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Spin-orbit deformation effects in (p,ṕ) from non-spherical nuclei at intermediate energies
Volume 102B, number 2,3
PHYSICS LETTERS
11 June 1981
SPIN-ORBIT DEFORMATION EFFECTS IN (p, p') FROM NON-SPHERICAL NUCLEI AT INTERMEDIATE ENERGIES L. RAY Department o f Physics, University of Texas at Austin, Austin, TX 78712, USA
Received 8 January 1981 Revised manuscript received 27 March 1981
Deformed spin-orbit, coupled-channels effects are investigated for 800 MeV proton inelastic scattering from 24Mg and lS4Sm. The influence of the spin-orbit potential on the inelastic angular distributions and on the deduced multipole moments of the optical potential is shown to be small. The predicted 4" and 6+ inelastic analyzing powers are, however, significantly affected by deformed spin-orbit coupling, multistep processes, and the large intrinsic quadrupole deformation of these two nuclei.
A current interest in nuclear physics is the study of ground-state matter density distributions in nuclei [1, 2]. Intermediate energy (Ein c ~ 1 GeV) p r o t o n - n u cleus elastic cross section and analyzing power data are plentiful, and several microscopic analyses have investigated the neutron densities of spherical nuclei [2]. Although, in principle, similar analyses can be done if the target nuclei are deformed, nucleon-nucleon amplitude uncertainties and the many theoretical refinements which must be considered [2] suggest that such extensions are premature at this time. ltowever, it is possible to obtain multipole moments of deformed matter densities by exploiting the validity of the folding model for generating the medium energy proton nucleus optical potential [2,3] and using Satchler's theorem [4]. Thus, the multipole moments of the underlying matter densities can be related to those of the deformed optical potential which is obtained by fitting elastic and inelastic angular distributions. Differences between the matter density multipole moments and those of the proton (charge) distribution provide information about differences between the neutron and proton distributions [3]. A recent coupled-channels (CC) analysis [3] of 800 MeV p + 154Sm, 176yb data explored these differences. However, the analysis neglected spin-dependence entirely. In fact, no spin-dependent CC calculations have 88
been reported for (p, p') at intermediate energies and therefore the importance of spin-orbit coupling in multistep transitions at medium energies has not been determined. Previous studies [5] have explored the importance of spin-orbit coupling in direct transitions to low-lying collective states. Here we extend such work to include multistep processes. This letter will report the results of an investigation primarily aimed at answering the following questions. (l) In the CC analysis does inclusion of the fully deformed proton-nucleus spin-orbit potential lead to a net improvement in fits to 800 MeV (p, p') angular distribution data for transitions to levels in the ground state rotational band? (2) Are the calculated multipole moments of the deformed optical potentials different when spin effects are included in the CC analysis'? (3) Would inelastic analyzing power data for these nuclei provide further constraints on the deduced multipole moments? Proton inelastic scattering at 800 MeV from 24Mg and 154Sm is considered as a first step in answering these questions. In this investigation, the deformed spin-orbit coupled-channels formalism of Raynal [6] is used. As in ref. [6] the deformed central and spin-orbit optical potentials are expanded in a multipole series, and the spin-orbit potential is assumed to be that of Sherif and Blair [7]. The calculations were perforlned
Volume 102B, number 2,3
PHYSICS LETTERS
with the coupled-channels code ECIS [8] assuming the strict rotational model [3]. The optical potentials were of the usual Woods-Saxon form with the radius parameter assumed to vary with angle according to [6]
R(O')-R 0 ( l +
11 June 1981
i O "1
.
