INTERMEDIATE ENERGY NUCLEAR PHYSICS WITH POLARISED DEUTERONS

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INTERMEDIATE ENERGY NUCLEAR PHYSICS WITH POLARISED DEUTERONS

C. Wilkin

To cite this version:

C. Wilkin. INTERMEDIATE ENERGY NUCLEAR PHYSICS WITH POLARISED DEUTERONS.

Journal de Physique Colloques, 1985, 46 (C2), pp.C2-309-C2-317. �10.1051/jphyscol:1985237�. �jpa- 00224551�

JOURNAL DE PHYSIQUE

Colloque C2, supplement au n°2, Tome *6, fevrier 1985 page C2-309

INTERMEDIATE ENERGY NUCLEAR PHYSICS WITH POLARISED DEUTERONS

C. Wilkin

University College London, London WC1E 8BT, U.K.

Résume - Nous examinons en particulier une sélection d'expériences possibles de première génération pour un faisceau de deuteron d'énergie intermédiaire.

Nous montrons que la réaction p(d,2p)n peut servir d'analyseur valable pour la polarisation tensorielle du deuteron dans l'intervalle 1-3 GeV/c. Nous discutons l'effet des interactions dans l'état final au polarimëtre vectoriel de LAMPF.

Abstract - A selection of possible first generation experiments is outlined for an intermediate energy deuteron beam. It is shown that the p(d,2p)n reaction can serve as a valuable analyser for the deuteron tensor polarisation in the 1 - 3 GeV/c range. The effect of final.state inter- actions on the LAMPF vector polarimeter is discussed.

The polarised deuteron beam at the Saturne accelerator is now working well and in the preceding talk Boudard described some of the experiments that have already been performed at this facility. I want to start by outlining a couple of the many experiments which would provide complementary nuclear or particle physics informa- tion if they were performed with this or higher energy beams.

The second half of the talk will be devoted to examining the vital question of how one can measure the polarisation of a deuteron produced in a high energy nuclear reaction. I shall present a proposal for a novel measurement of the tensor polari- sations t,- and t„. developed in collaboration with David Bugg. Apart from using this technique as the basis of a practical scattering polarimeter, the same physical ideas could be very helpful in separating the nuclear response functions to the probing by IT and p fields. I shall finish by considering briefly the LAMPF method for determining the vector analysing power of the deuteron.

Polarisation effects should persist in deuteron reactions up to arbitrarily high energies and to see this let me remind you of some undergraduate nuclear physics.

Due to the tensor force the deuteron ground state is not spherically symmetric:

there is a small amount of D-wave with a probability P of the order of 4 - 7%. The explicit wave functions for a deuteron with spin projections M = 1 and M = 0, in either configuration or momentum space, are

(la) (lb) where the proton and neutron spinors of spin up (down) are denoted by u+and v+(u_ and v_) respectively.

Since in configuration space both the S and D-state wave functions i|ig and i*^ are positive the deuteron has a cigar-like deformation. Even allowing for a Lorentz contraction a deuteron with helicity ± 1 coming towards you would look smaller than one with M = 0. There is thus at the very least a geometric contribution to the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985237

C2-310 JOURNAL DE PHYSIQUE

tensor polarisation which will not vanish at high energies.

You can see from the two typical potential model parameterisations of the momentum space wave functions shown in (Fig. 1) that J,D(p) is negative so that in momentum space the deuteron is more like a pancake. In

experiments which are sensitive to the Fermi momentum this deformation also will induce a tensor effect.

Most of the experimental verifications of these wave functions come from the form factors deter- -

mined in electron-deuteron scattering but these are convolutions of momentum space wave functions at different values of p. Can we measure J, (p)

D more directly? In a high energy deuteron break- up reaction d + p + n + p + p near the peak of quasi-free p-p scattering kinematics the

momentum of the neutron will reflect the initial Fermi momentum of the deuteron wave function.

This depends, through JI (p), on the deuteron alignment. I believe tRat higher order correc- tions can be controlled sufficiently to allow

J, (p) to be well determined in this way up to at ^{I I I I I}

D 0 1 2 3 6 5 6

least 250 MeV/c as it is for the average wave ^{P fm-'I} function shown in (Fig. 2).

