Tensor analysing power of (d, 3He) and (d, t) reactions and the D-state of the tri-nucleon system

Nuclear Physics A405 (1983) 69-87 @ North-Holland Publishing Company

TENSOR ANALYSING POWER OF (d, 3He) AND (d, t) REACTIONS AND THE D-STATE OF THE TRI-NUCLEON SYSTEM F. ENTEZAMI +,J. D. BROWN ++,J. M. BARNWELL, K. S. DHUGA +++,0. KARBAN, J. M. NELSON and S. ROMAN Department of Physics, The University of Birmingham, England Received 3 March 1983 Abstract: Tensor analysing powers of the (d, 3He) reaction on “F, %k, 63Cu, 64Zn and (d, t) reaction on 63Cu and 64Zn have been measured at 12.4 MeV incident deuteron energy. The results were compared with tbe ,DWBA theory including the D-state term in the tri-nucleon wave function expressed by the Dz parameter. The x2 criterion was applied to determine the value of the D, parameter. The effect of the tensor spin-orbit term Ta in the deuteron optical potential was investigated. The inclusion of the TR term lowers the magnitude of the “best fit” Rz value in all cases and the results for (d, t) and (d, ‘He) are very similar and in accordance with recent theoretical estimates.

E

NUCLEAR REACTIONS “F, ?Sc, 63Cu, “4Zn(polarized d, 3He); 63Cu, G”Zn(polarized d; t); measured c(e), iT, i, ‘1”0,T,, ; deduced tri-nucleon wave function D-state parameter. Natural i9F / ?5c >enriched ‘%u, 64Zn targets.

In recent years a number of tensor analysing power measurements have been made for (d,p) reactions, showing their pronounced sensitivity to the D-state (L G 2) component of the deuteron wave function id8). This effect has been successfully treated by the distorted-wave theory 9,10), which predicts a large tensor analysing power at small reaction angles due to the deuteron D-state, in agreement with experiment. Calculations with a pure S-state deuteron wave’ function grossly underestimate the observed tensor analysing power. With the high quality of the experimental data recently available, the asymptotic D- to S-state deuteron wavefunction ratio has been extracted reliably from DW analyses and the value obtained is consistent with theoretical two-body calculations assuming realistic NN forces l1 ).

+ Present address: TRIUMF, Vancouver, BC. ++ Present address: IUCF, Bloomington, Indiana. +++Present address: University of Pennsylvania, PhiIadeIphia, Pa. 69

70

F. Entezami

et al. J Tensor analyzing power

It has been shown r2,13) that in a (d, t) or (d, 3He) reaction the contribution of the incident deuteron D-state wave-function component is negligible in comparison with that of the outgoing tri-nucleon D-state wave function. Thus calculations are performed within the framework of the DWBA, utilising the local-energy approximation which incorporates the tri-nucleon D-state only via the D, parameter. The D2 parameter is a measure of the asymptotic D- to S-state ratio in the tri-nucleon (deuteron plus nucleon) wave function. Previous studies of the trinucleon wave function have concentrated on the (d, t) rather than the (d, 3He) reaction, and it has been shown that the D-state is necessary to describe the tensor analysing power data by DWBA calculations. By varying the D, parameter in the calculations and comparing the results with the tensor analysing power data a “best-fit” value for D, is determined. Resulting D, parameters have been found to be inconsistent and the agreement with theoretical predictions has been indecisive in both magnitude and in the value of the D2(3He) to D2(t) ratio. Although the Coulomb interaction of 3He is different from that of the triton the theoretical estimates of the ratio of the two D, values are close to unity. Experimentally derived D, values range from -0.21 to -0.296 fm2 for (d, t) reactions whereas for (d, 3He) the spread is from -0.17 to -0.37 fm’. Theoretical estimates are found to be in the region -0.22 to -0.24 for both (d, t) and (d, 3He). Suggestions have been put forward which indicate possible discrepancies in the treatment of the data. It has been proposed 14-i8) that the tensor potential terms in the deuteron channel may play an important role in evaluation of then D, value. First calculations including the tensor deuteron optical potential term as a correction have been performed by Seichert et al. ig) for the 208Pb(d, t) and 65Cu(d 23He) reactions, showing that the introduction of the TR term increases the magnitude of the predicted tensor analysing power, especially at large reaction angles, thus lowering the derived D2 value. A DWBA programme provided with the facility to include the deuteron tensor TR and TL terms has been developed by Tostevin 20), and calculations ‘I) with this code confirmed that the effect of the TR term is to increase the magnitude of the predicted tensor analysing power. A further question is the validity of the use of the local-energy approximation in the DWBA treatment. The local-energy approximation (LEA) is known ‘“) to be invalid for large values of momentum transfer and therefore analysis of backwardangle data, where the momentum transfer is greater, should be performed in the context of the “exact-finite-range” DWBA. Ioannides et al. “) have shown that when exact-finite-range calculations are performed the effect on the predicted tensor analysing power of the 64Zn(d, 3He)63Cu and 64Zn(d, t)63Zn reactions is manifest primarily at large angles and is more apparent in the T,,predictions where the disagreement with LEA calculation can be as high as 35 “/,. Some of the previous evaluations of the D, parameter have been carried out using large-angle data and also the local-energy approximation whilst others have been performed

