Evidence for the deuteron-nucleus tensor interaction

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Nuclear Physics A220 (1974) 381 -- 390; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprlnt or microfilm without written permission from the publisher

EVIDENCE FOR T H E D E U T E R O N - N U C L E U S T E N S O R I N T E R A C T I O N R. R O C H E t, N G U Y E N VAN SEN, G. PERRIN, J. C. G O N D R A N D ,

A. FIORE and H. MOLLERtt lnstitut des Sciences Nucldaires, BP 257, 38044 - Grenoble - Cedex, France

Received 27 September 1973 (Revised 14 December 1973) A~lract: Measurements for the elastic scattering of polarized deuterons from 4°Ca and 56Fe at 30 MeV and from 9°Zr and 2°aPb at 28.8 MeV are presented. Angular distributions of the cross section, of the vector analyzing power iT11 and of the quantity T22-a/~T2o were deduced. Analyses of the data in terms of the optical model present evidence for the deuteron-nucleus tensor interaction. E

NUCLEAR REACTIONS "°Ca, ~Fe (~, d), E = 30 MeV; 9°Zr, 2eapb (~, d), E -----28.8 MeV; measured ~(0), iT~(O), T 2 2 - ~ T2o; deduced optical-model parameters. Natural 4°Ca, enriched 56Fe, 9°Zr, ~°SPb.

1. Introduction The deuteron optical potential has been expected to contain a tensor term together with the central and the spin-orbit terms. It was suggested in 1958 by Watanabe 1) that the deuteron potential could be calculated by (zal 1I, + Vp[Xa), Vu and Vo being the neutron and proton potentials and Xa the internal deuteron wave function. Such a calculation gave rise in first order to a central potential approximately equal to the sum of the neutron and the proton potentials and provided a L • S spin-orbit term similar to the nucleon one. The tensor interaction came out from further calculations 2- 4). I f the deuteron interaction is required to behave like a scalar under rotation of coordinate axes and to conserve parity, three forms of tensor terms may be constructed f r o m the position, m o m e n t u m and angular m o m e n t u m vectors 2). The T R term could be obtained on the basis of the folding model if the internal deuteron D-state was taken into account. The extension to second order contribution of the nucleon-nucleus spin-orbit interaction introduced a Tr term 4). Until now the T e term has not been investigated. The Ts term should be the dominant component of the deuteron-nucleus tensor interaction 2- 6). Measurements of the tensor analyzing power T21 have been shown 7-1o) to be useful in the determination of the tensor interaction. On the basis of a perturbation calculation 10), the quantity X2 = T22-x/-~T20 have been suggested to be also suitable for such a determination. Investigations of this quantity have been carried t Part of a Doctorat de troisii~me cycle thesis, Universit6 Scientifique et M6dicale de Grenoble. t t On leave of absence from University of Ziirich, Switzerland. 381

382

R. R O C H E et al.

out recently using ' 60 [ref. 13)] and t2°Sn [ref. 1s)] targets. A more extensive study is performed in the present work which reports measurements for the elastic scattering of polarized deuterons from 4°Ca and 56Fe at 30 MeV and from 9°Zr and 2°Spb at 28.8 MeV. Angular distributions of the cross section, of the vector analyzing power iT11 and of the quantity X2 were deduced. The data were analyzed in terms of the optical model including a spin-orbit force and a T R tensor term. 2. Experimental procedure 2.1. EXPERIMENTAL SET-UP The present experiments were performed with the polarized beam from the Grenoble cyclotron. The maximum intensity of the beam focused on the target was about 20nA. The general features of the experimental arrangement have been given before 14-15). The measurements were made in a scattering chamber of 65 cm diameter. The scattered particles were detected by silicon solid-state detectors cooled to about - 2 5 °C. The deuterons are identified by using E" AE telescopes, mounted on two rotatable arms. The positioning accuracy of the telescopes was about +0.1 ° and their angular I

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TENSOR I N T E R A C T I O N

383

aperture was about _+0.7°. A monitoring detector was fixed at 45 ° so as to furnish a relative renormalization for the telescopes countings. Downstream of the main scattering chamber was placed a carbon polarimeter which furnished a continuous monitoring of the beam polarization. This polarimeter described in ref. a4), was in fact a scattering chamber of 40 cm diameter, containing i

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a (CH2). target and two solid-state detectors placed at 45 ° left and right of the beam direction. The beam particles were collected by a Faraday cup mounted behind the polarimeter. The electronic circuitry was similar to that of refs. 14-~ s). The spectra were stored on magnetic tapes and handled by means of a PDP-9 computer. The overall energy resolution of the deuteron spectra was about 150_+ 50 keV. The background was generally small; the spectra were comparable to those given previously 15). 2.2. M E A S U R E M E N T S

It has been shown 1s) that the cross section, the vector analyzing power and the quantity X2 could be deduced simultaneously from measurements at the azimuthal angle of 54.7 °.

