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WN’ER

LosAk{rnos National Laboratory

LosAlamns New Mexico 87545

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01 1111SUWIJMIAI ISUNI.IMITEO

SPIN OBSERVABLE AT INTERMEDIATE ENERGIES:

A TOOL IN VIEWING THE NUCLEUS

J. B. McClelland

Los AlarrrosNational Laboratory, Los Alamos, NH 85745

In this paper I attempt to summarize some of the advances made

in intermediate nuclear physics through measurements of spin observ-

able, notably in the range of bombarding energies from 100 to

1000 MeV. I leave the discussion of the important nucleon-nucleon

(NN) measurements to other speakers. Relative to measurements of

cross section, spin observable offer a highly selective filter in

viewing the nucleus.

Their general utility is found in their sensi-

tivity to particular nuclear transitions and is further augmented by

their simple connections to the NN force.

The advantage of higher

energies is apparent from the dominance of single-step mechanisms

even at large energy losses where general nuclearspin responses may

be made.

Experimentally, this is an energy range where efficient,

high-analyzing-pcwer polarimeters can be coupled with high resolu-

tion detection techniques.1

The first experiment to measure a corrpleteset of spin observ-

ablas for the elastic scattering of protons from a nucleus2 provided

the impetus

for a Dirac description of the scattering process.3 An

apparent failure of the

nonrelativistic

KMT

treatment

of

intermediate-energy proton elast~c

scattering data for cross sec-

tions and, most noticeably, analyzing powers had already been @exte-

nsively investigated looking at numerous corrections in order to

resolve the discrepancies. Furth**rmore,it was believed that the

dnta were driven by the geometries of the nucleus such that the

third independent observable for elastic scattering,

thq

spin-

rotation parameter, Q, wolll.dbe predicted from the other two, cross

section and analyzing power.

The data for Q turned out to be in to-

tal disagreement with this prediction and not explained by the stan-

dard KHT analysis,

Predictions of Q using the Dlrac phcnomenology,

however, provided e~cell.entagreement with the data,

An can

be see:~in Fig. 1, only small differences in the cross

section are seen between a more recent relntivistie imp~llse

approximation

(solid

curve)

nnd nonrelntivistic impulse

approximation (dashed

curve) predictions,

vhermn~

the

nnalyzing

power (or polnriza[ion

P) and the spin rotntion pnrnmeter (Q) ar~

both qualitatively and quantitatively different.

The ontierlyir)g

physics is quite different. The D{rnc nppronch incl~des processos

such as vittual pnir production and nnnihi]ntion in the field of the

lIUCIWS no~. present in nonrelnttv{stic dynnmic.s. The 500-tieVrl~tn

mnrkwily fnvo~ the Dirnc trentmont.

rt sho\lldbe pointed out,

how

ever,

thnt sp!n rotation data at other ~nergie~ and on othmr-targets

ar~ not in as good agreement,

h~lt it is prectsely these type 01 (Intn

tllnt nre

likely to shed light on this lssIIe.

p %3

497 MQV

-2-

P

-.

(b) ,.’

4*

1’

n

,-

0

10

m

m

+-

-1

L

I

Fig. 1.

40Ca(p,p) scattering at 500 MeV with relativistic

(solid curve) and

nonrelativistic calculations

fOr cross section, analyzing power, and spin

rotation parameter from Ref. 4.

A dir~ct connection can be mnde between spin ohslervables and

the squarad moduli of tha coofficienis of th~ ●ffective t.fNscatter-

ing amplitude given by

H(q) -

A + Bdlnu2n + c(ull~

+ u2n) +

Eulquzq + F@],pU2p ~

(1)

where 1(2) -tenotesthe tar et (p oj ctile) n cleon and the unit vec-

tors (h,~,$) are in the

fx~t, ~_K? #

and ~x directions, with K(K1)

ti]arelative momentum in the NN syst~m before(after) collision.