(1)
Each term of the optical potential (except Coulomb) is deformed as in eq. (1). The calculations assume coupling between the 0.0 MeV 0 ÷, 1.37 MeV 2 +, and 4.12 MeV 4 + members of the ground-state rotational band in 24Mg and the 0.0 MeV 0 +, 0.082 MeV 2 +, 0.267 MeV 4 ÷, and 0.544 MeV 6 + members of the same band for 154Sm. The 800 MeV p + 24Mg and 154Sm elastic and inelastic scattering data [3,9] were fit by varying parameters of the central spin-independent optical potential and the deformation parameters. Since neither elastic nor inelastic analyzing power data exist tor 800 MeV p + 24Mg and 154Sm, the parameters of the spin-orbit potentials were estimated from those empirically known for several spherical nuclei ( 1 6 0 , 40,48Ca, 58Ni, 90Zr ' 116,124Sn ' and 208pb). The empirical spin-orbit potential parameters demonstrate a linear dependence on the N/Z ratio of the target nucleus. The resulting potential parameters for 24Mg in the low-energy notation [10] V, W, WSF, Vso,Wso,r,a,ri,al,rSF,aSF, rso, aso, re, ~2,/34 and/36 are 4.7, 92.5, 16.0, 0.7, and 1.5 MeV, 0.93, 0.45,0.929, 0.554, 0.45, 0.40, 1.0, 0.78, and 1.05 fm, and 0.6, 0.01 and 0.0, respectively. Similarly for 154Sm they are, -5.35, 59.5, 0.0, 0.56, and 1.0 MeV, 1.08, 0.85, 1.085, 0.615, 1.0, 0.6, 1.1, 0.65, and 1.05 fro, and 0.315,0.I02 and -0.016, respectively. The spin-orbit deformation parameters of eq. (1) were equal to those of the spin-independent potential. The fits to the 0 ÷, 2 + and 4 + angular distributions for p + 24Mg are shown in fig. 1. The solid and dashed (from ref. [9]) curves indicate results obtained with and without the spin-orbit potential, respectively. Inclusion of the spin-orbit term causes some filling in of the diffractive minima and leads to slightly better agreement with the 2 + inelastic cross section data. For the case o f p + 154Sm the results of calculations with and without the spin-orbit term differ insignificantly and are not shown (see fig. 5 of ref. [3]). The angular distribution of the spin-independent calculation for the transition to the 6 ÷ state in 154Sm (ref. [3]) is
.
.
,
24 Mg (p,p') 102
~
I01
~ /3x Y x 0 ( 0 ' ) ) . h=2,even
.
. 0.8 GeV
COUPLED CHANNELS
,%'
~
6
--WITH
~
------ NO s.o. -
h j
D.S.O.
%,.(0.0.0")
\
iO~
~0 io-'
~';42
162
,~\
(4.12.4")
,% t',,~
"
','~. 5
,'o
~
2'0
2'5
3'0
~.m.(deg ) Fig. 1. Experimental data and coupled-channels calculations of the elastic and inelastic angular distributions for p + 24Mg at 800 MeV. The solid (dashed) curves are the best fits obtained in which the fully deformed spin-orbit potential is (is not) included. lowered toward the data when the deformed spin-orbit potential is included, but only by 20%. In contrast with the results obtained at proton energies around 35 MeV, where deformed spin-orbit effects in multistep excitations are important [I 1], the 800 MeV p r o t o n nucleus spin-orbit potential has little net effect on the calculated cross sections to collective states which are excited by direct or multistep mechanisms. This result is also in contrast to the large spin-orbit effects observed in ~ 150 MeV proton inelastic excitation of natural parity, high spin states [I 2]. The multipole moments, M(EX), of the spin-independent imaginary part (largest part) of the optical potential can be defined as [3] M(EX) = Ze
f rXr~,o(rZ')Im [ V(r, O')]r2dr d~2'
X (flm[V(r)]d3r) -1 .
(2) 89
Volume 102B, number 2,3
PtlYSICS LETTERS
11 June 1981
Table 1 Imaginary optical potential and charge density multipole moments in eb hI2 Nucleus
M(E2)
M(E4)
M(E6)
Reaction
Ref.
24 Mg 24Mg 24Mg 24Mg lS4Sm lS4Sm lS4Sm
0.189 0.184 0.22 ± 0.01 0.21 ± 0.008 2.12 2.12 2.09 a)
0.0099 0.0076 0.0041 ± 0.0014 0.54 0.58 0.52 a)
--
(p, p') 800 MeV, with dso (p, p') 800 MeV, no s-o (e, e') 183,250 MeV Coulomb excitation (p, p') 800 MeV, with dso (p, p') 800 MeV, no s-o typical Coul. ex., (e, e')
This work 9 13 14 This work 3 3
0.088 0.099 _
a) These are error weighted averages of several Coulomb excitation and (e, e') measurements, see ref. [3] for a compilation of individual values. 1 . . . . . .