F. &termi

ei d. ! Tmxw andyzirig

puwer

71

on light nuclei. These results should therefore be viewed with caution in the light of the use of the LEA at such large angles and also the possible introduction of compound effects into the usually assumed direct reaction mechanism. The previously published Dz parameter values appear to be inconsistent : some of the values obtained at Wisconsin 15s18*23) are appreciably larger than those determined from measurements at Birmingham 25), Wisconsin 26) and Munich I’), where the smaller magnitude D, value is in agreement with theoretical predictions. In the present work, measurements of the analysing powers iT,,, T,, and Tz2 have been carried out for (d, t) reactions on 63Cu and 64Zn and (d, 3He) on “‘F, 45Sc3 63Cu, and 64Zn. The ef$ect of the tensor potential TRin the deuteron channel on the “best-fit” f)z value is investigated by performing DWBA calculations including the real and ~ma~nary FR tensor terms and varying the D, parameter; the results are compared with predictions of similar calculations when the tensor terms were set to zero.

2. Experimental method and results The measurements were carried out using the 12.4 MeV tensor-polarised deuteron beam from the atomic-beam ion source on the University of Birmingham Radial Ridge cyclotron. The e~~er~ental method involved rapid three-way switching of the ~olari2ation state of the beam by means of the high-fre~ne~c~ transitions at the ion source and azimuthal rotation of the scattering chamber by 90”. Beam polarization was monitored continuously in a polarimefer placed upstream with respect to the scattering chamber and using the 12C(d, p,)13C reaction as an analyser. In addition to the normal polarimeter, another of the same con~guration was placed downstream of the scattering chamber. From these two polarimeter readings it was possible to check if any depolarisation of the beam accrued from its passing through either the polarimeter or chamber target. These results were cross-checked with data taken in the main scattering chamber with a centralfy placed “C target and with the protons detected by detector telescopes at the same angle as the polarimeter. The tensor analysing power of the t2C(d, p)“C polarimeter has been determined from comparison with the high-precision 3He(d, p)“He datum at O” of Gruebler et al 24). The “left-right” and “up-down” asymmetries were obtained in separate runs for each scattering angle. Details of the arrangement and the data reduction method have been described previously *). The reaction products were detected in four silicon AE x E detector telescopes, spaced 10” apart and mounted on two rotatable arms, set at symmetric angles Sr8 with respect to the incident beam direction. Due to the negative Q-values of the (d, 3He) reactions it was necessary to use thin (30 qt) At; detectors to identify the low-energy 3He particles. The signals produced by each detector telescope were processed in analogue particle-iden~~er circuits providing suitable “mass” signals

F. Entezami et ai. / Tensor ~na~yz~~ power

_ ENERGY

(G S-1

d

!I

175

200

225

Ch. NGff

Fig. 1. A typical “mass” and “energy” spectrum of “He particles from the 63Cu(d, 3He)62Ni reaction at 12.4 MeV incident deuteron energy at an angle of 25”.