Fig. 1 - Two typical deuteron wave functions $(p) "in momentum

2 2

space multiplied by (p +a ) where

ci2 = mN X deuteron binding energy:

Solid line (Humberston), dashed line (Paris).

There are two total cross sections for the interaction of a polarised deuteron with an unpolarised target, viz o T

M=O and u

.

-

ment dependence of o (dp) where just

-

la the proton and we must investigate a

series of more interesting effects such as

lo-' - A) There is a double scattering term

since there is a greater chance of one nucleon being shadowed by the other when the cigar is pointing towards the target. In the crudest Glauber estimate / 3 / the difference depends only upon the average nucleon-nucleon

0 I 2 cross section oN and deuteron matrix

P lfm-'1 elements.

Fig. 2 - Average deuteron density in momentum space. The points were deduced from a d(~,2p) experiment 121.

which of course vanishes if PD = 0. A slightly more realistic figure including real parts and finite N-N slopes yields (ao - ^ol)/o - ⁼ 1% for a 2 GeV deuteron with a relatively weak energy dependence above this.

B) I do not need to tell the present audience that the forward nucleon-nucleon amplitudes are strongly spin dependent in the GeV region. As a consequence there is a double scattering contribution linked to repeated N-N spin flips even for a purely S-wave deuteron. In the simplest Glauber model where we keep only imaginary parts of the amplitudes for point nucleons this yields / 4 /

where AaL and Aa are the differences in the longitudinal and transverse N-N total T

cross sections. At 2 GeV this effect is also predicted to be positive and about +0.5%. The inclusion of the real parts of the amplitudes in Eqn 3 will modify the result somewhat but the effect gets smaller at high energies.

C) I expect the most exciting contribution to come from inelastic intermediate states in double scattering which may also be treated as exchange current efects /5/. A proton produces a mass of particles on the first nucleon in the deuteron and these are then absorbed on the second as illustrated in Fig. 3a. We can try to

( a ) ( b )

Fig. 3 - (a) Multiparticle inelastic intermediate state in double scattering induced by Reggeon exchange. (b) The same effect but treated as a Reggeon exchange current.

estimate such effects using triple Regge language for the product of high energy production and absorption. This then looks like the exchange current diagram of Fig. 3b where the proton scatters elastically from a Reggeon in the deuteron. A

~articularly important term for the spin dependence comes for the production through pion exchange. The Reggeon in Fig. 3b is replaced by a pion and the diagram

estimated by feeding in pion-nucleon amplitudes. As can be seen from Fig. 4 the effect is large for 2 GeV deuterons due to the virtual production of the A resonance but even at the highest energies it remains similar in magnitude to that coming from the geometric deformation.

There are other smaller effects /3/ connected with Fermi motion and multiple scattering but the estimates given so far for a 2 GeV deuteron add up to

- ^a

) / o

0 1

experiment tZ0 should be obtained to parts per thousand but no experiment has yet been attempted. The above estimate is however reassuringly close to half the forward elastic dp value (t20 + = - ⁵ + 2%) /6/ which one would expect if all the

c2-312 JOURNAL DE PHYSIQUE

Table I: Suggested first generation experiments with a polarised deuteron beam amplitudes were purely imaginary.

1.5

1.0

-

- b:

b"

-

0.5

r

Experiments

..

+3 dp : a T

3

dF: ^{-+ ppn} : d a

& & dE dE p1 p2 p1 p2

L .

+ + d2a

dp + ppn :

-

+ do

dp ^-+ dp : - _m

3 d A - t d A : oT do

& z i

3 d20

d A 3 n X : -

dnrdEn

Let me close this section with an incom-

- plete list of other possible first

generation experiments 171. Under the motivation heading I have been very conservative since I do not know how isobar or quark degrees of freedom would

- affect the spin dependence.