Table 1 presents theM(EX) obtained with and without the s p i n - o r b i t potential. Electromagnetic measurements o f the moments of the charge density are also given for comparison [3,13,14]. The M(E2) moments are unaffected by the s p i n - o r b i t term, consistent with previous work [5], whereas both M(E4) moments and the M(E6) for 154Sm differ by 10-20%. This variation is similar in magnitude to that which results from optical model ambiguities [3]. The rms radius of the best fit central, imaginary optical potential differs by 0.02 (0.04) fm for 24Mg (154Sm ) between spin-independent and dependent calculations. Deformed spin--orbit coupling is well known to significantly affect inelastic analyzing power predictions [5,7,12,15 ]. Since the large quadrupole deformation and multistep processes must be included to explain the 4 ÷ and 6 ÷ angular distributions [3,9], they should be expected to play a major role in determining the details of the corresponding analyzing powers. The deformed spin - o r b i t , coupled-channels predictions for 800 MeV ~ * 24Mg and 154Sm analyzing powers are indicated by the solid curves in figs. 2 and 3, respectively. In order to see how multistep processes influence the calculated analyzing powers for the 4 + transitions, calculations were done in which the 2 + channels were omitted from the sets of coupled equations. Similarly, to see the influence of multistep processes on the calculated 6 + analyzing power, a calculation was done in which the 2 ÷ and 4 ÷ channels were omitted. These calculations were done using the same deformation parameters as in the full coupling calculations. The fits to the elastic cross section and pseudo-analyzing power data (generated from the full CC elastic analyzing power pre90
i
24Mg(p,p'
),0.8
GeV
COUPLED CHANNELS
(0.0,0") 0,,.~
0,.( -
-
cr w O O_
C C (O*®2" ~4")
. . . . . .
Z 0.5 U >. J
r~
,',\ \
DWBA
(I.37,2"1
Z
0 , ( - -
If'\ \ ~I
1
~
I \:
/ .......
I
cc
F [
~
,o-,o., / i \ ' \ / __ / t
5
I0
,5
'
\f
t
'
[ \j \
; ,~
//
20
25
Fig. 2. Predicted elastic and inelastic analyzing powers for p" + 24Mg at 800 MeV. See text for explanation of the various CUI'VCS.
Volume 102B, number 2,3 , •
--7
.
.
.
PtIYSICS LETTERS .
.
-r
154Sm(p,p'),O.8 GeV
COUPLEDCHANNELS '.oF CL8-
CC (0" • 2" ~4"~ 6")
/
...... D,~A 0.6~-
I
/ "~ i
r.
0,4
'
/r'~
it
',~'~Z~
i~ I
i
0)
0.0I. . . . 0"2 0,8 ],i
~J O.)i <
I.Ot
•
.....
cc,o...)
,
.
! C', F ~ ,~. "Rr
tX\ . "x /
~.4-
O.O[-. . . . . . . . O.Bi
(0"~CC6")~
....
• 0.6'
~
\
If",\
~o.~ ~.,
°.°°';"1
.
I "\; l]".X.."\b' _,/Z?',~t',,I / - ' w -
o.4. °.~
,i..
,\ ! '\, / ~ ' \ I I~ 1 1 " ~ X ,' I iI ~ " :"
~i 4
~
;,
.....
