ELASTIC AND INELASTIC d-p SCATTERING WITH POLARIZED PARTICLES

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ELASTIC AND INELASTIC d-p SCATTERING WITH POLARIZED PARTICLES

A. Boudard

To cite this version:

A. Boudard. ELASTIC AND INELASTIC d-p SCATTERING WITH POLARIZED PARTICLES.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-365-C2-374. �10.1051/jphyscol:1985242�. �jpa- 00224556�

JOURNAL DE PHYSIQUE

Colloque C2, supplement au n°2, Tome 46, fevrier 1985 page C2-365

ELASTIC AND INELASTIC d-p SCATTERING WITH POLARIZED PARTICLES A. Boudard

Laboratoire National Saturne, 91191 Gif-sur-Ivette Cedex, France Résumé - Nous présentons une revue des expériences récentes et de leur interprétation dans le domaine des énergies intermédiaires. La diffusion élastique à l'avant et à l'arrière ainsi que la production d'un 7T et d'un % dans des réactions à deux corps posent encore d'intéressants problèmes d'interprétation.

Abstract - We present a review of the recent experimental and theore- tical progress of the p-d system in the range of intermediate energies.

Interesting open questions about the interpretation of forward and backward elastic scattering as well as TT or & production in two-body outgoing systems still remain.

Since the subject of the conference is "High Energy Spin Physics" we will not speak about the d-p problem at energies of a few tens of MeV or below. We will present a review of the recent progresses for energies from a few hundred MeV to several GeV and try to answer two questions :

- Why is it interesting to study this particular system ? - What is added by using polarized particles ?

This is first of all a few body problem. The inelastic channels studied with polarized particles up to now have been mainly 17t+,3 He It6 and 3H e # . The wave functions involved are rather well known (deuteron, triton) and a microscopic description in terms of elementary forces or mesons exchanged is possible. There- fore we can hope to have a good theoretical understanding of the reactions (to first order), so that more constraints on the elementary forces (which are used here off shell), as well as better knowledge of details in the reaction mecha- nisms can be obtained by a comparison with experimental data. In the final analy- sis those reactions are a step between the elementary processes (nucleon-nucleon force, meson-nucleon vertex) and nuclear physics involving larger nuclei.

- Forward elastic scattering involved small momentum and energy transfer. Its description is naturally multiple scattering with the NN amplitudes from the phase shift analysis as an ingredient. It is connected with proton-nucleus elastic scattering.

- The backward elastic scattering implies large momentum transfer (all the nu- cleons reverse their momentum) so that inelastic processes such as NN—*• NAas have to play a role. It could be understood as the most simple one neutron trans- fer reaction A(p,d)B.

- In the inelastic processes going to He"^ , He It0 or 171* both energy and momen- tum are transferred. The explicit Jf -nucleon or to* -nucleon coupling means that in the 500 MeV-1 GeV domain the A 3 S will play a dominant part. The connections with the A(p,'X')B or A(p,tf )B nucleon reactions are obvious.

In addition the deuteron can be considered as a source of neutrons. For example the np analyzing power could be measured at Saturne with an interaction between a vector polarized deuteron beam and an hydrogen target (communication to this conference by F. Perrot).

ELASTIC SCATTERING IN THE FORWARD DIRECTION

An extensive- and complete study is justified by the good theoretical situation.

As a matter of fact, only two nucleonic scatterers are present in the weakly

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985242

C2-366 JOURNAL DE PHYSIQUE

bound deuteron so that multiple scattering is well justified and can be treated in much detail. The non eikonal and full spin trestment (deuteron with S and D states and five amplitudes of NN) of Alberi, Bleszynski and Jaroszewicz /1/

gives a very good fit to the deuteron vector and tensor analyzing prowers measured at Argonne /2/ (Fig. 1).

Fig. 1 - Multiple scattering calcula- tion of ref./l/ compared with the deu- teron analyzing powers reported in ref.

/2/ at 1600 MeV. The effect of the ei- konal approximation is shown on the left part, and the sensitivity to the double spin flip term of NN on the right part.

The cross section (well reproduced) is almost unaffected by the eikonal appro- ximation. A sensitivity to the inaccu- rate double spin flip terms of NN is also found even at small transfer (-t 0,2 Gev2) especially for the vector analyzing power, so that we can expect a better knowledge of that NN term.

