- Email: [email protected]
Studies of spin observables in (p, p′) and (p, p′γ) reactions at intermediate energies
NUCLEAR PHYSICS A
Nuclear Physms A577 (1994) 27c-32c North-Holland, Amsterdam
Studies of spin observables in (I~, if') and (t~, P'7) reactmns at intermediate energies S Vv Wissmk ~ ~Department of Physics, I n & a n a Unl~erslty, and Indiana Umverslty Cyclotron Eaohty, Bloomington, I n & a n a 47408, USA Recent measurements at 200 MeV of (i~,l~') spin transfer observables for exc~tatlon of discrete states show slgmficant dewatlons from theoretmal pre&ctlons based on the free NN t-matt1,: Because the nuclear structure and &stortmns for these tranmtlons are beheved to be constrmned by other data, this suggests that modifications of the ~z-med~um NN lnteractmn are needed, beyond Pauh blocking, to describe these processes As a first ~tep towards identifying the phymc41 mechanisms that underhe these modlhcatlons, several phenomenolog~(al approaches have been tried to m~prove agreement between experiment and theory The successes and hm~tatmns of these approaches will be &scussed P w l m n n a r y results flora a detailed study ot the (I~, P'7) reaction for the 1+, T = I state in t~(, at 15 11 MeV will also be presented 1
INTRODUCTION
AND
OVERVIEW
OF PROGRAM
The inelastic scattering of nucleons fiom nuclei remains one of inn lwhest sources of information on nucleaI structure, the l n - m e d m m effective interaction, and the reaction mechanisms involved Work at lnterme&ate energies (100-500 MeV) provides a regime m which the spin-orbit and tensor terms of the underlying nucleon-nucleon (NN) interaction are enhanced relative to the usually dominant central term, and in which the relatmnshlp between the nucleon-nucleus (NA) and NN interaction may be made transparent through use of the mlpulse approxHnatmn O~er the past few years, the high count rate and hlgh-resolutmn (25 keV) capablhtles ot the I U ( ' F K600 spectrometer and its associated focal-plane p o l a n m e t e r have made possible detaded inveqtlgatmns of several specific nuclear tranmtlons, where the selectlvlt 3 of the q u a n t u m numbers ln~ol~ed can be exploited to xsolate or enhance specific terms in the effective NN interaction To m~e~tlgate the spin-dependence of these terms, we ha~e concentrated on unnatural pant> transitions (_XS = 1), choosing state~ for which the nu( lear stlucture is understood oi talrly simple, such as the "stretched" states m l°B, 1('O, and 28S1 We have stu&ed both low- and tngh-spm transitions, to map out the q dependence of the mtel action, and, when possible, have looked at ~eta of states for which the nuclem stlucture is beheved to be similar, but winch differ in lsospm ( T = 0 vs T = I ) To the extent that the mapulse apWoxlnaatlon 1~ valid, a complete set of spin transfer ~oe~clent~, {D,3}, serxes to constrain the in-medium effective Interaction in nmch the same way that NN spin observables help to determine the scattering amplitudes for the tlee lntetactmn The relationship between the nucleon-nucleus (NA) obseivables and 0375-9474/94/$07 00 © 1994 - Elsewer Science B V All nghts reserved SSDI 0375-9474(94)00342-4
28c
S W Wtssmk / Stu&es of spm observables
those that parametenze nucleon-nucleon (NN) scattering can be shown expllcltl2 ~ t h m tile framework of the plane-~ave impulse approxunatlon (PW IA) [1,2] In tins case the amphtude for excitation of a 0+ target nucleus to a J~ final state takes the form
M(q) = ( l,u[ ~ Mt(q)e-'~'~'~lO}
(1)
t
where 3It is tile (free) amphtude for scattering of the incident proton from the t th target nucleon All polarlzatmn transfer coefficients can now be ngowusly defined in terms oI M(q) and the nucleon spin, using, for example, tile conventions of ~ o l i e n s t e l n [3] IoD,, =- ~ T r [ M c ~ , ~ l % ]
(e)
whele or, (o-a) IS the Pauh spin matrix for tile ,t~ (3th) component ot tile incident (s(attered) nucleon polarization, and whine I0 is the unpolanzed &fferentlal cross section More lntmt~vel~¢, we see that D,~ ielates the zth component of the ln(~dent proton polarization to the ./th component of the scattered proton polarization General descnptmns of the experimental facilities a~adable at IUCF, the K600 spectrometer and ~ts associated polanmeter, and the anal vs~s techmques we have employed to extract reformation on these spin observables are prowded elsewhere [4] 2
EFFECTIVE
INTERACTION
STUDIES