for routing the total-energy signals into the online computer interface according to the mass of the particles. A typical mass spectrum is shown in fig. 1. The experimental difficulty of the identification of the low-energy and low-intensity 3He particles in the presence of an intense flux of a-particles from (d, a) reactions whose Q-values are positive, was minimised using additional single-channel analysers thereby rejecting the high-energy a-particles prior to the mass separation of ‘He and ol-particles. The following targets were used: (i) ‘%c, natural, self-supporting, 2.0 mg/cm2 ; (ii) 63Cu, 99.5 7; enriched, self-supporting, 2.0 mg/cm’; (iii) 64Zn, 98.5 % enriched, self supporting, 2.0 and 1.0 mg/cm’ ; (iv) 19F, natural “Teflon” film. The latter suffered damage under bombardment with the beam current of 30 nA and had to be frequently replaced; this did not affect the analysing power measurements but the cross section could not be reliably determined. The transitions studied are listed in table 1 and the experimental angular distributions are shown in figs. 2, 3 and 4. The uncertainties of the cross-section data include in addition to statistical errors, uncertainties of target thickness, target angle and the solid angles of the detectors. The uncertainties of the analysing power data show statistical errors

F. Enterami et al. / Tensor analyzing power TABLE

Summary Reaction

Tll(&

%k(& 3He)44Ca 19F(d, 3He)180

A

j;

A,

1tr

0.0 0.0 0.0 0.41

-2.214 - 5.599 -0.631 -4.638

0+ 0+ J:-

3s;+ 2+

3 5 7I t

1 1

0.0 0.0

- 1.395 - 2.499

:2 1+ z

0+ 0+

2 4

3 0

1 1

lqF (d ,3He I'*0

45Sc( d :3Hej44Ca /

studied

Q WV)

E,

tpzu

1

of the transitions

(MeV) “4Zn($, ‘H~)‘%I 64Zn(d, t)“‘Zn “‘CL@, 3He)62Ni

73

I

20

LO

60

80

C.M. Fig. 2. The vector and tensor analysing powers of the ?k(d, 3He)44Ca(g.s.) (C, = 3 ; j,, = 5) and at E, = 12.4 MeV. The lines are DWBA predictions 19F(d, 3He)180(g.s.) (I,, = 0; j,, = f) reactions including the 3He D-state contributions with D, = -0.21 fm’, calculated using the optical-model parameters given in table 2 for TR = 0.

20 LO GO 80 0” C.M.

20 20

60 80

Fig. 3. Differential cross sections and anaiysing powers of the 63Cu(d, 3He)6”Ni(g.s.) and %&(d, tJ6Q E, = 0.041 McV reactions at E, = 12.4 &ieV, both with I,, = 1; j,, = 3. The lines are DWBA predictians including the “He(t) D-state contributions with D, = -0.21 fm’. calculated using the optical-model parameters given in table 2 for TR= 0.

only; in add.ition they are subject to an overall normalization uncertainty of 12 “/,. The observed tensor analysing powers are large, reaching values of 0.3 but regular oscillatory patterns are not established. The magnitude of the tensor analysing power is clearly too large to be explained by distorted-wave calculations without D-state effects, which predict negligible tensor analysing power values. Whereas the analysing powers of the E, = 1 and E, = 3 transitions are larger than those of the 1, = 0 reaction on 19F, the features of the vector and tensor analysing power angular distributions of the latter tr~sition are sharper than those observed for the other reactions. The measurements for the 64Zn(d, t)h3Zn(g.s.) and 64Zn(d, 3He)63Cu(g.s.) reactions cover an angular range from 20” to 145”(Iab). Compa~son of the small-angle data for the 64Znfd, 3He)“3Cu reaction with those of Brandan and Haeberli 23) at a slightly higher (13 MeV) energy, shown in fig. 5, reveals that the two sets are disparate. The recalibration of the polarimeter discussed above, and searches for possible depolarization effects have confirmed the present tensor analysing power values and failed to reveal the cause of the observed difference.