Recently, the 1200 MeV deuteron analy- zing powers Ay and Ayy measured at Argonne were extended up to 180° at Saclay /3/ (Fig. 2 ) .

plXd)p Td=1.2 GeV I

0 ldegreesl

Fig. 2 - The vector Ay and tensor Ayy analyzing power measured at Saturne ( Q and t ⁾ ref. /3/ compared with the data from Argonne ( + ^{) ref. /2/.}

1.0

"

0 5 -

0

-0.5

Another class of experiments has been done at LAMPF with measurements of spin rotation parameters at 500, 650 and 800 MeV. A. Rahbar et a1 /4/ and Sun Tsu- hsun et al. /5/ have measured DNN , DSS, D L . , DSL and DLL up to -t iu 1 Gev2 (N is normal to the scattering plan, L along the direction of motion and S so that S = N A L. The first index refers to the incoming proton and the last to the outgoing one in the lab.). Sun Tsu-hsun et al. have in addition measured the proton analyzing power A and the polarization of the outgoing proton P. As we have here elastic scattering on a non zero spin target and a QN spin transfer which differs from 1, they can test time reversal invariance (TRI) and they con- clude that there is no violation (Fig. 3). Because they have a complete measure- ment of the spin rotation parmaeters, they can also deduce separately the values of D e b and Dde in the center of mass.

p l z d l p Td=l.Z GeV

-

Mas 1 2

g d ~ ^{i "XoL. 1 2}

d l ^t " ^{1- n} .I

P I I I -

,' 1

3 t

1 1 , ^$

t

i f

- ⁺ _t 3 ^{f i} -

I I

50 100 150

8 ldegreesl

0 5

o*

03

; ^{0 2 -}

4 m 0.1

o

-0.1 QZ

Fig. 4 - Measurement of the spin rotation parameters ref. /5/ compared with standard multiple scattering calculations ref. /I/.

0.1 0 -0.1

I < -02- -01 q.4

.os

Fig. 5 - Some spin rotation parameters and proton analyzing power (A) at 500 MeV ref. /4/ compared with the standard calculations (full line) and a first estima- tion of relativistic effects in the multiple scattering (dashed line ref. / 7 / ) .

1 0 a a 3 0 4 o Y I 6 o T O

&(d.ol In a theoretical paper /6/, it was pointed

02 , out that such complete measurements allow

Fig. 3 - Comparison between P and A repop

T p ' 6 4 7 Y . V ~ P I S U ~ I

- _$

A l l U n l .

-

- 11' { I , ,

- _t 1 ' _b

- _{t t} t

~ z o s o 4 o s ~ 1 6 o m

B b t a o ] data. It has recently become known that

relativistic treatment greatly improves the calculations of multiple scattering, especially in the case of spin observables. A first estimate of these effects in p-d elactic scattering has been done by Adams and Bleszynski /7/. In their calculation, only a central and an incoming proton spin dependent term are used as NN amplitudes. The changes obtained in the spin rotation parameters are very substantial and a real improvement is obtained (Fig. 5).

- ^{T 4 % M ' 6} ; i s w * j '

0 AIlU", -

- -

+, 11 I 01 I * +

-

. '$1

ted in ref. /5/ as a test of Time Reversal Invariance.

TRI results in the relation D b e = - ~ e b

which is also well satisfied at 496 MeV and 647 MeV.

one to extract depolarizations,among these DX and Dr would be expecially interesting because they are strongly dependent on the double spin flip terms of NN. In spite of the accurate formalism described in ref. / I / , agreement with the data is so poor (Fig. 4) that some shortcoming in the formalism seems more plausible to the authors /4,5/ than inaccuracies in the NN

C2-368 JOURNAL DE PHYSIQUE

The authors have pointed out that the negative energy part in the propagator of the double scattering amplitude is mainly responsible for the difference between relativistic and non relativistic calculations. It is now of great interest to wait for a complete relativistic calculation of all the spin observables, but a difficulty could be that NN data also have to be considered to determine unam- biguously the relativistic amplitudes, as shown by the same authors /8/.

We also cannot forget the absolute phase of the NN amplitude which is by definition unknown from NN experimental study. In the region of interference (0.2( -t < O . ~ G ~ V ~ ) between single and double scattering this phase can probably change a lot the results of spin observable calculations. It could be in fact a way to know it at a momentum larger than in the coulomb nuclear interference.