For many nuclear reactions such as pp ³ nd it is important for the under-

Primary Motivation Neutron amplitudes

Deuteron wave functions. Away from the quasi- elastic peak the results are susceptible to mesonic degrees of freedom. Link with

3

nd -t pp.

Deuteron wave functions and vector polarimeter Test of multiple scattering theory. Spin amplitudes and exchange currents

Multiple scattering theory, bit of deuteronomy, nuclear physics and exchange currents.

Test of models of pion production in regions kinematically forbidden for single nucleon production.

1

-

0.0 I 1 I

standing of the dynamics to be able to analyse the final deuteron polarisation.

In the case of electron-deuteron elastic scattering a measurement of the tensor polarisation is necessary in order to separate the charge and quadrupole form factors 181. However practical tensor

I 10 a0 two polarimeters do not exist in the 100 MeV

pd ( Gevlc I

-

exploring the possibility that the charge Fig. 4 - Predicted pionic exchange exchange reaction dp -t (pp)n taking place current contribution of Fig. 3b to the on either hydrogen or a complex nucleus proton-deuteron total cross section might be a useful analyser. If the two

difference. protons are selected to emerge with low

relative excitation energies then the Pauli principle ensures that they are in singlet states and this imposes strong constraints on the spin-dependence of the reaction.

In impulse approximation the amplitude for such a chaxge exchange reaction is

Let me express the n-p charge exchange amplitudes in the conventional form

A A

normalised such that do/dt = J U J ' + etc. Here N, Q and are orthogonal unit + + + -r + -t

vectors with P = {(k, + k 1, 8 ^{= g.}

-

1 E

in Eqn, 4 ran easily be carried out if we take only the deuteron S-wave function.

For the singlet p-p final states this yields.

where the transition form factor is

and k is the relative momentum of the di-proton pair. The formulae should really + be applied in a system such as the Breit frame where there is no energy loss by the projectile but for the small angles that we are interested in this is essentially the same as the deuteron laboratory system. The formulae have also been derived with the quantisation axis along 3 but it is trivial to rotate to a beam quanti- sation /lo/.

In Fig. 5 are shown the values (11) of the

142 MeV small angle charge exchange ampli- _0.6 tudes as functions of momentum transfer but

normalised to du/dSlcm. The sharp variation _0.4

- .

in the 6 am~litude is a reflection of one- -\.

'x

.

pion-exchange and in the poor man's absorp-

2 .# .-.-. 1.

tion model 6 = C and 6 = C(U - ^{q2)/(p2+ q2)}

where C is constant and p is the pion mass.

Such a situation would lead to a maximal value of t (1142) and a tZ2 which would

20 P

also be maximal ($43) for s = u. However QE -0.2

P-exchange contributes to ;he 6 ^amplitude

and at low energies changes the sign of the predicted value of t20 though merely dilu-

ting the value of t22. Double scattering 0

in the deuteron should change only slightly the re dictions shown in Fig. 6.

We must now repeat the analysis for the ^{q ( MeVIc I}

triplet p-p final states and of course the Fig. 5 - (a) Real and (b) imaginary signs of t,, and t,, are opposite to those parts of the n-p charge exchange ampli-

LU L L . .

of Eqn. 6 so that tudes at 142 M ~ V / 111; 0 (long-dashes), iycdash-dot).. 6 (full line) and E

(short dashes)

.

JOURNAL DE PHYSIQUE

and similarly for t22. It is therefore crucial to find regions of phase space where -+ +

the singlet form factor S (jq,k) dominates over the triplet. Is this possible?

At low energies the p-p cross section is dominated bv the singlet "deuteron" virtual

state d* which suggests that a 120 t2z

useful region might be possible 0.6 0.8 - ( b )

but to investigate further we

need to look at p-p scattering 0.1 wave functions Yz(r). 4 For the

triplet states we take just 0.2 antisymmetric plane waves but

for the singlet we take syrmnetric 0 ones modified with a Yamaguchi

separable potential to account -0.2 for the d* 3 t p e /1_?/+

(

;

) = (eik.r+ .-ik.r +

S -0.1

i 6

2 e sin6(eikr - ^{e-Br )lkr)l42} ( 9 ) _-0.6

where 6(k) is the 'so p-p phase 100 200 JM) 100 MO

q IMeVlc) q (MeVIcl

shift and 118 is the Yamaguchi

range. _{Fig. 6} - Prediction for t20 and tZ2 for dp + +

Explicit calculations with

these scattering wave functions singlet n versus momentum transfer between the show that the singlet dominates deuteron and di-proton. Numbers indicate nucleon not only for small k laboratory energies Tp in MeV.