384

R. R O C H E e t al.

Angular distributions were obtained from 15° to 130° with a natural 4 ° C a target and enriched targets of S6Fe (99 %), 9°Zr (95 %), 2°apb (99 %). The beam energy was determined with an accuracy of about _ 200 keV by means of cross over techniques 16) using a (CD2) n target. The measurements were performed at 30 MeV for +°Ca and 56Fe, and at 28.8 MeV for 9°Zr and 2°spb.

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Fig. 3. Tensor quantities T22--~/~ T2o. The optical model curves follow the same conventions as in figs. 1 and 2. The experimental data are shown in figs. 1-3 together with the error bars coming from statistics. The uncertainty on the absolute normalization was about + 10 % for the cross section and the vector analyzing power and + 15 % for the tensor quantity X2. The beam vector and tensor polarizations determined with the methods discussed elsewhere 1+-1 s) were about 65 % of their maximum possible values in the measurements for +°Ca and S6Fe and about 84 % in the other measurements. 3. Analyses and discussions 3.1. OPTICAL POTENTIAL The experimental data were analyzed in terms of the optical model including spin-orbit and tensor forces, with the search code M A G A L I 17). The potential is

TENSOR INTERACTION

385

given by

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1)

(o- v(e + 1)-' + 4i

+ (h/m

× (eX"+

S - VT[(S"

where Vc(r ) is the Coulomb potential of a uniformly charged sphere of radius 1.3 A ~ fm, x = ( r - r v A~)/av,

x' = ( r - r D A¢)/aD,

f ( y ) = 6x/3(d2/dy2)(C+l) -~,

x " = (r-- rLs A¢)/aLs,

y = (r--rrA¢)/a1,,

m a x f ( y ) = 1.

The real potential well depth V was restricted to approximately the sum of neutron and proton potential depths, in accordance with the folding model results 1). In addition, the radius r v was confined to values about 1.1 fm because of the continuous ambiguity of the type Vr:, ,~ constant. Starting with values deduced from previous analyses of the deuteron scattering [refs. ta-2a)] a best-fit parameter set with Vz,s = VT = 0 was first determined by search on the cross section angular distribution. The spin-orbit term was then included so as to reproduce both the cross section and the iTl t data. Finally the tensor TABLE 1 Optical potential parameters Nucleus Set V

rv

av

WD

ra

aD

VLs

rLs

aLs

JR

Ji (RE2) ~ ( R l 2 ) ~

*°Ca

A 93 A1 102.7

1.13 0.8 1.05 0.85

10.23 1.39 0.75 11.2 1.43 0.69

5.07 5.46

0.9 0.9

0.56 0.558

400 387

l i b 4.21 124 4.22

5.64 5.63

S6Fe

A B

92.4 60.3

1 . 1 3 0.76 0.99 0.89

12.34 8.83

1.34 1.4

0.78 0.848

5.33 5.03

0.9 0.606 1.01 0.387

364 188

122 4.38 105 4.41

6.02 6.37

9°Zr

A B

96.4 62

1 . 1 3 0.825 1.09 0.94

12.28 9.68

1.3 1.39

0.861 0.821

5.33 0.77 5 . 1 1 1.04

0.435 0.531

368 191

107 4.98 101 5.15

6.79 7.06

1.13

1 2 . 3 1 1.37

0.815

5.71

0.45

355

2°apb

A 100

0.89

1.0

83

6.15

8.76

The potential depths are in MeV, the geometrical parameters in fm and the volume integrals in MeV" fm a. TABLE 2 Optical potential parameters used in the analyses including a T~ tensor term Nucleus

Vta (MeV)

rLs (fro)

aLs (fro)

Vr (MeV)

rT (fm)

aT (fm)

4°Ca 56Fe 9OZr 2°apb

5.07 5.39 5.17 5.71

0.9 0.9 0.77 1.0

0.56 0.59 0.435 0.45

1.36 0.72 0.487 0.8

1.4 1.4 1.4 1.4

0.492 0.468 0.587 0.6

The parameters V, r v , a v , WD, rD, aa are identical to those of the potentials A in table 1.

rr M (fm)

1.59 1.56 1.58 1.53

386

R. ROCHE et al.

component X2 was taken into account and the whole potential was searched again. The whole process was repeated several times with different sets of starting values for the parameters. The optimum parameters gave the potentials A in table 1 whereas the dashed lines in figs. 1-3 represented the theoretical curves together with the experimental data. The cross section and the iT11 data are well reproduced by the theoretical results while the calculated X2 component is clearly smaller than the measured one, except at backward angles. l l I 1 °'/~ t 0.5

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100

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In the second step the tensor interaction in eq. (4) was incorporated into the potential A and the whole potential so obtained was readjusted by fitting simultaneously all the data. However the parameter search on the whole potential did not improve substantially the fit obtained by the potential in table 2, (denoted by C) deduced from the search on only the spin-dependent terms. In figs. 1-3 the theoretical curves calculated from the potentials C are shown as a solid line. Inclusion of a tensor interaction clearly improves the fits of the X 2 components whereas the cross sections and the vector analyzing powers are not substantially changed.