From the experimental point of view, a third kind of experiment involving three spins (if + ?? --.; + d) is underway at LAMPF. Data with deuteron vector polarizations along N and L axis are still obtained. The third possibility is planed for next year. For completeness a collaboration proposes the same sort of measurements with the vector and tensor polarized deuteron beam of Saturne. All these data will surpass the 23 independent measurements needed to determine all the amplitudes at 800 MeV (proton) in the forward direction. At 500 MeV a lot of data have also been measured giving an accurate energy dependence, so that the p-d elastic scat- tering could become a test for a lot of details in the theoretical treatment of multiple scattering. Among them relativistic effects seem the most promising.

Details of the NN interaction as double spin-flip, absolute phase and off shell corrections could be studied. Sophisticated calculations with full spin treatment are already available and are in the process of being refined by means oE compari- son with the data ; so that it is important to finish that study which can help lead to a better and detailed understanding of medium energy hadron elastic scat- tering.

BACKWARD ELASTIC SCATTERING

In this particular kinematics, the particles are reversing their motion during the reaction so that large momentums (7.3 fm-I at 600 MeV) are transferred. The cross section is sharply peaked around 180' at all energies and the excitation function at 180° decreases slowly with increasing incident energy up to 300 MeV (Fig. 6). For these reasons, the exchange of a neutron between the incoming and outgoing deuteron is thought to be the dominant mecanism. If computed in plane waves this gives a reasonable account of the data but with a cross section larger than the experiment. Distortion effects need to be considered.

Fig. 6 - Compilation of the elastic scattering cross section at 180° as a function of the laboratory proton kine- tic energy (from ref. /9/). The dashed and dashed dotted lines are the one neutron exchange contribution with dif- ferent approximations. The full line is the A contribution excited by a 7(

rescattering.

Above this slowly decreasing component in the excitation function, a bump was found and carefully measured around 5 0 0 ~ 600 MeV (see ref. /9/ and included refe- rences). It is tempting to connect it to the pp ---+ dfl cross section which also has a resonant behaviour at the same energy, mainly due to the A33 (1232) reso- nance. A direct connection using the experimental pp --. d7T' as an input was first established in the so-called triangular graph (Fig. 7) by Craigie and Wilkin /lo/ and Barry /11/.

Fig. 7 - Different contributions to the p-d backward elastic scattering discussed in the text.

,. ..

TRtranCULAR 0. N .T. T. M.E.

6 R A Q H

In the same spirit, microscopic calculations of the 4 excitation in the inter- mediate state (TME) added to the one neutron exchange (ONE) give a reasonable description of d r / d n (180°) from 300 MeV up to N 1 GeV /12/.

As an alternative a model based on experimental NN cross sections (equal at O0 and 180°) used in a multiple scattering description and summed with the ONE was proposed to explain the backward scattering between 200 MeV and 1.4 GeV /13/.

In this case, the bump around 600 MeV was believed to come from a corresponding structure in the deuteron form factor, but this structure is hardly found in the experimental electric deuteron form factor /14/ around 2.5 GeV/cz (Fig. 8).

q 2 b w / c ~ Z ] Fig. 8 - Comparison between the

I 2 3 ⁴ 5 6 7 8 deuteron form factor needed to

0 w k-lo(lo.

reproduce the bump of the exci- tation function in the multiple scattering approach (left side from ref. /13/) and the experi-

S mental one (right side from ref.

" 0 y ,ja -- ^{1141 1.}

r = ^{s 16}

l1KI

" V ) -

'. the single scattering is negli-

10 gible above 400 MeV /15/ so it

will be interesting to have an

, ,, , ,, ,, , estimate with the code of Alberi-

6 2

q'(~vnrP ^{02 (fm-2)} Bleszynski, which treats in a non

eikonal way the full NN amplitu- de obtained from phase shift analysis.

the triangular model predicts an equality of the pd--rdp and of the pp-d'TT analy- zing power at the same proton energy in the laboratory system. From the direct comparison of the data it was noted that asymmetries are very similar just at the resonance but different above /16/ (1.03 GeV) and below /17/ (316 MeV). This cannot be a strong argument against the triangular graph which has to be summed at least with the ONE which is an important contribution outside the resonance.

Of the tensor analyzing powers, only T20 is non vanishing at 180". This observable was measured at Saclay with the first vector and tensor polarized deuteron beam available at Saturne. The valueof T20 was measured at 180' (or very close to that angle) between 300 MeV and 2300 MeV (corresponding to 150 MeV and 1150 MeV for a proton beam) /3/. The excitation function exhibits a first deep minimum at Tp fU 250 MeV which is expected in the ONE but at a larger energy (350-400 MeV).

To understand the entire energy domain of this experiment, we have computed /18/

the coherent sum between ONE and a LJ formed on any of the nucleons by exchange of 7T or ,f mesons. The meson exchange is treated in a non relativistic way.