I"
~
14
16
b
2"0
e~4deg) Fig. 3. Same as fig. 2, except for ~" + lS4Sm.
diction) were recovered by varying the optical potential parameters. The results of these calculations are shown in figs. 2 and 3 by the d a s h - d o t curves. Multistep processes thus account for the differences between the corresponding solid and d a s h - d o t curves. In order to determine the effect of the large quadrupole deformation on the inelastic analyzing powers for the 4 ÷ and 6 + states, distorted wave Born approximation (DWBA) calculations were carried out as described in refs. [3,15]. In these calculations the deformed, spin-dependent optical potential was expanded to first order in the deformation parameters so that the 4 + and 6 ÷ states were only excited via/34 Y4 or
11 June 1981
f16 Y6 terms, respectively. Again the fits to the elastic channel observables were recovered, as discussed above. The dashed curves in figs. 2 and 3 result from the DWBA calculations. Comparison of the dashed and dash dot curves indicates the effects of the large/32 . Significant deformation and rnultistep effects are also seen for the 2 + inelastic analyzing powers. The qualitative features to be noticed in figs. 2 and 3 are the large shifts in the angular positions of the maxima and minima as higher order/32 ,/32/34,/33, etc. deformations and multistep processes are included in the inelastic transitions to the 4 + and 6 + states. In summary, in contrast to results obtained at lower energies (~<200 MeV), refs. [11,12] the ~ 1 GeV proton-nucleus spin-orbit potential has only minor effects on elastic and inelastic angular distributions tot collective states. The reduced importance of spin effects in ~ 1 GeV proton inelastic transitions to natural parity, collective states compared to that for 150 MeV proton scattering is a result of the increasing dominance of the spin-independent, isoscalar proton-nucleon interaction over the spin-orbit term for E > 200 MeV [12]. The empirical multipole moments M(E2) are unaffected whereas the M(E4) and M(E6) change by 10-20% when the spin-orbit potential is included in the CC analysis. The large quadrupole deformation and multistcp processes produce sizeable shifts in the predicted angular positions of the analyzing power maxima and minima for inelastic transitions to the 4 + and 6 + states. This observation suggests that inelastic analyzing power data when analyzed with a full deformed spin-orbit, CC calculation could provide important, additional constraints on the phenomenological deformation parameters. In general however, at ~ I GeV, descriptions of low-lying collective state inelastic angular distributions and deduced multipole moments remain fairly accurate when the numerically much faster spin-independent calculations are performed, even when large deformation and multistep processes are important. The author would like to thank Drs. M.A. Franey and G.W. Hoffmann for valuable comments regarding the manuscript. This research was supported in part by the US Department of Energy.
91
Volume 102B, number 2,3
PHYSICS LETTERS
References [ 1 } H. Rebel, in: Radial shape of nuclei, eds. A.Budzanowski and A. Kapuscik (JageUonian University, Cracow, 1976) p. 164. [21 L. Ray. Phys. Rev. C19 (1979) 1855; and references therein. [31 M.L. Barlett et al., Phys. Rev. C22 (1980) 1168. [4] G.R. Satetder, J. Math. Phys. 13 (1972) 1118. [51 R.P. Liljestrand et al., Phys. Rev. Lett. 42 (1979) 363. [6] J. Raynal, Proc. Fourth Intern. Symp. on Polarization phenomena in nuclear reactions, eds. W. Griiebler and V. K/Snig (Ziirich, 1975) p. 271. [7] H. Sherif and J.S. Blair, Nucl. Phys. AI40 (1970) 33; Phys. Lett. 26B (1968) 489. [8] J. Raynal, ECIS80, private communication.
92
11 June 1981
[9] G. Blanpied et al., Phys. Rev. C20 (1979) 1490. [101 C.M. Perey and F.G. Perey, At. Data Nucl. Data Tables 13 (1974) 293. [I 1 ] C.H. King, J.E. Finck, G.M. Crawley, J.A. Nolen Jr. and R.M. Ronningen, Phys. Rev. C20 (1979) 2084. [12] F. Petrovich and W.G. Love, LAMPF Workshop on Pion single charge exchange, LA-7892-C (Los Alamos, 1979), unpublished; W.G. Love, LAMPF Workshop on Nuclear structure with intermediate-energy probes, LA-8303-C (Los Alamos, 1980) p. 26, unpublished. [13] Y. Horikawa et al., Phys. Lett. 36B (1971) 9. [14] S.F. Biagi, W.R. Phillips and A.R. Barnett, Nucl. Phys. A242 (1975) 160. [151 L. Ray and W.R. Coker, Phys. Lett. 79B (1978) 182.
