Nuclear Physics A208 (1973) 221 --235; ~ ) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

V E C T O R A N D T E N S O R A N A L Y S I N G P O W E R O F (d, p) R E A C T I O N S

A N D D E U T E R O N D - S T A T E E F F E C T S

R. C. JOHNSON

Department of Physics, University of Surrey, Guildford, Surrey

and

F. D. SANTOS t

Laboratorio de Fisica e Engenharia Nucleares, Sacavem, Portugal

and

R. C. BROWN tt, A. A. DEBENHAMttt, G. W. GREENLEESt, J. A. R. GRIFFITH, O. KARBAN, D. C. KOCHER St and S. ROMAN

Department of Physics, University of Birminoham, Birmingham

Received 18 December 1972 (Revised 2 April 1973)

Abstract: The vector and tensor analysing power was measured for (d, p) reactions on 9Be, ~2C, 160, 19F, ZSMg, 2sSi and 4°Ca for lab reaction angles from 0 ° to 50 ° at 12.3 MeV incident deuteron energy. Fifteen transitions were studied including orbital angular momentum transfers In = 0, 1,2, 3. The experimental results were analysed in terms of distorted-wave theory including deuteron D-state effects. The calculations show that the deuteron D-state cannot be ignored in the description of the tensor analysing power. The j-dependence of D-state effects is discussed.

NUCLEAR REACTIONS 9Be, J2C, 160, 19F, 25Mg, 2aSi, 4°Ca (polarized d, p), E = 12.3 MeV, measured analysing powers iT11 (0), T2o(O), 7"22 (0). Enriched 25Mg

and '*°Ca targets. Deduced importance of D-state effects.

1. Introduction

Recently a number o f measurements o f tensor analysing power in (d, p) s t r ipping

reactions have bee.n made l - a ) . These data show that the tensor analysing powers

T2q can be quite large in reactions which are expected to be reasonably well described

by the D W B A theory. It is well known that according to this theory, assuming spin-

independent dis tor t ion and a pure S-state deuteron internal wave function, the T2~

t On leave at University of Surrey, September-October 1972. tt Now at Physics Department, Queen Mary College, London.

ttt Now at Laboratorium fiir Kernphysik, ETH, Zurich, Switzerland. SRC Senior Visiting Fellow on leave from University of Minnesota, Minneapolis, Minnesota

55455, USA. t.* Present address: Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA.

221

July 1973

222 R.C. JOHNSON et aL

are predicted to be zero 4). The inclusion of spin-orbit terms in the optical potentials results in T2q values which are consistently smaller than experiment, often by an order of magnitude. The suppression of spin-orbit contributions is particularly noticeable in lx = 0 transitions. In fact the T2q are predicted to be zero with a spin-orbit force in the proton channel only, and the effect of a deuteron spin-orbit force alone is of second order in its strength 4).

When contributions from the deuteron D-state are included, non-vanishing T2q are predicted even in the absence of spin-dependent distortion. Furthermore, plane- wave estimates 5) predict T2q values that are a significant fraction of their maximum possible values. These results suggest that the D-state plays a very important role in determining the T2q.

In this paper measurements of the vector and tensor analysing power for (d, p) transitions in nuclei ranging from Be to Ca are analysed using the DWBA theory with D-state effects included. The calculations do not include tensor terms in the deuteron optical potential 6). One of the objectives of the investigation is to deter- mine to what extent agreement with the experimental T2~ angular distributions can be obtained by inclusion of D-state effects. A more extended set of calculations than pre- viously published ~) has been performed and attention is given to the question of the importance of the effects of distortion on the D-state contribution. The j-dependence of the D-state effect on vector and tensor polarization is also discussed.

A number of the measurements reported here are on light nuclei where the dis- torted-wave theory is known to be less reliable. At incident energies up to several MeV, deuteron reactions with light nuclei can show pronounced resonances which can give rise to large tensor analysing powers. While vector analysing powers are always interference effects between matrix elements corresponding to different quan- tum numbers, a non-vanishing tensor analysing power can arise from a single matrix element. Thus the tensor analysing powers can be particularly useful observables in an analysis of the reaction mechanism 7). It is therefore important to determine to what extent the direct reaction contribution to T2q can be reliably reproduced by the distorted-wave theory if the mechanism of the reactions involving light targets is to be understood.