Repulsive short range correlations ( L o exchange) as well as recoil corrections are taken into account to first order /19/. The different amplitudes are then obtained by integration on the wave function coordinates (deuteron from the Paris potential with S and D state). The only approximation made is to consider the momentum of the mesons as aligned along the scattering axis, an approximation which must be good considering the large momentum involved. A rough distorsion

C2-370 JOURNAL DE PHYSIQUE

in an eikonal approximation (central term only without effects of the spins) is introduced for the ONE and improves the low energy ( N 200 MeV) computed cross sections. We found a reasonable agreement with the cross section, but only the gross features of T20 are reproduced (Fig. 9). The structure observed in the TZ0 experiment between 500 MeV and 700 MeV (a equal 3.07 GeV to 3.30 GeV) is not predicted by our calculation. The same sort of conclusions can be drawn from a calculation containing similar reaction mechanisms (ONE+TME) but with different technical evaluations /20/. The exchange of a N* (1680), which opuld be present in the deuteron wave function with a 1% probability as proposed by Kerman and Kisslinger /21/, pushes the calculation of the cross section around 1 GeV closer to the data without a significant change in TZ0(Fig. 10).

Fig. 9 - Excitation function of the cross section and of T20 for p-d elastic scattering at T80° as a function of the proton kinetic energy in the laboratory.

The calculations are from ref./l8/ and are the coherent sum between ONE in plane wave (PW) or distorted wave (DW) and excitation (TME) by a pion re- scattering (IT ) or by a TT and ? ^rescat-

tering with correlation effects ( T T , P ,

w ) .

Fig. 10 - Addition of a contribution from an N* (1680) exchange to the " n ,

f ^{, W I'} calculation of Fig. 9. The N* is supposed to have a 1% probability in the deuteron as proposed in ref./21/.

The long dashed curve (T20) is given by the addition of tribaryons to the stan- dard ONE plus A, contribution (dashed dot line in 0- ) as computed by

Kondratyuk et al. ref. /25/ . ^{The ( * )}

are obtained from ASP measurements of

- 4

PP -4 d K (ref. /24/) .

The excitation of ~"(1520) in the TME must peak at Tpr.1450 MeV. It could change the calculations around 1 GeV, as could a relativistic treatment of the ONE /22/.

As pointed out by Wilkin /23/ a value of T20(1800) in the pp--r d T reaction can be obtained from an extrapolation of A l i measurements /24/. It has to be equal to that for pd ----. dp at the same proton energy in the triangular picture, but is in fact closer to our calculations than to the zp - pd experiment (Fig.10).

Kondratyuk and Shevechenko /25/ have added to the ONT and TME tribaryon resonances (at 3070 MeV, 3180 and 3330 MeV) and found a shape of T20 much closer to the expe- rimental one (Fig. 101, but with a a + ONT which is incredibly small around 600 MeV where we believe that a excitation produces almost all the cross section.

We can conclude by saying that the structure observed in T around the energy is a challenge to the theory and could be of basip interest.20 It is not understood up to now in terms of ONT plus A excitation and N* exchange, models which are related to the more phenomenological triangular graph and which give a reasonable

account of the cross section. More information has to come from experiments. Does the same problem exist in the two nucleon system ? A complete measure of T

20 for pp d dTf at backward angles might provide an answer. Other spin observables such as spin correlations or spin transfers, which are planned to be measured at LAMPF could also constraint the theory. Other channels such as pd --+ t T must also be experimentally investigated and understood by the models in a consistent way. It is clear that improvements of the classical picture such as relativistic effects, distorsions, phases and multiple scattering contributions have to be investigated before any believable conclusion about a tribaryon effect can be drawn. But even if no exoctic effects are found in the end, these experiments and their interpretation will help provide a better understanding of the mechanisms which allow the transfer of momentum and energy and involve an accurate treatment of the A (1232), which is so important in intermediate energy physics.

INELASTIC CHANNELS t R+, ~e~ x0 He3 8

Those reactions are understood in terms of fl -nucleon scattering (non resonant in the S, P and D waves and resonant via the 4 33 ) up to N 800 MeV proton enera.

They are a step between the basic processes such as pp - ^{dT(' , pn- dg and}

(p,X ) or (p,g ) reactions on heavy nuclei. In addition to the experimental angular distributions of cross sections, which have been measured more accurately in the last three years, data on asymmetries are now available.