(< 100 MeV/c) but a130 when

<

is perpendicular to k. This is

due to the antisymmetry of It. We are therefore not restricted to working with just the narrow d* peak. If we empirically select events by imposing either

then with such cuts is about 85% of the value shown for the pure singlet state in Fig. 6.

A more satisfactory approach is to weight every part of phase space by t 2 2 20 t22 ) which avoids sharp cut-offs in acceptance. We want to use the known regions of positive and negative values of t20 in the construction of a polarimeter. Hence we are interested in an effective Itlwhere we average over the absolute value of t

20 20'

with an effective cross section

The values of

lG1,

-

Tp l MeV I 25 100 200 400

10, , , , , I ⁸⁰⁰ I

Fig. 7 - (a) Effective cross section for t20 (full line) and t (dashed line) defined by Eqn. 11. _(b) The corresponding values of 17₂₀ 1^and 22- I ^t221 .

One way around this problem might be to use a moderate size nucleus such as carbon as the target in the polarimeter. In a nucleus the 6 amplitude should be damped much less than the B or E due to the long range of the pion field. The cross-over from negative to positive t20 should then occur at lower energies. Detailed estimates of the distortion are underway but the surest way is to carry out a test measurement with the Saclay beam. The choice of nucleus is important due to the Pauli blocking of the final nuclear states. Even without distortion we only expect something less than two out of the six protons in 12c to contribute.effectively to such a small angle charge exchange reaction.

The same arguments can be applied to the monitoring of the tensor polarisation of a deuterium target by measuring the forward-going neutron produced by a charge

exchange of a high energy proton beam. Summing over all p-p final states we can get closure sum rules

where S(q) is the deuteron S-wave form factor. The deuteron D-state reduces the tensor polarisations very slightly and the results of the sum rules including the D-state are shown in Fig. 8. The appreciable signal for small momentum transfers

C2-316 JOURNAL DE PHYSIQUE

is mainly due to the 3 ~ 1 + S' transi-

tions. 1

The deuteron charge exchange reaction may prove to be the basis of a useful polarimeter but it has other uses as well. There has been much interest in recent years in the extraction of Gamow-Teller transition strengths in nuclei from intermediate energy (p,n) 1131 and (3~e,t) 1141 reactions. It is important in such studies to separate the * ^{and P} exchanges in the p A + nX cross sections. One approach is to measure the spins of both the initial and final nucleons and the transverse spin-correlation coeffici- ent has been measured 1151 for a number of nuclei at T = 160 MeV.

P

However a Saclay collaboration 1161 has proposed to measure (d,2p)

reactions by observing the two protons in the same large angle spectrometer with a resolution on the final nuclear

0 50 100 150 200 250

q ( MeVlc )

Fig. 8

-

including the deuteron D-state.

state of the order of an MeV. This

experiment is just as easy or difficult to do with polarised as unpolarised deuterons at Saturne. This is clearly not the experimental set-up that one would use for a polarimeter but the technique should allow one to distinguish between exchanges responsible for the 6, 6 and E amplitudes. Tests of this are expected soon.

Deuteron vector polarimeters are much easier to construct than tensor at high energies due to the high nucleon-nucleon analysing powers. Their calibration can be a problem though. I want to finish the talk with a few thoughts on the Los Alamos vector polarimeter 1171.

Look at the M = 1 wave function in Eqn. la. The excess of protons with spin up over

spin down is ₃

P+ - ^{P- = (1} - ^{- P} _{2 D} ^{) " 0.90} (13) If we can strip the neutron from a high energy polarised deuteron beam without upsetting the proton spin a measure of the proton polarisation would provide a measure of the deuteron vector polarisation with efficiency (P+ - ^{P-) x} the proton analyser efficiency. This reasoning works well for the dp + ^-+ ppn reaction in the region of quasi-free p-p kinematics at moderate t 1181.