PHYSICS LETTERS
11 June 1981
SPIN-ORBIT DEFORMATION EFFECTS IN (p, p') FROM NON-SPHERICAL NUCLEI AT INTERMEDIATE ENERGIES L. RAY Department o f Physics, University of Texas at Austin, Austin, TX 78712, USA
Received 8 January 1981 Revised manuscript received 27 March 1981
Deformed spin-orbit, coupled-channels effects are investigated for 800 MeV proton inelastic scattering from 24Mg and lS4Sm. The influence of the spin-orbit potential on the inelastic angular distributions and on the deduced multipole moments of the optical potential is shown to be small. The predicted 4" and 6+ inelastic analyzing powers are, however, significantly affected by deformed spin-orbit coupling, multistep processes, and the large intrinsic quadrupole deformation of these two nuclei.
A current interest in nuclear physics is the study of ground-state matter density distributions in nuclei [1, 2]. Intermediate energy (Ein c ~ 1 GeV) p r o t o n - n u cleus elastic cross section and analyzing power data are plentiful, and several microscopic analyses have investigated the neutron densities of spherical nuclei [2]. Although, in principle, similar analyses can be done if the target nuclei are deformed, nucleon-nucleon amplitude uncertainties and the many theoretical refinements which must be considered [2] suggest that such extensions are premature at this time. ltowever, it is possible to obtain multipole moments of deformed matter densities by exploiting the validity of the folding model for generating the medium energy proton nucleus optical potential [2,3] and using Satchler's theorem [4]. Thus, the multipole moments of the underlying matter densities can be related to those of the deformed optical potential which is obtained by fitting elastic and inelastic angular distributions. Differences between the matter density multipole moments and those of the proton (charge) distribution provide information about differences between the neutron and proton distributions [3]. A recent coupled-channels (CC) analysis [3] of 800 MeV p + 154Sm, 176yb data explored these differences. However, the analysis neglected spin-dependence entirely. In fact, no spin-dependent CC calculations have 88
been reported for (p, p') at intermediate energies and therefore the importance of spin-orbit coupling in multistep transitions at medium energies has not been determined. Previous studies [5] have explored the importance of spin-orbit coupling in direct transitions to low-lying collective states. Here we extend such work to include multistep processes. This letter will report the results of an investigation primarily aimed at answering the following questions. (l) In the CC analysis does inclusion of the fully deformed proton-nucleus spin-orbit potential lead to a net improvement in fits to 800 MeV (p, p') angular distribution data for transitions to levels in the ground state rotational band? (2) Are the calculated multipole moments of the deformed optical potentials different when spin effects are included in the CC analysis'? (3) Would inelastic analyzing power data for these nuclei provide further constraints on the deduced multipole moments? Proton inelastic scattering at 800 MeV from 24Mg and 154Sm is considered as a first step in answering these questions. In this investigation, the deformed spin-orbit coupled-channels formalism of Raynal [6] is used. As in ref. [6] the deformed central and spin-orbit optical potentials are expanded in a multipole series, and the spin-orbit potential is assumed to be that of Sherif and Blair [7]. The calculations were perforlned
Volume 102B, number 2,3
PHYSICS LETTERS
with the coupled-channels code ECIS [8] assuming the strict rotational model [3]. The optical potentials were of the usual Woods-Saxon form with the radius parameter assumed to vary with angle according to [6]
R(O')-R 0 ( l +
11 June 1981
i O "1
.