TENSOR INTERACTION

387

3.2. D I S C U S S I O N

The optimum fits shown in figs. 1-3 were obtained with rz fixed to 1.13 fm and with small variations of WD, ro and VLs. The value of rv is different from that found out in several previous analyses ls-2a). Actually, in the present work good fits could also be obtained for 4°Ca with the value rv = 1.05 fm which has been adopted by other authors 20-23). The results calculated from the potential A1 of table 1 are shown in fig. 4. The fits are comparable to those obtained with 1.13 fro. However for the heavier nuclei, the fits with 1.05 fm are inferior. 1

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Fig. 5. Tensor quantity

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t

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T2z--~,/~ T2o of z°Spb(d, d). fig. 5.

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The curves obey the same conventions as in

388

R. ROCHE et al.

L I I I t I I I I I I o'/~ r 0.5 ~ - ~ , , (

O' 1L..-

d* 56 Fe 30 MeV

I'

0.!

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,

50

loo

lillll

Oc.m.(deg) Fig. 7. Optical model fits for 56Fe(d, d) obtained with the shallow potential B of table 1

~

0.5

l [ L I I I t l I l l l l

,

0.1

-

~"

d* Zr 28.8 MeV

0. -

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/

o

-0.5 -n

t r i t t~i

5o

I I I r I t 100

ec.m.(deg) Fig. 8, Optical model fits for °°Zr(d, d) obtained with the shallow potential B of table 1,

TENSOR INTERACTION

389

Together with the tensor potential parameters is also given in table 2 the reduced radius r ~ defined so as f[A~(rUr-rr)/ar]

= m a x f ( y ) = 1,

w h e r e f ( y ) is the second-derivative form factor of eq. (1), i.e. r ~ = r r + a r A - ~ In (2+~/3).

This radius r ~ could be qualitatively compared to the corresponding values obtained from calculations based on nucleon-nucleus interaction a, 24) and to the radii adopted in phenomenological analyses pzrformed with Gaussian or first-derivative form factors. The radii rru = 1.56+0.03 fm are somewhat larger than the radius of 1.4 fm adopted by Schwandt and Haeberli 5, 6) and much smaller than those found by the Australian group 7,9,11-13). A recent analysis of 12°Sn(d, do) at 28.6 MeV had given r r = 1.1 fm, r ~ = 1.43 fm, however the fits of the quantity T 2 2 - x / ~ T2o at backward angles would be improved if the radius had been about r r = 1.4 fro. Figs. 5 and 6 show that the oscillation patterns of X2 at backward angles are very sensitive to the radius of the tensor potential. The curves correspond to the optimum fits obtained with r r = 1.3 fm (dashed line), r r = 1.4 fm (solid line)and r r = 1.5 fm (dashed-dotted line). The cross section and the iT11 data are also included in the parameter search however their fits are not substantially sensitive to the tensor potential radius. It should be noted furthermore that the diffuseness parameter a r has the same order of magnitude as that of the spin-orbit potential. The strengths Vr are slightly smaller than those predicted by calculations based on the nucleon-nucleus interaction 3, 24). In an analysis of the cross section and the polarization data from the 4°Ca(d, do) scattering at 21.7 MeV, Raynal a) could obtain acceptable fit only with V ~ 100 MeV. In the present work such an investigation of the discrete ambiguities was repeated for 56Fe and 9°Zr. The fits obtained with the shallow potentials of table 1 are shown in figs. 7 and 8. The iT11 data are as well reproduced as with the deep potentials whereas the fits of the cross section are somewhat inferior. Particularly at backward angles the calculated results are lower than the experimental ones; this effect has been observed by Percy and Percy 25). Together with the parameters of the optical potential are also reported the volume integrals per pair of interacting particles and the mean square radii for the real and the imaginary parts, using the formulae of refs. 26-2a). It is notable that for 4°Ca the parameter set with rr, = 1.05 fm gives approximately the same real and imaginary mean-square radii as those provided by the set with rv = 1.13 fro; that is the feature of the continuous ambiguity 28).

390

R. ROCHE et al.

4. Conclusion M e a s u r e m e n t s of the q u a n t i t y T 2 2 - x / 3 T20 have been shown to be useful i n the investigation of the d e u t e r o n - n u c l e u s tensor interaction. Optical m o d e l analyses using central a n d L . S spin-orbit potentials reproduced satisfactorily the experim e n t a l cross sections a n d vector analyzing powers whereas the predicted T22 -x/~5 7,2 ° c o m p o n e n t s could n o t a c c o u n t for the measured data. A tensor t e r m h a d to be i n t r o duced into the optical potential so as to o b t a i n a reasonable description of these data. W i t h the radius of the second-derivative f o r m factor fixed to 1.4 fro, the tensor i n t e r a c t i o n h a d i n the present w o r k strengths of 0.5 to 1.4 MeV. These values are somewhat smaller t h a n the theoretical results f r o m calculations based o n the n u c l e o n nucleus interaction whereas the radius is slightly greater t h a n the predicted one.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28)

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