PHOTOPRODUCTION

Measurements of zd

-

FigA1l - Experimental analyzing power of p + d -+ 21 + 3 ~ e from ref. / 2 7 / compared with Laget calculations ref.

/27/ and /29/.

PION PRODUCTION

Thd analyzing power of the pd d + tnc reaction has been measured from 280 XeV up to 1100 MeV. The different measure- ments done at TRIUMF 130/ give a good experimental knowledge below and up to the resonance (around 450 MeV). An extremum around 90° goes from negative values ( A N - 0.5) at the lower energies to positive ones (A N 0.3) at 500 MeV.

At the backward angles (110°-160°) a

r.1- 41-3 more detailed study of the energy depen-

dence was recently done /31/ from 425 MeV to 500 MeV by steps of 25 MeV. The cross sections are found to be flat with angle and the largest values measured are around -0.55 in contrast with the extreme value of -1.06 which had been some- times reported.

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An interesting comparison between the analyzing powers of Fd

-

-. pd + ~e3l't~shows (Fig. 12) that there is no evidence for charge symmetry breaking for this observable which is free of absolute normalization problems.

Fig. 12 - Comparison between fSd ---r tx* and

4 pd - ^{3 ~ e 7T0} analyzing powers from ref.

/32/.

1

:$5 - ^nF zing power of the zd ----r t ~ +reaction are studied at 600, 650, 700 and 800 MeV

(LAMPF, /33/, Fig. 13) and at 900, 1000 and 1100 MeV (Saturne, /34/, Fig. 14). A

. s , G c g ? $ large structure at backward angles in the

a ; ^{6,. 3w n . ~} analyzing power, which does not exist at

.1.:- 500 MeV, begins to appear'at 800 MeV and

Q M ':- 60 Y, iW a0 continues up to the highest energy measu- red (1100 MeV). A corresponding bump is observed in the cross section at 800 MeV, 900 and 1000 MeV in contrast to the flat backward distribution measured at 500 MeV. It must be noted that this structure in the cross section is not at 180°, and is neither at a constant 4-momentum transfer -t (0.82 Gev2 at 800 MeV, 1.15 at 1000 MeV) nor at a constant u (2.21 Gev2 at 800 MeV, 1.78 at 1000 MeV).

Fig. 14 - Analyzing power of

--. pd --+ t TT' from 900 MeV to 1100 MeV (ref. /34/).

Fig. 13 - Analyzifg power and cross section of pd - ^{tTTC up}

to 800 MeV from ref. /33/.

Nevertheless, the excitation function of the cross section (180°) measured up to higher energies /35/ (Fig. 15) begins to present a bump which is fully developed at 1200 MeV. There is a clear need for some other measurements of A in the backward region up to rv1400 MeV to cover completely this interesting phenomena.

Fig. 15 - Excitation function of the ;d - ^{t ~ *}

cross section at 180° (between p a n d N ) from ref. /35/.

The latest microscopic interpretation of this reaction is presented by Laget and Lecolley /36/. It is interesting that they present on the same footing analysis of Zp -dT and

-b pd -- - - r t

n , in much the same way as they

handle deuteron photodesintegration. The model treats the Born term pion production from pro- ton and deuteron as well as rescattering of7f or p through the S, P and D waves and through the a33 resonance.

For the pd - ^{t T} cross section a good overall description of the energy and angular dependence is given up to 500 MeV over the complete angular range. A t 800 MeV an important feature is missed by this approach at backward angles for the cross section as well as for the analyzing power (Fig. 16).

Fig. 16 - Cross section and proton analyzing power at 500 MeV and 800 MeV computed by Laget and Lecolley (ref. /36/) compared with the data

Around one GeV in the backward direction new contributions must certainly be consi- dered. If we compute the contribution of the resonance propagator to the cross section we found that the N* (1520) (which has a large coupling constant with

XN) reach a maximum at 1000 MeV. But a (1232) state excited in the reaction has a maximum contribution at 1050 MeV. Despite having more vertices the con- tribution could be favoured here because all the nucleons inverting their momentum at backward angles can participate to the reaction. Only complete calculations with wave functions and interference effects will help us to understand in detail.

From the experimental point of view, excitation functions of T20 , which are pro- posed to be measured at Saturne could also add an important test for the models.

ACENOWLEDGEMENTS

I have received the help of many physicists in preparing this paper. Among them I would especially like to thank M. Dillig, J. Cameron, J.Arvieux, G.Igo,B.Silverman.

C2-374 JOURNAL DE PHYSIQUE

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