(1)
Each term of the optical potential (except Coulomb) is deformed as in eq. (1). The calculations assume coupling between the 0.0 MeV 0 ÷, 1.37 MeV 2 +, and 4.12 MeV 4 + members of the ground-state rotational band in 24Mg and the 0.0 MeV 0 +, 0.082 MeV 2 +, 0.267 MeV 4 ÷, and 0.544 MeV 6 + members of the same band for 154Sm. The 800 MeV p + 24Mg and 154Sm elastic and inelastic scattering data [3,9] were fit by varying parameters of the central spin-independent optical potential and the deformation parameters. Since neither elastic nor inelastic analyzing power data exist tor 800 MeV p + 24Mg and 154Sm, the parameters of the spin-orbit potentials were estimated from those empirically known for several spherical nuclei ( 1 6 0 , 40,48Ca, 58Ni, 90Zr ' 116,124Sn ' and 208pb). The empirical spin-orbit potential parameters demonstrate a linear dependence on the N/Z ratio of the target nucleus. The resulting potential parameters for 24Mg in the low-energy notation [10] V, W, WSF, Vso,Wso,r,a,ri,al,rSF,aSF, rso, aso, re, ~2,/34 and/36 are 4.7, 92.5, 16.0, 0.7, and 1.5 MeV, 0.93, 0.45,0.929, 0.554, 0.45, 0.40, 1.0, 0.78, and 1.05 fm, and 0.6, 0.01 and 0.0, respectively. Similarly for 154Sm they are, -5.35, 59.5, 0.0, 0.56, and 1.0 MeV, 1.08, 0.85, 1.085, 0.615, 1.0, 0.6, 1.1, 0.65, and 1.05 fro, and 0.315,0.I02 and -0.016, respectively. The spin-orbit deformation parameters of eq. (1) were equal to those of the spin-independent potential. The fits to the 0 ÷, 2 + and 4 + angular distributions for p + 24Mg are shown in fig. 1. The solid and dashed (from ref. [9]) curves indicate results obtained with and without the spin-orbit potential, respectively. Inclusion of the spin-orbit term causes some filling in of the diffractive minima and leads to slightly better agreement with the 2 + inelastic cross section data. For the case o f p + 154Sm the results of calculations with and without the spin-orbit term differ insignificantly and are not shown (see fig. 5 of ref. [3]). The angular distribution of the spin-independent calculation for the transition to the 6 ÷ state in 154Sm (ref. [3]) is
.
.
,
24 Mg (p,p') 102
~
I01
~ /3x Y x 0 ( 0 ' ) ) . h=2,even
.
. 0.8 GeV
COUPLED CHANNELS
,%'
~
6
--WITH
~
------ NO s.o. -
h j
D.S.O.
%,.(0.0.0")
\
iO~
~0 io-'
~';42
162
,~\
(4.12.4")
,% t',,~
"
','~. 5
,'o
~
2'0
2'5
3'0
~.m.(deg ) Fig. 1. Experimental data and coupled-channels calculations of the elastic and inelastic angular distributions for p + 24Mg at 800 MeV. The solid (dashed) curves are the best fits obtained in which the fully deformed spin-orbit potential is (is not) included. lowered toward the data when the deformed spin-orbit potential is included, but only by 20%. In contrast with the results obtained at proton energies around 35 MeV, where deformed spin-orbit effects in multistep excitations are important [I 1], the 800 MeV p r o t o n nucleus spin-orbit potential has little net effect on the calculated cross sections to collective states which are excited by direct or multistep mechanisms. This result is also in contrast to the large spin-orbit effects observed in ~ 150 MeV proton inelastic excitation of natural parity, high spin states [I 2]. The multipole moments, M(EX), of the spin-independent imaginary part (largest part) of the optical potential can be defined as [3] M(EX) = Ze
f rXr~,o(rZ')Im [ V(r, O')]r2dr d~2'
X (flm[V(r)]d3r) -1 .
(2) 89
Volume 102B, number 2,3
PtlYSICS LETTERS
11 June 1981
Table 1 Imaginary optical potential and charge density multipole moments in eb hI2 Nucleus
M(E2)
M(E4)
M(E6)
Reaction
Ref.
24 Mg 24Mg 24Mg 24Mg lS4Sm lS4Sm lS4Sm
0.189 0.184 0.22 ± 0.01 0.21 ± 0.008 2.12 2.12 2.09 a)
0.0099 0.0076 0.0041 ± 0.0014 0.54 0.58 0.52 a)
--
(p, p') 800 MeV, with dso (p, p') 800 MeV, no s-o (e, e') 183,250 MeV Coulomb excitation (p, p') 800 MeV, with dso (p, p') 800 MeV, no s-o typical Coul. ex., (e, e')
This work 9 13 14 This work 3 3
0.088 0.099 _
a) These are error weighted averages of several Coulomb excitation and (e, e') measurements, see ref. [3] for a compilation of individual values. 1 . . . . . .