2. Experimental method

The measurements were carried out using the 12.3 MeV polarized deuteron beam extracted from the University of Birmingham Radial Ridge cyclotron a, 9). In the polarized deuteron source operating in the normal configuration ~ o), a pure vector- polarized beam is obtained by selecting the appropriate states when the atomic beam is passed through an r.f. transition apparatus consisting of a tapered magnet producing a static magnetic field gradient and two r.f. magnetic fields of 7.5 MHz and 329 MHz. By alternate switching of the two r.f. oscillators, the vector polarization state of the beam is switched between the " u p " and "down" directions as defined by the magnetic axis of the cyclotron.

(d, p) REACTION ANALYSING POWERS 223

In the present experiment the tensor-polarized beam was obtained by a method de- veloped by Oh x o), the state of the beam polarization being rapidly switched between the polarization "on" and "o f f " conditions with a switching frequency of 6 Hz. It has been shown 1 o, 11) that under these conditions the beam polarization is specified in terms of the expectation values of spin-1 operators, by the vector polarization i q t

and two tensor polarization components t20 and t22, in a coordinate frame having its z-axis along the beam direction and the y-axis pointing vertically upwards. The tensor polarization components axe related by

t22 = t21 = o. (1)

These relationships were used in analysing the data. The 12.3 MeV polarized deuteron beam was transported into the 76 cm diameter

scattering chamber 12) and the protons from the (d, p) reactions were detected in six silicon surface-barrier E - A E detector telescopes mounted on two rotatable arms set at symmetric angles 0 and - 0 with respect to the incident beam direction. The chamber could be rotated about the beam axis in a plane perpendicular to the incident beam direction. The selection of protons from other reaction products was achieved by means of analogue logarithmic particle-identifier circuits 13).

The beam polarization was monitored continuously in two polarimeters. The vector polarization i t 1 ~ was monitored using the 12C(d, p)~ 3Cg.s. reaction, whose analysing power is well known a 4), in a polarimeter described previously ~ 5) placed upstream with respect to the main scattering chamber. The tensor polarization of the beam t2o was monitored continuously in a aHe gas-cell polarimeter placed downstream of the main scattering chamber. The reaction 3He(d, p)4He (Q -- 18.35 MeV) was used at an angle of 0 °, at which point the analysing power T2 o has been determined against an absolute standard by Grfiebler et al. ~ 6) and K6nig et aL ~ 7). At 6 MeV the magni- tude of the tensor analysing power is nearly at its highest and at the same time it varies slowly with energy 16) and, therefore, the 3He polaximeter was designed to work at this energy. The polarimeter used an angular acceptance of _ 5 ° for the detection of protons, and its analysing power was obtained by taking an average of the values at 0 ° and 5 ° from the angular distribution determined by Grtiebler et al. 18). The value used in the present work was T2o(3He) -- -1.27_+0.04.

The gas-cell polarimeter contained permanently sealed volume of 3He gas at 7.1 atm. The cell was machined from a solid brass block, about 4 cm long, having a uni- form 0.9 mm thick brass exit window left at the far end; deuterons entered the cell through a window of 38.1 pm thick "Havar" foil bonded to brass; 63.3 mg]cm 2 of aluminium was placed over the entrance window in order that the deuteron energy at the centre of the cell would be 6 MeV. The deuteron energy loss in one half of the gas target was approximately 220 keV and, by virtue of the slow variation of the tensor analysing power of 3He with energy in this region, the analysing power of the polarim- eter was practically independent of the gas pressure in the cell. The cell was mounted on an insulating plate, and, since all the deuterons were stopped in the exit window,

224 R .C . JOHNSON et al.

the cell could be used for beam-current monitoring. The protons from the aHe(d, p) 4He reaction were detected by a silicon lithium-drifted detector and a proton spectrum routed in accord with the switching of the polarization state at the source is shown in fig. 1.

