak is also observed, displaced toward lower energy along the kinematic locus in the E,, E, plane. The analyzing power is generally negative in the vicinity of the strong QFR peak, and increases to a maximum with A, - 0.2-0.4 in the region between the two peaks in the cross section. The analyzing-power data, and to a lesser extent the cross-section data, are reasonably well reproduced by DWIA calculations which assume the QFR to be the dominant mechanism. A coherent combination of two amplitudes is used in the calculations, corresponding to each of the two protons in the final state being the spectator. Best agreement with the measurements is obtained when the radial integrals are cut off at a maximum radius of r - 15 fm. The calculated analyzing powers are relatively insensitive to the details of the two-body quasi-free reaction, but rather are a consequence of the spin-orbit terms in the distorting potentials, a situation similar to what occurs in nucleon transfer reactions having a transferred orbital angular momentum of zero. The authors would like to express their appreciation to Prof. N.S. Chant for providing the program THREEDEE and for some useful discussions. We also acknowledge the help of John Metcalfe during the early stages of the analysis. We

58

SE.

Darden et al. / Polarization

effects

are grateful to Prof. George Morrison for his enthusiastic support of this research. Partial support of this research was provided by the U.S. National Science Foundation under Grant No. PHY88-03035. Note added in proof: After submission of the manuscript, an error was in the procedure used to combine coherently some of the amplitudes in ref. ‘I). The correct calculations differ very little from those of figs. 2-4, effect being to increase the predicted values of A, for S> -25 MeV by of about 0.09.

discovered eq. (16) of the largest an average

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