For

unnatural parity

transitions, i:

hnr

b@en ~hovn~~s that in the

stntic limit

10

_

(cZ + B1 + FZ)X; + EZX; ,

(2.1)

IoDnn . (0 +

B~ - F2)X; - E2X~ ,

(2.2)

ID

o PP

=(c2 -Bz

,Fz)x&E]X; ,

(2.3)

rD

Oqq”

(cl

B2 _ F2))(: , E~x: ,

(?.4)

IoDno . loDon -

2x;ne(Bc*) ,

(2.5)

It)

()

qp -

-IoDpq - 2X~1m(BC”) .

(2.6)

-3-

where Xf(~) is the

static lorgitudinal(transverse)

One cay see ~from Eq. 2 that

form factor.

if the nuclear structure is known

(i.e. XL and ~), the q dependence of the effective ~ interaction

mav be mapped out by measuring a complete set of spin observable to

discrete final states at several momentum transfers.

Although

Eqs, 2 are strictly valid in the plane wave impulse approximation

(PWIA), full distorted wave (DWIA) calculations have shown that dis-

tortion or details of the transition density have little effect on

the spin

observable for a transition dominated by a single

multipolarity near the peak of the associated form factor.

Thus,

Eqs. 2 are expected to still be valid under these conditions.

T$e first complete set of spin observable at intermediate

energy for

Jlelasticscattering used the two lowest 1+ states in 12C

at 500 MeV to map the q dependence of the individual coefficients of

the NN spin-dependent

interaction for both isospin channels.7 The

results were consistent with the free NN amplitudes.

Further meas-

urements are needed to improve the accuracy of these results

as well

as extending

them

to larger q

by choosing states of higher

multipolarity. In principle one can be divorced from uncertainties

in nuclear structure by doing similar measurements in quasi-free

scattering.a It is no longer possible to make the isospin decomposi-

tion in (p,p’) directly, but similar measurements will soon be

pos-

sible in the (p,n) reaction, which is purely isovector in nature.q

The combination of (p,p’) and (p,n) vould be complimentary and

both

would requi~e only modest energy resolution.

Spin observable have also been shown to be more sensitive to

convection (~) and composite (~ x ~) currents than unpolarized cross

sections

alone.io

Observable such

as u(P-A) and u(D1~+Dsl) have

been found to be most useful in detecting and confronting composite

currents,

Nonrelativistic and relativistic theories all contain

these

currents at

some level of approximation, althou~h

the

relativistic treatment

gives

rise to

these currents in a more

natural way thuough the lower component,

As an e.mmp~e of the selectivity and sensitivity of sp{~l ob--

servables to particular nuclear transitions, consider Fig. 2, which

is the spectrum of inelastic states in ‘2C at 39? MeV fron 7 to

23 MeV in excitation.

This is seen in the top portiorlof the

figure. The spectrum

is dominated by

the

nature]. pnrity dS=O

transitions

at 7.6 and 9.6 PleV. Genernl.symmetry properties of

the

scattering amplitu(ieim ly

R

that

for

transitions involving spin-

p~ri:y

transfer of

J 4)”,

DN --1,

Y

nnd for transitions involving

J -0 , DNN=+l. In general

a pOs ti’~evalue of I?NNis a signat(lreot

AS=() strength, ~hile 6S=1 transitions yiel(ia negative or zero val(le

of DNN.

This is seen directly in the bottom portion of Fig. 2

for

the spin--flip ‘ -

transverse

Cr:s-’ ‘ecti”r”

‘:u’dQ’sN!il,~

‘t1~7e ‘NN-(l”DNN)/2 ‘s ‘])e

spill-fl,lp probFlbll\ty. Ilfi:!lrtll

pat I ty

As-()

tran3iti0ns4 111 the

top spectrum are completely sIIpptessJ*d {n tt)e

spin flip (’roQssection.

r)nly

tll@ Ilnnatllrnl parity As-1; 1’ RI:d Y

~tld

nntulal pnrily AS-1; 2’” stnt,espetsist.