3He(d,p)4He O=O*

.a,

POLARIZED -~

I01 oo UNPOLARIZED o o -,

o- i

~ o zs~- o * -~ o L o o I

i o o o ~o LL D o o o LID _ LO o.. . 0". Oo i

i i i i t l I I , ~ n l , ! I ! I I I I I t t I ° c ~ I I i i

0 64 128 192 256 CHANNEL NUMBER

Fig. 1. Energy spectra of protons from the 3He(d, p)4He reaction accumulated during the un- polarized (oh. 0-128) and polarized (oh. 128-256) states of the ion source over equal numbers of

polarization switching cycles of precisely equal duration.

The vector and tensor analysing powers of the (d, p) reactions were found from measurements at 4- 0 carried out in runs with the main scattering chamber plane alter- nately in horizontal and vertical positions. The cross section for a reaction induced by a polarized beam specified above is given by

o = t r o ( l + 2 i t l t i T l l C O S d p + t z o T 2 o + 2 t 2 2 T 2 2 cos 2~b), (2)

where t# is the azimuthal angle. In the horizontal configuration of the chamber the counting rates or cross sections

observed to the left (L) and to the right (R) (~b = 0 and re) can be expressed in terms of two asymmetries e and fl defined by

~L = ~ o 0 + ~ + P), ~R = ~ o ( 1 - ~ + p), (3)

where go is the cross section for an unpolarized beam and

e = 2 i t l l i T x x , fl = t 2 o T 2 o + 2 t 2 2 T 2 2 . (4)

I f X L and X R indicate ratios of the number of counts in a particular peak during the r.f. transition at the source " o n " to that during the polarization "of f " period, mea- sured to the left and to the right, then

(d, p) REACTION ANALYSING POWERS 225

= ½(x,-xR). p = ½(x. + x.-2), (5)

In the vertical configuration of the chamber cross sections in the up (U) and down (D) directions are observed

where , ~ = a~, = ao(1 +~),

= t 2 o T 2 o - 2 t 2 2 T 2 2 .

(6)

(7)

In terms of the ratios of the numbers of counts up ($ = ½n) and down (~b = in ) the asymmetry x is given by

= ( x u - a) or ~ = ( x , , - O, (8)

the mean value 0t = ½(X v +XD--2) being used in practice. Expressions for the anal- ysing powers of a reaction in terms of the experimentally determined asymmetries are

iTll 2itll

T2o = ~ + ,

T22= 1 ( fl ~t ) (9) 2(6)--~ t2~h) t2~(v) '

where it 11 is the vector beam polarization measured in the upstream polarimeter, and t20 (h) and t2o (v) are tensor beam polarizations during the horizontal and vertical runs respectively, measured in the 3He polarimeter.

It is noteworthy that with the given specification of the beam polarization the statis- tical errors of the 7"20 measurements are larger than those for T22, in accordance with the factor (6) * in the denominator of the expression for the latter component.

The measurements of the vector and tensor analysing power were restricted to the angular range from 0 ° to 50 °. To facilitate separation of (d, p) reaction protons from the intense flux of elastically scattered deuterons at small scattering angles, aluminium foils of sufficient thickness were placed in front of each detector telescope. For mea- surements at 0 = 0 °, a single telescope was used together with enough tantalum foil to stop the unscattered deuteron beam. The 3He tensor polarimeter could not be operated when data were taken at 0 ° in the main chamber. For these runs t2 o was taken as a mean of the readings before and after the run assuming steady operation of the source. The 7"20 at 0 ° points are, therefore, subject to a slight additional un- certainty.

Results were obtained for fifteen (d, p)transitions on 9Be, lzc, 160, 19F, 25Mg, 2SSi and #°Ca targets with transferred angular momenta 1. = 0, 1, 2, 3 andjn = ½, {-, {-, {-. The T2 o data have been reported previously x). A list of the transitions studied

226 R.C. JOHNSON et al.

is given in table 1 and the angular distributions of the analysing powers iT11, 7"2 o and 7"22 are shown in figs. 2-9 t.