F. Entezami et al. / Tensor analyzing power

6LZn(d,kef3Cu

6’Zn[d,tf3Zn

9.5.

g.s.

r------l

Fig. 4. Differential cross sections and analysing 64Zn(d, t)63Zn(g.s.) reactions at E, = 12.4 Me%‘, both predictions including the 3He(t) D-state contributions optical-model parameters given

powers of the “%(d, 3He)63Cu(g.s.) and with l,, = 1; jf, = 3. The lines are DWBA with D, = -0.21 fm’, calculated using the in table 2 for Ta = 0.

3. DWBA analysis

The DWBA calculations were carried out using the local-energy approximation which is known to work reasonably well for calculations of the D-state effects in low-energy (d, p) reactions 1,4,7*8) and for (d, t) and (d, 3He) reactions for not-too-

F. Entezami

et al. / Tensor analyzing power

_-O-l

-1 0.2 I

30

90 Ref.15

Fig. 5. Comparison 64Zn(d,3He)63Cu(g.s.)

150

(13MeVl

I

I

30 o”c.

m.

I 150

I

90 1

present

I

data

of the present measurements of the tensor analysing powers TzO and Tzz of the reaction at 12.4 MeV incident deuteron energy with the data of Brandan and Haeberli 23) at 13 MeV.

large scattering angles 25,26). The magnitude value of a single parameter 9, D, given by

of the D-state

effect depends

on the

which determines the asymptotic D-state to S-state ratio in the wave function of the proton relative to the deuteron in 3He. Present calculations were carried out using the computer code TRCODE 20) which is an adaptation for .(d, t) and (d, 3He) reactions of the programme described by Harvey and Santos 27). This code incorporates the two deuteron tensor potentials TR and TL of which only the TR term is expected to be significant as a consequence of the D-state of the deuteron 30). It has been shown 28) that at the low energies used here the effects of Tp are very similar to TR.The transferred nucleon wave function was generated in a Woods-Saxon potential with parameters r 0 = 1.25, a, = 0.65 fm and V,,,. = 6.0 MeV. The depth of the central potential was adjusted to give the correct binding energy of the transferred nucleon. All the calculations were performed with no radial cut-off allowing the radial integrals to extend to 20 fm including 15 partial waves. Predictions of the tensor analysing powers were obtained with a D, value that was varied from -0.46 to -0.06 fm2 in steps of 0.02 fm2. The “best-fit” D, parameter was extracted by employing a x2 criterion for all the values of the D2 parameter used.

3.1. THE ?Zn(&

The interest

t)63Zn AND

64Zn(& 3He)63Cu

REACTIONS

in these two g.s. reactions

lies in the fact that

the final states

are

F. Emtezami et al. 1 Tensor analyzing power

17

both populated by a 3- transfer for which the spectroscopic factors are similar ?). Therefore a study of these reactions would yield information on the ratio D,(3He) to Dz(t). Optical potential sets were taken from literature and it was found that the deuteron potential which best reproduced the reaction data was that due to lBurgi et al. 29), whilst the 3He and triton potentials were those used by Brandan and Haeberli 23); the potentials used in the present calculations are given in table 2. The deuteron potential incorporated both a real and an imaginary TR term whose radial variations contained the second and third Woods-Saxon derivatives respectively 30). It was found that this potential also reproduced the trend of the elastic scattering data reasonably well. An investigation into the effect of an imaginary spin-orbit term on the tensor and vector analysing powers revealed that its exclusion from the calculation had only a minimal effect on the predictions and hence it was neglected in subsequent calculations. An increase in L), produced an increase in the predicted Tzqma~itude which was approximateIy linear as can be seen in figs. 6 and 7. In the case of the 7& predictions all the calculations produced the same cross-over point on the 7& = 0 axis. The introduction of TR in the deuteron channel caused very little effect on the shape of the predicted distributions as seen in figs. 6 and 7, but increased the magnitude of the tensor analysing power thereby producing a smaller (in magnitude) “best-lit” D, parameter. The “best-fit” D, parameter could be determined from the x2 plots obtained from DWBA calculations with D, values varied in steps, as shown in fig. 8. These calculations were carried out both with and without the deuteron tensor spin-orbit potential TR. The “best-fit” D, values are listed in table 3. From fig. 8 it can be seen that the introduction of the TRterm reduces the magnitude of the “best-fit” D, parameter and improves the fit to the data. The vector analysing power predictions were less affected by changes of the D, parameter. 3.2. THE Wu(d,