Table 1 presents theM(EX) obtained with and without the s p i n - o r b i t potential. Electromagnetic measurements o f the moments of the charge density are also given for comparison [3,13,14]. The M(E2) moments are unaffected by the s p i n - o r b i t term, consistent with previous work [5], whereas both M(E4) moments and the M(E6) for 154Sm differ by 10-20%. This variation is similar in magnitude to that which results from optical model ambiguities [3]. The rms radius of the best fit central, imaginary optical potential differs by 0.02 (0.04) fm for 24Mg (154Sm ) between spin-independent and dependent calculations. Deformed spin--orbit coupling is well known to significantly affect inelastic analyzing power predictions [5,7,12,15 ]. Since the large quadrupole deformation and multistep processes must be included to explain the 4 ÷ and 6 ÷ angular distributions [3,9], they should be expected to play a major role in determining the details of the corresponding analyzing powers. The deformed spin - o r b i t , coupled-channels predictions for 800 MeV ~ * 24Mg and 154Sm analyzing powers are indicated by the solid curves in figs. 2 and 3, respectively. In order to see how multistep processes influence the calculated analyzing powers for the 4 + transitions, calculations were done in which the 2 + channels were omitted from the sets of coupled equations. Similarly, to see the influence of multistep processes on the calculated 6 + analyzing power, a calculation was done in which the 2 ÷ and 4 ÷ channels were omitted. These calculations were done using the same deformation parameters as in the full coupling calculations. The fits to the elastic cross section and pseudo-analyzing power data (generated from the full CC elastic analyzing power pre90
i
24Mg(p,p'
),0.8
GeV
COUPLED CHANNELS
(0.0,0") 0,,.~
0,.( -
-
cr w O O_
C C (O*®2" ~4")
. . . . . .
Z 0.5 U >. J
r~
,',\ \
DWBA
(I.37,2"1
Z
0 , ( - -
If'\ \ ~I
1
~
I \:
/ .......
I
cc
F [
~
,o-,o., / i \ ' \ / __ / t
5
I0
,5
'
\f
t
'
[ \j \
; ,~
//
20
25
Fig. 2. Predicted elastic and inelastic analyzing powers for p" + 24Mg at 800 MeV. See text for explanation of the various CUI'VCS.
Volume 102B, number 2,3 , •
--7
.
.
.
PtIYSICS LETTERS .
.
-r
154Sm(p,p'),O.8 GeV
COUPLEDCHANNELS '.oF CL8-
CC (0" • 2" ~4"~ 6")
/
...... D,~A 0.6~-
I
/ "~ i
r.
0,4
'
/r'~
it
',~'~Z~
i~ I
i
0)
0.0I. . . . 0"2 0,8 ],i
~J O.)i <
I.Ot
•
.....
cc,o...)
,
.
! C', F ~ ,~. "Rr
tX\ . "x /
~.4-
O.O[-. . . . . . . . O.Bi
(0"~CC6")~
....
• 0.6'
~
\
If",\
~o.~ ~.,
°.°°';"1
.
I "\; l]".X.."\b' _,/Z?',~t',,I / - ' w -
o.4. °.~
,i..
,\ ! '\, / ~ ' \ I I~ 1 1 " ~ X ,' I iI ~ " :"
~i 4
~
;,
.....