TABLE 1

List of transitions studied showing Io and jo values used in the analysis

l, j , Reaction E~ I, Jn Reaction Ex (MeV) (MeV)

0 ½ 12C(d, p)13C 3.09 1 ~ 9Be(d, p)l°Be g.s, 0 ~ 160(d, p)170 0.87 1 ] 9Be(d, p)l°Be 3.37 0 ½ 2SMg(d, p)26Mg 1.81 1 ~t 4°Ca(d, p)4aCa 1.95 0 ½ 25Mg(d, p)ZdMg 2.94 0 ½ 2 sSi(d, p)29Si g.s. 2 ~ 2aSi(d, p)29Si 1.28

1 ½ x2C(d, p)laC g.s. 2 ~ adO(d, p)XTO g.s. 1 ½ 4°Ca(d, p)41Ca 3.95 2 ~ 19F(d, p)2O F g.s.

2 ~ 2SMg(d, p)26Mg g.s.

3 ~ '*°Ca(d, p)¢lCa g.s.

3. The j-dependence of D-state effects

Taking into account the deuteron D-state and assuming spin-independent distor- tion, simple formulas can be derived for the vector and tensor polarization which display the dependence on the total angular momentum transferred in the reaction. For a (d, p) transition, where the neutron is transferred with orbital angular momen- tum 1. and total angular momentum j. , the deuteron vector analysing power iT 11 and polarization of the outgoing proton P are given by x 9)

i T,,(O) = 3~(- 1)tn+s"-* (St.(O) + Ct.(O)), (10) (2j, + 1)at.(0)

P(O) = ( - (11) (2j, + 1)atn(0 ) (S,.(O) + 4Ct.(O)),

where 0 is the reaction scattering angle, (2b+ 1)a,. is the proton differential cross section corresponding to unpolarised deuterons and b is the spin of the residual nu- cleus. The terms St. and Ct. are respectively the incoherent S-state and the coherent D-state contributions and depend on j , only through the radial part of the neutron wave function and the energy dependence of the proton distorted wave. This depen- dence is usually weak. Thus both the incoherent S-state and the coherent D-state contributions have essentially the same dependence onj , . This well-known], depen- dence gives good agreement with experiment and can be used for the identification o f j , [ref. 2x)]. Eqs. (10) and (11) suggest that relatively larger D-state effects are

t The data in numerical form are available on request from the authors,

(d, p) REACTION ANALYSING POWERS 227

tO be expected in P than in iTI~. Incoherent D-state contributions are neglected since they are expected to be considerably smaller than the coherent contributions.

For the tensor analysing power the incoherent S-state contribution vanishes with spin-independent distortion and the coherent D-state contribution is given by

r2q(0) = E (12)

The major dependence o n j . arises through the quantity at~a~ t which is given by

a~.~n ~ = 1 + ( - 1)In+Jn+~ [1.(I~+ 1) + 6-- l(l+ 1)]. (13) 2(2in + 1)

These formulae are obtained using eq. (28b) of ref. 22) and the results explained in the last paragraph on p. 288 of the same reference. The quantities B~ t depend weakly on j . through the same mechanism as Sl~ and Ct~ in eqs. (10) and (11). The sum over l in eq. (12) is over the orbital angular momentum transferred from the relative motion in the deuteron channel to the relative motion in the proton channel 2oh 22). It can take the values between [I . -2[ and l . + I i f j . = l . -½, and between l l ~ - 2 l + l and I. + 2 i f j . = In + ½ and l. ~ 1, 0. For In = 1, j . = ~, l = 1, 2, 3, and for l. = 0, 1 = 2 only.