3He)62Ni AND Wu(d,

t)62Cu REACTIONS

The 63Cu target was chosen for the comparatively high Q-value (Q = -0.631 MeV) of the 63Cu(d 3He)62Ni g.s. transition which is unique in this mass region. The DWBA calculatfons were carried out for the I, = 1, j = 3 transition using all possible combinations of five incident deuteron and four outgoing channe1 opticalmodel parameter sets given in the literature 31). The results of the calculations without the tensor terms were found to be more sensitive to the choice of the deuteron potential parameters than to the outgoing channel (3He, triton) potentials. This may indicate that the deuteron potentials have been forced to compensate for the lack of the tensor terms in these calculations, hence the predictions were less affected by the changes of the 3He and t parameter sets. The tensor potential TR used in the deuteron channel was taken from ref. 30) in preference to that used in ref. I’). This potential along with the exit channel

38.34” (1.4 38.34” (1.4

163.45 (1.2 ;0.72) 163.45 (1.2 ;0.72) ;0.84) iO.84)

;0.84 ) ;0.84 ) ;0.88 ) ;0.63)

_

%I

2.5 (1.2 2.5 (1.2

2.5 (1.2 2.5 (1.2 2.5 (1.2 7.4q1.3 ;0.72) ;0.72)

;0.72) ;0.72) ;0.72) ;0.2 )

4.4 (0.76 :0.25) 5.76(0.706; 0.5 ) 7.0 (0.75 ;0..5 ) X56(0.89 ; 0.39)

Ursa

All potential depths are in MeV with the radii and diffusenesses in fm. “) Volume and surface forms are denoted by a V and D superscript, respectively.

t f6ZCU

“1

(1.41 ;0.76 ) (1.333 ; 0.703) (1.38 ;0.66 ) (1.58 ;0.599)

4

t +%n

14.61n 18.4O 16.03D 13.32n

Wrb

4K3v (1.4 41.8” (1.4 43.495”(1.4 20.13” (1.71

(1.14;0.8 ) (1.08; 0.86) (1.05 ; 0.86) (1.0 iO.95)

‘%i

154.02 (1.2 ;0.72) 154.02 (1.2 ;0.72) 154.794( 1.2 ; 0.72) 164.87 (1.16;0.69)

94.18 106.01 103.72 97.1

V,trR,

‘He+‘j3Cu 3He+62Ni 3He+44Ca aHe+‘%

d fe4Zn d+63Cu d+45Sc d+‘sF

Channel

_

1.73(1.59;0.2) 1.73(1.59; 0.2) 1.73(1.62;0.2) 1.73(1.62; 0.2)

VTn@TR+ uTR)

Optical-model parameters used in DWBA calculations

TABLE 2

_

_

2.9q0.99; 2.9qo.99; 2.9qo.99; 2.98(0.99;

0.37) 0.37) 0.37) 0.37)

vTR~~rT,?~’ aTng)

F. Entezami

et al. 1 Tensor analyzing power

79

T22,

30

90

‘50

30

r\o

90

150

I=I c.m. Fig. 6. The effects of the tensor potential TR and variation of the D, parameter on the tensor analysing by DWBA using the powers of the 64Zn(d , 3He)63Cu(g.s.) reaction. The curves have been calculated optical-model parameters of table 2 and varying the D, parameters in steps between D, = -0.16 and D, = -0.36 fm’. The “best-fit” D, values obtained are given in table 3.

c

30

0.1

T22

90

150 150

0”c.m.

3o

go

Fig. 7. The effects of the tensor potential Ts and variation of the D, parameter on the tensor analysing powers of the 64Zn(d, t)63Zn(g.s.) reaction. The curves have been calculated by DWBA using the opticalmodel parameters of table 2 and varying the D, parameter in steps between D, = -0.16 and D, = -0.36 fm’. The “best-fit” II, values obtained are given in table 3.

