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ALJIHORIS!
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DE86 011241
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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.