The form of eq. (12) shows that the T2q are not expected to have the simple j . dependence found in vector polarization 2o, 21). The j . dependent effects in the T2~ depend crucially on the relative importance of the contributions to the/-sum in eq. (12), as a function of scattering angle, from the two terms on the right hand side of eq. (13). For example, when the amplitudes B~. t are evaluated using plane waves the second term in eq. (13) gives a vanishing net contribution to the/-sum and the T2~ are independent of I n andj . . In the presence of distortion different/-values contribute amplitudes with a characteristic angular dependence similar to the usual dependence of stripping amplitudes on transferred orbital angular momentum 2% At angles larger than the main stripping peak an important contribution comes from the 1 --- ln+2 amplitude. However for reasons of angular momentum conservation this amplitude does not contribute i f j . = In [ref. 22)]. Furthermore the coefficients at.j.z increase with l forjn = In+½. The result is therefore that at angles beyond the main stripping peak D-state effects tend to be larger in Jn = In + ½ transitions than in j . = l . - ½ transitions with similar Q-values.

The interpretation of l as the transferred orbital angular momentum also suggests that at 0 ° the lower values of l are dominant. The transformation properties of the B° z under rotations of the coordinate axes imply that in the forward direction they vanish unless l has the same parity as In. Thus for In = 1, neglecting the contribution from l = 3 we find that

(T2°(0°))J"=~r- 10. (14)

228 R.C. JOHNSON et aL

For l, > 1 similar simple predictions are not possible without further assumptions

about the B°n~.

4. Results of DWBA calculations

In order to analyse the data, D W B A calculations with spin-dependent distortion have been performed using the D W C O D E programme which permits the inclusion o f deuteron D-state effects as described in ref. 22). The approximate deuteron in-

ternal wave function used depends on parameters D o, fl and D2, defined in ref. 22), which have the same values as in the calculations o f that reference. As discussed in ref. 22) the D-state probabili ty is not treated as a free parameter in these calculations. The only quanti ty that specifically characterizes the deuteron D-state wave function

is D 2 and this is essentially determined by the deuteron quadrupole moment . There- fore the D W B A results with D-state effects included are not very sensitive to the de- tailed properties o f the neut ron-proton interaction at short distances and in partic- ular to the value o f the D-state probability. For example, the parameter D 2 is easily evaluated for all the deuteron wave functions given in ref. 2a) p. 92, which cover a wide range o f D-state probabilities consistent with low-energy nucleon-nucleon data. Variations in D2 of less than 5 % are obtained 24). The lack o f sensitivity to the D- state probabili ty in the calculations is associated with the fact that in the approxima- t ion 22) used here for treating finite-range effects, it is assumed that only low-momen- tum components of the D-state wave function are important and these are determined by D2.

TABLE 2 Deuteron optical potentials

Target V ro a W r ' a' Vs.o. rs.o. a,.o. Ref. nucleus

12C 118 0.9395 1.00 10.17 1.831 0.4961 19.32 0.9673 0.45 t4) 115 0.9 0.9 10.56 2.04 0.45 6 0.9 0.9 2s)

160 81.76 1.25 0.617 8.03* 1.483 1.435 7.07 1.25 0.617 26) 32.74 1.35 0.582 4.72* 1.929 1.235 0 1.25 0.617 26)

2SSi 108.2 1.07 0.858 20.8 1.488 0.535 6.99 0.955 0.5 27)

*°Ca 106 1.05 0.85 11.0 1.59 0.564 7 0.9 0.6 29) 109.7 1.031 0.809 10.3 1.508 0.596 8.16 1 .031 0.809 30)

The deuteron and proton optical potentials have the form

V c ( r ) - - V f ( x ) - - i 4 W d ~ f ( x ' ) + (m~c) 2 ~z l d l - s V( r )= V s ' ° ' , u, f ( x s ' ° ' ) s "

where f ( x ) : (1 +eX) -t , x = ( r - - roA~) /a , x ' ~ (r--r 'A~;)/a' , x .... = (r- -rs .o .A~)/a .....

and Vc is a Coulomb potential of a uniformly charged sphere of radius 1.3A¢. The neutron potential is of Saxon-Woods form with parameters rn = 1.25, an : 0.65 and a spin-orbit term with Vs.o. = 9.7.

* Volume imaginary term: - - i W f ( x ' ) .

(d, p) REACTION ANALYSING POWERS 229

The deuteron optical-model potentials used are taken from optical-model analyses of deuteron elastic scattering data which in most cases included polarization data. They are displayed in table 2. In the proton channel the optical-model potentials of Becchetti and Greenlees 25) were used. No attempt was made to improve the fit to the data by variation of the optical-model parameters.