80 TABLE

3

Values of the D, parameter Reaction

TR

T22

T20

Sum(T,,+T,J

(Yes/No) 64Zn(d, 3He)63Cu 63Cu(d, 3He)63Ni 45Sc(d, 3He)44Sc @Zn(d, t)63Zn 63Cu(d, t)=Cu

N Y N Y N Y N Y N Y

- 0.29 - 0.22 - 0.22 - 0.20 -0.22 -0.22 -0.34 -0.24 -0.22 -0.20

-0.22 -0.19 - 0.22 -0.16 -0.15 -0.12 -0.22 -0.18 -0.20 -0.13

-0.24 -0.20 - 0.22 -0.16 -0.17 -0.15 - 0.24 -0.18 -0.20 -0.14

potential is given in table 2. Calculations were then carried out including the TR term in the deuteron distorting potential. Results of these calculations are presented in figs. 9 and 10, showing that the introduction of the TR term has improved the fit at small angles. At large angles the gradient of the T,, predictions seems a little too steep in comparison with the trend of the data. This may suggest that the TR potential needs to be further optimised. It is worth pointing out here

-0.32

-02L

-0.1

D2 Fig. 8. The x2 values per point for the DWBA fits to the tensor analysing powers of the both with and 64Zn(d, 3He)6’Cu and 64Zn(d, t)63Zn reactions plotted against II, for calculations without TR term, represented by the continuous and broken lines respectively.

81

F. Entezami et al. / Tensor analyzing power

0 -0

.l

-0-2

T22

0

-0 .l

t30

90

-.3b I 30

150Q”c.nl.

L

I 90

/

I 150

Fig. 9. The effects of the tensor potential TK and variation of the D, parameter on the tensor analysing powers of the 63Cu(d, 3He)62Ni(g.s.) reaction. The curves have been calculated by DW3A using the optical-model parameters of table 2 and varying the D, parameter in steps between the values indicated. The “best-fit” D2 values obtained are given in table 3.

-c 0

Fig. 10. The effects of the tensor potential TR and variation of the D2 parameter on the tensor analysing powers of the 63Cu(d, t)62Cu(g.s.) reaction. The curves have been calculated by DWBA using the opticalmodel parameters of table 2 and varying the D2 parameter in steps between the values indicated. The “best-fit” D, values obtained are given in table 3.

82

F. Entezami

that the distorted-wave more accurate

et al. / Tensor analyzing power

approximations

for small angles.

A further

are more suitable, possible

of the LEA, which had been shown by Ioannides T20 values somewhat larger in magnitude than DWBA.

difficulty

and are expected

to be

may be due to the use

et al. 22) to give at large angles those of the exact-finite-range

The effect of the inclusion of the tensor term and the variation of the D, parameter in both reactions was similar to the Zn case in that an approximate linearity between D, and T2qcould be seen (figs. 9 and lo), and that the effect of the introduction of the TR term was to lower the magnitude of the “best-fit” D, parameter, with the relevant D, values given in table 3.

3.3. THE %k(d,

3He)44Ca REACTION

The reactions discussed above all involve $- angular momentum transfer. It was considered important to investigate a z- transition, such as the 45Sc(d, 3He)44Ca g.s. reaction, to see whether the findings concerning the D, parameter and the effect of the TR terms are upheld for a larger value of angular momentum transfer. The entrance and exit channels potentials used are given in table 2 and are a result of an investigation into finding the best possible combination of six deuteron and four 3He parameter sets. As in the 63Cu case it was found that the greatest sensitivity to the predictions came from the choice of the deuteron potential, especially the reproduction of the forward-angle region when using different spin-orbit potentials. As before a TR term was added to the deuteron potential, in order to investigate the tensor potential effects. The real and imaginary forms were again those of Burgi et al. 29). DWBA calculations with these potentials are shown in fig. 11 from where it can be seen that the introduction of a 'I-, term only slightly affects the shape of the predicted distribution whilst producing a smaller, in magnitude, D, parameter. The “best-fit” D, values for the case when the TRterm was both included and excluded from the calculation are given in table 3.