This technique has been employed reasonably successfully at LAMPF by firing deuterons into a carbon dissociator and taking off the produced protons in the forward direction. In principle this is quite dangerous because in such small momentum transfer reactions the n-p final pair is at low relative energy and the final state interaction between them is then very strong. After all it is this which can change the classification of an event from one of break-up back to elastic scattering. In this region the strong n-p tensor force could then upset the simple estimate based upon Eqn. 13.

Boudard and I have made a preliminary estimate using a spin-transfer closure sum rule 1191. We find that the final state interaction globally increases the effici- ency of the polarimeter and the 90% factor in Eqn. 13 is improved on average to about 95% depending upon the experimental conditions. Of oourse we should really do a more complete estimate folding in the experimental cuts. We cannot then use sum rules and must go back to the separable potential description of the n-p final state wave function.

In conclusion there are plenty of interesting experiments to do with a polarised deuteron beam. I am also quite optimistic concerning both vector and tensor

polarimeters in the intermediate energy range. The moral for both polarimeters is though clear: don't trust the theoreticians. They may give you ideas where to look but in the end you have to calibrate your polarimeters against some known standards.

I am grateful to Alain Boudard and David Bugg for many of the ideas I have here presented on polarimeters.

References

1. HUMBERSTON, J.W. & WALLACE J.B.G., Nucl. Phys. A141 (1970) 362:

LACOMBE, M. et al., Phys. Rev. (1980) 861.

2. WITTEN, T.R. et al., Nucl. Phys. A254 (1975) 269.

3. BUTTERWORTH, D.S. GERMOND, J.-F. & WILKIN C., J.Phys. 62 (1976) 657.

4. SORENSEN, C., Phys. Rev. 2 (1979) 1444.

5. GERMOND, J.-F. & WILKIN C . in Mesons and Nuclei, ed. RHO, M & WILKINSON, D.H., (North Holland, Amsterdam 1979) 437.

6. BLESZYNSKI, M et al., Phys. Lett. 87B (1979) 198.

7. Further details on some experiments may be found in WILKIN, C, Proceedings of

~ournees dlQtudes Saturne, Roscoff, Ed. BORDRY M., (L.N.S. 1979) 47.

8. LOMON, E., Ann. Phys. (N.Y.) 125 (1980) 309:

HAFTEL, M. I. et al. , ^{Phys. ~ e} (1980) 1285 ^r : ^~ SCHULZE M.E., et al., Phys. Rev. Lett. 52 (1984) 597.

BUGG, D.V. & WILKIN C., "An analyser of deuteron tensor polarisation for the GeV/c momentum range", (to be submitted for publication).

See for example FICK, D. ~infihrung in die Kernphysik mit Polarisierten Teilchen (MANNHEIM, B.I., 1971).

DUBOIS, R. et al., Nucl. Phys. A377 (1982) 554.

ALADASHVILI, B.S. et al., J. Phys. 63 (1977) 1225.

GOODMAN, C.D. et al., Phys. Rev. Lett. 4 f ! (1980) 1755.

ELLEGARD, C et al., Phys. Rev. Lett. 50 (1983) 1745.

TADDEUCHI, T.N. et al., Phys. Rev. Lett. 52 (1984) 1960.

GAARDE, C. et al., L.N.S. proposal 115, "La rgaction (d,2~e)" (1984) 17. TURPIN, S.E. et al., in Few Body Problems in Physics, ed. ZEITNITZ, B.

(Elsevier, Amsterdam 1984) Vol. 2, 189.

18. BYSTRICKY, J. et al., "Measurement of n-p and p-p asyaunetry with accelerated polarised deuteron beam" (Contribution to this conference).

19. BOUDARD, A. & WILKIN, C., "Spin transfer effects in high energy deuteron break-up reactions", (In preparation).