Figs. 2-9 show the result of calculations for the angular distributions of/'20, 7"22, and iTa i up to 90 °. Distinctly better agreement with experiment was obtained for the heavier nuclei. Calculations for two In = 0 transitions on 160 and asSi are shown in figs. 2 and 3 respectively. Large D-state effects in 7"20 and T22 are found over all the angular range. The magnitude of the T2q without the D-state is generally larger for the lighter nucleus thus reflecting the greater importance of spin-dependent distortion in this case. The calculations with the D-state effect included reproduce the qualitative features of the data but the fits are better for 2SSi than for 160. Recently Corrigan et al. 2) analysing the 160(d, p)170 reaction at E a = 9.3 and 13.3 MeV found evi- dence for non-direct effects which might account for the difficulty in reproducing some of the data. Not shown in the figures are data and calculations for the 25Mg target which show similar features to the 2sSi(g.s.) results.

Calculations for 1, = 1 transitions on 12C and 4°Ca are shown in figs. 4-6. Again we find that the 4°Ca data are considerably better reproduced than the t2C data. At forward angles the T2o data of ref. 1) for ½- transitions are consistently smaller than for ] - transitions. In particular for the I. = 1 pair in 4°Ca they are in a ratio of 18 : 1 in approximate agreement with eq. (14). It is clear from the calculations of figs. 5 and 6 that this ratio is very strongly angle-dependent near 0 °. Calculations for the ½- transition on lzC (fig. 4) reproduce the gross features of T2o and T22. The detailed agreement with experiment is not very good particularly for angles smaller than 40 ° . Calculations for T2o with two different deuteron optical-model potentials which fit deuteron elastic scattering cross sections are also shown in fig. 4. It is found that the spin-orbit contributions are non-negligible and the results rather sensitive to the deuteron potential. At forward angles the effect of the D-state is to make/20 more negative by approximately the same amount in both calculations.

The measurements for two I n = 1 transitions with differentjn in 4°Ca (figs. 5 and 6) clearly show that the tensor analysing powers do not exhibit the simplejn dependence found for iT11. The same conclusion can be derived from the recent data of Rohrig and Haeberli 3). The calculations of fig. 5 show that unlike the case of 12C the effect of changing the deuteron optical potential while retaining the D-state effect is small for all three analysing powers. The calculations reproduce satisfactorily the experi- ment except for 7"2o in the ] - transition. The latter discrepancy may reflect the fact that according to eq. (14) the D-state is expected to have a considerably smaller effect at forward angles in ½- transitions, thus making the contribution from the compari- tively uncertain spin-dependent distortions relatively more important.

Fig. 7 shows the result of calculations for a ]+ transition in 16 0 using two sets of deuteron optical-model parameters, one without a spin-orbit term. The inclusion of

230 R . C . JOHNSON et a t

°'~ I 0"4 f T20 T22

f f I

-o.~ l' " " o~ _ <+.;, S D STATES

- 0.4 - 0.4 ~- .... S STATE ONLY

L 16 O(d,p)i70 E×=0.87MeV

o.~ ~T11 Ed--IZ.3 M~v

9c.rn. ~jJI Fig. 2. Vector and tensor analysing power for the ~60(d, p )~O, Ez = 0.87 MeV, In = 0 transition induced by 12.3 MeV deuterons. The DWBA predictions were obtained with the deuteron potential dl of table. 2. The broken curves correspond to the neglect of the D-state component in the deuteron

internal wave function.

0'2 !

- 0 . 2

- 0'~

O.L,

-0.41

0./.

- 0'~

-0.

28Si (d,p) 295i g.s. it11 I n =0

• La_.~j,,,,~e~----J ~ I .(--~,,L I I L Ed=12.3MeV

~ o .... S STATE ONLY ~ u

- - S+D STATES

O¢.m.

Fig. 3. Vector and tensor analysing power for the ~sSi(d, p)29Si ground state transition. The deuteron potential used is given in table 2.