I"
~
14
16
b
2"0
e~4deg) Fig. 3. Same as fig. 2, except for ~" + lS4Sm.
diction) were recovered by varying the optical potential parameters. The results of these calculations are shown in figs. 2 and 3 by the d a s h - d o t curves. Multistep processes thus account for the differences between the corresponding solid and d a s h - d o t curves. In order to determine the effect of the large quadrupole deformation on the inelastic analyzing powers for the 4 ÷ and 6 + states, distorted wave Born approximation (DWBA) calculations were carried out as described in refs. [3,15]. In these calculations the deformed, spin-dependent optical potential was expanded to first order in the deformation parameters so that the 4 + and 6 ÷ states were only excited via/34 Y4 or
11 June 1981
f16 Y6 terms, respectively. Again the fits to the elastic channel observables were recovered, as discussed above. The dashed curves in figs. 2 and 3 result from the DWBA calculations. Comparison of the dashed and dash dot curves indicates the effects of the large/32 . Significant deformation and rnultistep effects are also seen for the 2 + inelastic analyzing powers. The qualitative features to be noticed in figs. 2 and 3 are the large shifts in the angular positions of the maxima and minima as higher order/32 ,/32/34,/33, etc. deformations and multistep processes are included in the inelastic transitions to the 4 + and 6 + states. In summary, in contrast to results obtained at lower energies (~<200 MeV), refs. [11,12] the ~ 1 GeV proton-nucleus spin-orbit potential has only minor effects on elastic and inelastic angular distributions tot collective states. The reduced importance of spin effects in ~ 1 GeV proton inelastic transitions to natural parity, collective states compared to that for 150 MeV proton scattering is a result of the increasing dominance of the spin-independent, isoscalar proton-nucleon interaction over the spin-orbit term for E > 200 MeV [12]. The empirical multipole moments M(E2) are unaffected whereas the M(E4) and M(E6) change by 10-20% when the spin-orbit potential is included in the CC analysis. The large quadrupole deformation and multistcp processes produce sizeable shifts in the predicted angular positions of the analyzing power maxima and minima for inelastic transitions to the 4 + and 6 + states. This observation suggests that inelastic analyzing power data when analyzed with a full deformed spin-orbit, CC calculation could provide important, additional constraints on the phenomenological deformation parameters. In general however, at ~ I GeV, descriptions of low-lying collective state inelastic angular distributions and deduced multipole moments remain fairly accurate when the numerically much faster spin-independent calculations are performed, even when large deformation and multistep processes are important. The author would like to thank Drs. M.A. Franey and G.W. Hoffmann for valuable comments regarding the manuscript. This research was supported in part by the US Department of Energy.
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References [ 1 } H. Rebel, in: Radial shape of nuclei, eds. A.Budzanowski and A. Kapuscik (JageUonian University, Cracow, 1976) p. 164. [21 L. Ray. Phys. Rev. C19 (1979) 1855; and references therein. [31 M.L. Barlett et al., Phys. Rev. C22 (1980) 1168. [4] G.R. Satetder, J. Math. Phys. 13 (1972) 1118. [51 R.P. Liljestrand et al., Phys. Rev. Lett. 42 (1979) 363. [6] J. Raynal, Proc. Fourth Intern. Symp. on Polarization phenomena in nuclear reactions, eds. W. Griiebler and V. K/Snig (Ziirich, 1975) p. 271. [7] H. Sherif and J.S. Blair, Nucl. Phys. AI40 (1970) 33; Phys. Lett. 26B (1968) 489. [8] J. Raynal, ECIS80, private communication.
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[9] G. Blanpied et al., Phys. Rev. C20 (1979) 1490. [101 C.M. Perey and F.G. Perey, At. Data Nucl. Data Tables 13 (1974) 293. [I 1 ] C.H. King, J.E. Finck, G.M. Crawley, J.A. Nolen Jr. and R.M. Ronningen, Phys. Rev. C20 (1979) 2084. [12] F. Petrovich and W.G. Love, LAMPF Workshop on Pion single charge exchange, LA-7892-C (Los Alamos, 1979), unpublished; W.G. Love, LAMPF Workshop on Nuclear structure with intermediate-energy probes, LA-8303-C (Los Alamos, 1980) p. 26, unpublished. [13] Y. Horikawa et al., Phys. Lett. 36B (1971) 9. [14] S.F. Biagi, W.R. Phillips and A.R. Barnett, Nucl. Phys. A242 (1975) 160. [151 L. Ray and W.R. Coker, Phys. Lett. 79B (1978) 182.