3.4. THE “F(d,

3He)*80 REACTION

The main interest in 19F was to study the 19F(d, 3He)180 ground-state transition, where the angular momentum transfer is I, = 0. Processes in which the nucleon is captured with zero orbital angular momentum are expected to be particularly sensitive to the effects of spin-dependent interactions, since without these DWBA theory predicts zero vector analysing power 32). On the other hand, both the distorted-wave and optical-model descriptions are not expected to work particularly well for light targets such as 19F , due to possible failure of some of the approximations involved. The DWBA calculations for the 19F(d, 3He)1sO(g.s.) reaction have been carried out using six sets of optical-model parameters for the

F. Entezami

et al. / Tensor analyzing power

83

0.2

-0

-0.2

with I 30

90

150

30 8°C

T, I

I 90

I

I 150

.m.

Fig. 11. The effects of the variation of the D, parameter on the tensor analysing powers of the 45Sc(d, 3He)44Ca(g.s.) reaction. The curves shown have been calculated by DWBA including the deuteron tensor potential TR with the optical-model parameters of table 2 and varying the D, parameter in steps between the values indicated. The “best-fit” Dz values obtained are given in table 3.

deuteron channel and two sets for the outgoing 3He channel, taken from the combinations. It was found that none of the literature 31), in all possible predictions reproduced details of the experimental distributions. Investigations of the spin-orbit part of the distorting potentials showed that the predictions are very sensitive to the diffuseness of the 3He spin-orbit potential, affecting especially the analysing power for small reaction angles (15O-300), where smaller as.0 values produced better fits to the data. This finding is consistent with the small diffuseness of the spin-orbit part of the optical-model potential determined from the elastic scattering of polarised 3He, characterised by u~,~, within the range 0.2 5 Q. I 0.4 fm for most nuclei 33-35). Whereas the sensitivity to the spin-orbit term of the outgoing 3He is confined to the small-angle region, the DWBA predictions for large angles were more sensitive to the spin-orbit potential strength .of the incident deuterons. As a whole, it was found that the DWBA predictions were more sensitive to the choice of the incident deuteron optical potential than that of the outgoing 3He channel. The best DWBA predictions for the 19F(d 3He) reaction analysing powers are shown in fig. 2 and the optical-model parameters used in the calculations are given in table 2. The deuteron optical-model parameters were determined from the elastic scattering of 12.4 MeV vector polarised deuterons on “F [ref. ““)I ; for the 3He channel the potential parameters of ref. 37) were used. Results of calculations with various D, parameter values are shown in fig. 12. It is evident that this I, = 0 reaction is not very sensitive to the value of the D, parameter used in the DWBA calculations and the quality of the description of the data is disappointing in comparison with the other transitions studied.

84

F. Entezami

et al. / Tensor analyzing power

with

U

TR

c.m

Fig. 12. The effects of the variation of the D, parameter on the tensor analysing powers of the 19F(d, 3He)180(g.s.) reaction. The curves shown have been calculated by DWBA including the deuteron tensor potential TR with the optical-model parameters of table 2 and varying the D, parameter in steps between D, = -0.16 and D, = -0.36 fm2.

4. Discussion The large tensor analysing powers of (d, 3He) and (d, t) reactions observed in the present work on r9F, 45Sc, 63Cu, and 64Zn can only be explained by taking into account the D-state of the tri-nucleon system. The effect of the D-state on the differential cross section is imperceptible while the vector analysing power is only slightly affected. DWBA calculations incorporating the LEA with the tri-nucleon D-state included via the D, parameter give a satisfactory description of the reactions, better for the heavier targets used. It was found that the DWBA calculations were not very sensitive to the choice of optical potential with the incident channel being in general somewhat more important. Variation of the D, parameter in both (d, t) and (d, 3He) calculations produced a linear type of relationship between D, and the magnitude of the predicted tensor analysing powers. The introduction of the real and imaginary spin-orbit tensor terms TR in the deuteron optical potential had little effect upon the shape of the predicted analysing powers. However, with the TRterm the magnitude of the predicted tensor analysing power was increased ; consequently the ensuing “best-fit” D, parameters were smaller in magnitude than for the corresponding values obtained when the tensor term was omitted in the calculation. Quantitative fits to the data using the x2 criterion reveal that the introduction of the TK term produced a smaller in magnitude “best-fit” D, parameter and generally improved the reproduction of the data. For 63Cu and 45Sc the calculations which include the TR term predict a T2,, distribution whose large-angle trend is questionable. Measurements at large angles