(d, p) REACTION ANALYSING POWERS 231

°+ F : ,, o . 4 r T I ~ ~ \ \ 0.~

[_ ,o / A ' , I ~o,', + ~;" °'I , 4~ ' [/,,Q o, ' + / v

0 90 o 0 ~ k-----~ . ~ f ~ I+ ~''O°-J

- O'Z, / / " - 0.4

, , / 0"4 - ,,~ ".T11 -0 .6 j ~ L

0 ~ I I r I • :e °

- 1.0 L / ~ S+D STATES \ ~

. . . . S STATE ONLY -0 '8 Oc.m.

Fig. 4. Vector and tensor analysing power for the 12C(d, p) laC ground state transition. The DWBA predictions were obtained with the deuteron potential of ref. z,t) (table 1) except for the theoretical curves (a) in T2o which were obtained with the deuteron potential of ref. 2 a) (table 1). The vector and tensor analysing power are for a deuteron incident energy respectively of 12.1 [ref. 1 s) ] and 12.3 MeV.

0.2

-0.2

-0"4

T20 T22 0"2 r ~"~

, : r • ._F f \ ' ~

.... '~;---" // >".~'° t . ~ _ . " ' , . ' :L. ' " ~/./~, ~ ~! -0.2 ~ { - - S.I-D STATES (a)

- / / / ~ . / ' / ]'11 . . . . . S STATE ONLY (a) - - - - - SI-D STAT ES (b) i-%

. , 40Ca(d,p)41Ca

_. ~++ _ L ~ ~ I I J o Ex=3.95Me V I/ \ \ .90

" , . - ,,7 \\ ] \ : , .,7 t,.,:l j.:74 I ;12.3 MeV E d

L ec.m.

Fig. 5. Vector and tensor analysing power for the +°Ca(d, p)¢lCa, E~ = 3.95 MeV transition. The curves (a) were obtained with the deuteron potential of ref. 29) (table 1). Predictions (b),

including the D-state effect, were obtained with the deuteron potential of ref. no) (table 1).

232 R .C . JOHNSON et aL

0.4

0-2

0

- 0.~

~0..

~0

0.4

- 0.4

0.4

0'2

0

- 0.2

-0.4

T11

_ f I "~'% f I i ~ f i °

9c.m.

T22

. . . . S STATE ONLY - - S D STATES

40Co(d,p)41Ca

Exl.75 MeV

In=l in=3/2

E d =12.3 MeV

Fig. 6, Vector and tensor analysing power for the 4°Ca(d, p)41Ca, E~ = 1.95 MeV transition. The deuteron optical parameters are from ref. zg) and are listed in table 2.

04 t - \

0.2

-0,2

j " 0"4

\ T20 . / " • /

o o ~ T ~ i } _ _ 7., } ~ 90

-0.~

-O.z -O.Z, L

% O.Z,

o

-o-41

T22

• ."i T°° "\ /

. . . . S STATE ONLY D

- - ' - - S + D STATES VS; 0

S+D STATES VsDo=7"67MeV

1%(d. p)170g s.

lr,:2 jo :% Ed=12.31~V

Fig. 7. Vector and tensor analysing power for the 160(d, p)l~O, ground state transition. The dot- dash and broken theoretical curves were obtained with the deuteron potential d2 and the solid with

the deuteron potential d~ of table 2.

(d, p) REACTION ANALYSING POWERS 233

o.,. I 0.2h"

-0'2!

-0'4

- 0 ' 6

T 20

F t~

i- • o -

- 0.~- I 8c.m.

0'4 F T 22

i 0'2~-

" ~ i ~i y,"~\,

! \ -0.2

-0"4 ~- . . . . S STATE ONLY , S*D STATES

2 ~Si (d, p)29Si

Ex=I.28MeV

t,.,= z i~ ' /z E d =12, 3 MeV

Fig. 8. Vector and tensor analysing power for the 2sSi(d, p)29Si, Ez = 1.28 MeV transition obtained with the deuteron potential of table 2.

