Spin observables at intermediate energies: A tool in viewing the nucleus

TL;DR: Experimental determination of recent advances in spin observables in nuclei is reviewed in this article, where data from elastic and charge exchange proton scattering from 13C, 40Ca, 90Zr, and 208Pb at proton energies ranging from 100-1000 MeV are discussed.

Abstract: Experimental determination of recent advances in spin observables in nuclei is reviewed. Data from elastic and charge‐exchange proton scattering from 13‐C, 40‐Ca, 90‐Zr, and 208‐Pb at proton energies ranging from 100–1000 MeV are discussed.

Summary

Resolution of this problem

• Seems to rest with experiments that are sensitive to thinly distributed GT strength t[~the contin\lum.
• Cross-section angular distributions are primarily sensitive to the orbital angular momentum transfer AL rather than the total angular momentum trmsfer &l.
• These giant resonances aL-ñ o t systematically obsorved in back-angle electron scattering, presumably sensitive to tllstrength.

energies (500 MeV).

• The connection between the two is through -6- explanations of the European rfuon Collaboration (EMC) effect and their implications for inclusive proton scattering.
• In both scattering processes the enhancement of the mNN vertex arises in the same way, and any explanation of the EMC effect invoking enhanced pion fields within the nucleus must confront the lower-energy hadron scattering data.
• Several corrections must be made to the proton data, however, before the Level of sens~tivity to the predicted enhancement of RL can be determined.
• ~u~t be made for the mixed isospin contributions for (p,p') scattering, This is accomplished using the isospin decomposition of the NN interaction from t e 500-MeV phase-shift solution of Arndt. !.
• The work and ideas presented here include those of many of my colleagues and collaborqtcrs.

Full text

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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.