F. Entezami et al. / Tensor analyzing power

may improve description

the choice of tensor of the

small-angle

terms, however data

it is to be noted

is satisfactory,

calculations may be needed at large angles. Averaging the D, parameters of table

85

3 gives

whereas values

of

that the DWBA exact-finite-range -0.16

?0.03

and

-0.17 +0.04 fm’ respectively for (d, t) and (d, 3He) reactions from calculations including the tensor spin-orbit interaction in the incident deuteron channel. With no tensor term the corresponding average D, values are -0.22 *0.03 and - 0.21 kO.04 fm’. The value of the parameter D, = -0.21 fin’ determined in the present work for T, = 0 is in agreement with the value of D, = -0.22 fm2 obtained previously for value for the triton the 27Al(d, 3He)26Mg reaction “) and with the corresponding from (d, t) reactions on ‘l*Sn and 208Pb [ref.26)] (D, = -0.24 fm”), but in disagreement with the findings from (d, 3He) reactions on 64Zn [ref. ““)I and ‘j3Cu [ref. ‘“)I (D, = -0.37 and D, = -0.339 fm2 respectively). All experiments refer to incident deuteron energy between 12 and 13 MeV, except for the measurements on 63Cu of ref. i5) where 9 MeV deuterons were used. At sub-Coulomb energies (d, t) reactions on Zr, Sn and Pb isotopes yielded 14*17) D, = -0.279 fm’, and for 91Zr and 147Sm D, values of -0.288 and -0.259 fm2 respectively have been recently quoted I’). The value of the D2 parameter of the present work is somewhat lower, but the difference is within the quoted normalization uncertainties. At the same time the present results are in excellent agreement with the D, values determined from (d, t) and (d, 3He) measurements on Cu and Pb targets at a higher energy of 22 MeV [ref. ‘“)I. Comparison of the calculations including the deuteron tensor spin-orbit term with experimental tensor analysing powers confirmed that the effect of the TR term is to reduce the-value of the 3He (or triton) D, parameter by nearly 20 %. The value ‘D, = -0.17 kO.04 fm’ obtained for 3He in the present work including the TR term is in good agreement with recent theoretical predictions for the trinucleon system. Santos et al. 38) have obtained D, = -0.20 fm? using the triton wave function of Jackson and Riska in a first-order perturbation calculation corresponding to a triton D-state probability of 8 %. They have also shown that a more realistic triton wave function leads to a somewhat smaller value of the asymptotic constant. In a calculation using the Strayer and Sauer triton wave function, which is generated through a variational procedure from the softcore Reid NN potential, a value D, = -0.17 fm? was obtained. Santos et al. have also considered the difference between the triton and 3He D, values obtained from tensor analysing powers of (d, t) and (d, 3He) reactions showing that the D2(3H)/D,lD,(3He) ratio is close to one. The D, value of the present experiment is also in agreement with the recent result of Kim and Muslim 39), who have carried out an exact non-perturbative calculation of the triton D-state asymptotic normalisation constant using the trinucleon wave function obtained from a solution of the Faddeev equations with the

86

E. Entezami et al. / Tensor analyzing power

Reid soft-core potential. The triton wave function had an 8.8 “/: D-state probability and their estimate of the 3He asymptotic constant including Coulomb correction gave the value of the 3He constant equal to that of the triton. The authors wish to thank Dr. R. C. Johnson for many useful discussions, Professor F. D. Santos and Dr. Ana M. Eiro for making the DTCODE available and for their help and Professor G. C. Morrison for his continued interest in this work. Thanks are due to Dr. J. A. Tostevin for the TRCODE and for his helpful suggestions, Mr. W. C. Hardy and the cyclotron staff for efficient running of the machine and to the University Computer Centre for allocation of substantial computing time on the ICL 1906A computer.

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R. A.

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