0.ZI~ J T 20 f o,L

-0 '4

O.z~- iT11

~2 0-2-

-0.2[ " - - /

. . . . S STATE ONLY

S4.D STATES

40Ca (d,p) 41Ca g.s.

In=3 'in= 7//2

Ed=12.3HeV

-0,4~ 8 c.r/1.

Fig. 9. Vector and tensor analysing power for the 4°Ca(d, p)41Ca, ground state transition obtained with the deuteron optical potential of table 2.

a spin-orbit force improves the agreement with experiment particularly in Tz2 but it remains poor beyond 30 ° in/'20. Calculations in fig. 8 for a ~+ transition on 28Si show that a large D-state effect in I"2o gives good agreement with experiment over all the angular range. According to simple plane-wave predictions T2~ are independent

234 R.C. JOHNSON et al.

of the neutron quantum numbers In, Jn and T2o is always negative at 0 °. The rather strong dependence on I n andjn at forward angles in both In = i and 2 transitions indi- cates that central distortion can play an important role in determining D-state effects. The same conclusion derives from the calculation of fig. 7 without a deuteron spin- orbit force which gives a positive value for T20 at small angles.

In the calculations for the 4°Ca(d, p)41Ca ground state transition (fig. 9) the theo- retical curves with the D-state effect follow closely the experimental values except for T20 at very small angles.

The present data show that in the angular region of the main peak in the cross sec- tion T22 tends to be strongly negative forjn = In + ½ transitions and positive but small for Jn = In- ½ transitions. This feature of the data is qualitatively reproduced by the calculations only when the D-state is included.

5. Summary and conclusions

Measurements of the vector and tensor analysing power for (d, p) transitions on 9Be ' 12C, ~ 60, 19F, 25Mg ' 28Si and 4°Ca have been analysed using the DWBA theory including the deuteron D-state but without tensor terms in the deuteron optical poten- tial. The calculations confirm the generally good agreement with the small-angle T20 data reported earlier 1). Furthermore, the inclusion of the D-state is found to be essential for an understanding of the qualitative features of the angular distributions of T2 o and T22. Both central and spin-dependent distortion are found to be important if detailed agreement with experiment is to be obtained.

No simple correlation between the sign of the T2~ and the value of in, such as that found in vector polarization, is observed experimentally. This can be understood as an effect due to the D-state. Assuming spin-independent distortion and neglecting inco- herent D-state effects the major Jn dependence of the T2q arises through the quantity al~n z ofeq. (13) which is a sum of two terms, one of which is independent ofln andjn. In the absence of D-state effects it can be shown that the DWBA does predict a simple Jn dependence for the T2q , at least to first order in spin-orbit forces, and some indication of this can be seen in the dashed curves in figs. 5 and 6. Evidence for other systematic Jn dependence is discussed at the end of sect. 4.

Considerably better agreement with experiment was obtained for 2sSi and 4°Ca than for the lighter nuclei. This result suggests that contribution from non-direct processes are important in lighter nuclei particularly in view of the fact that large tensor analysing powers can arise from resonances. In addition the calculations show that the D-state effect is more sensitive to distortion in the lighter nuclei. Spin-depen- dent distortion in T2o and T22 is also more important for these nuclei.

In all calculations performed the inclusion of the D-state effect improved the agree- ment with experimental T20 and T22 angular distributions. The calculations reproduce quite satisfactorily the gross features of both tensor analysing powers. The detailed agreement was in a majority of cases better for I"22. In the angular region under con-

(d, p) REACTION ANALYSING POWERS 235

siderat ion the D-state effect is often larger in 7"20 than i n / ' 2 2 [ref. 31)]. The quali ty

of the fit to experiment for vector and tensor analysing power data is comparable

a l though D-state effects are much larger for the latter.

I t appears that the D-state effect cannot be ignored in the analysis of tensor ana-

lysing power data. The inclusion of a tensor term T R in the deuteron channel might

account for some of the discrepancies found between theory and experiment.

The help of K. R. Knight and J. M. Hi l ton and the Universi ty of Surrey Comput ing

Un i t in performing the calculations is gratefully acknowledged. This work was sup-

ported by grants f rom the Science Research Council.

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