For our fit~t set ot d,,ta we me,~sured the three normal-conlponent spin observables and Ay at 200 Me~ for the 1+, T = 0 (12 71 Me\') and T = I (15 11 MeV) states m 12(, and fm the ~trong 4- T = 0 (17 79 and lq 80 MeV) and T = I (18 98 M e \ ) states In 1~O [5] The measurements were performed at the same angles at which the m-plane spin transfel obselvables had been determined previousl 3 for these tranmtlons [6] Tile mare conclusions reached from these measurements have been reported plexmusl? [4,5] The D?v~,~,results foI the lso~ector transltlons exhibited the most interesting behavior, and ~re presented m Figure 1 Foi the 12(, 1+ state, we sho~ fore DVVlA calculations, each of ~hlch lIse', ('ohen-Ixmath waxe tim( tlons [7] and tile same d~btolted wa~es Also *hown > a calculation ha~ed on the lelatlxlstlc nnpul~e approxllnatlon code DREX [8] Fol the 4- ~tate m 160 the wa~e functmn > a @/ep.7/12configuration and is assumed to he putel,¢ >ovectol The DWIA calculations are described m the fi~me captmn Although no single calculatmn fits the 12(, data over the whole range oI q, most follo~ the general trend of the data, at least over the first lobe ot the foim factor The sltuatum is qmte dlffeient for the 18 98 MeV state in 160 m that all of the calculations are quite similar to each other over the range ot q coxered bx the data but all pull awax from the nea>zero ;alue of the data foI m o m e n t u m transfms aboxe 200 MeV/c Because one expects an u n n a t m a l pant3, lsovector transltmn to be driven p n m a t d y bs the tensol term m the effective mteractmn, winch m turn is me&ated by the mte~pla} bet,~een 7c and p meson exchange, the s3stematlc d~sclepanc~es observed ,~re of particular mterebt, m that they may lend support to ~ecent QCD-based ple&ctlons [q,10] for the mod~flcatmu ot meson masses and couphng constants m the nuclear medium Motivated b3 the abo~e concerns Stephen~on [15] cmrled out a DVvBA anMvs~s m winch the central and tensor terms of the Franev-Love/-matrix Ill] ~ere allo~ed to xarv
DNN,, P,
29c
S W Wtssmk I Studtes of spm observables
laC 15 11 MeV, 1 +
160 18 9 8 MeV, 4 -
10
-''"l .... DNN,
I ....
I':t
05
00
-05
-10
,,,I 0
100
EO0
q (MeV/e)
300
0
........ 400 q (MeV/e)
200
I, 600
Figure 1 Values of DXN, for the lSO'vector states m & c a t e d The calculations shown are the Frane3-Lo~e [11] (solid) and free Bonn [12] (short-dashed), density-dependent Bonn [1 ~] (long-dashed) and P a n s [14] (dotted) and the RIA code DREX [8] (dot-dashed)
m order to mlprove agreement between theory and experiment foi the 4 - , T = I , t a t e at 18 98 MeV m 160 The results [15] were encouraging, m that the quaht~ of fit to a large number ot spin observable d a t a increased sigmflcantly Moreover, because the changes to the interaction were assumed to xary llnearlx with density, it was possible to e x t r a p o l a t e the changes to full nuclear density Comparison of the full-denmt 3 results for the tensor interaction to those predicted in a boson-exchange potential model m wlnch the p mass had been reduced by 20% showed excellent agreement for q < 2 t"111-1, favoring a reduced attraction in the lsovector tensor channel Despite such successes, however, there are severe llmltatmns to this approach At large momentum transfer, where the deviations ot theory from the d a t a are most pronounced, excltatmn of the 4 - states contains large knock-on exchange conttlbut~ons, for which changes to elthel the lsovector or lSOscalar interaction affects both T = 0 and T = 1 trans> tlonq via lsospln couphng A t t e m p t s to leproduce spin observables for the two lSOScalar 4 - states in 1~O, howexer, have had hmlted success While it is tempting to sunplv in crease the number of adjustable parameters in the fitting procedure, the physics content of these modifications tends to become ambiguous at best, unless there is a corresponding m t t e a s e 111 the d a t a b a s e used to constrain the interaction Improved "second-generation" phenomenologlcal fits should not only a c c o m m o d a t e ad&tlonal (i3,13') data, but must remare consistent with results from other studms (e g , Ref [16]) that are more sensitive to pieces of the lntmactlon only weakly probed m our A,g = 1 measmements such as the central teHn, To augment the e×mtlng (t3,1~') database, particularly at tngh momentum transfer, we ha~e begun detaded investigations of the t+ --+ 0 + (1 74 MeV, T = I ) U a u s m o n In 1°B and
30c
S W Wtssmk / Studtes of spm observables
2BS~ 14 36 MeV, 6-
~°B 1 74 MeV, 0 +
t DNN,
0
-~.
0
200 400 600 q (MeV/e)
800
-I
,,,I,,,,I,,,,I,,, 0
200
400
600
800
q (MeV/~)
Figure 2 Values of D~N, fo, the lsovector states indicated The dashed (urv( ubes the Franev-Love interaction [11] The sohd curve ~s explained m the text
the two dominant 0 + --+ 6- (11 58 MeV, T = 0 , and 14 36 Me\ r, T = I ) transitions m ebS1 The l°B state, being a "stretched" 0h~o transition oI low excltahon energy, lb ot partwula, interest m that the form factor for this transition has been measured m (e,e') studies [17] out to about 4 f i n - ' The 6- states m 28S1 have a more conventional lhw stretched structure, similar to that of 160 Extracted values oi DNN, tor the two lsovector transitions are shown In F'lgure 2, P, 4y, and two linear combinations of the tour m-plane D,j's have also been measured Fol b01h transitions, D,,~, is (lose to zero at all m o m e n t m n t~ansiets and ~b m malke(l dlbagleement with theoretical pied1( tlons that emt)loy the tree NN lnterac)lon (dashed curves m figure), e(homg the 1~O results discussed above The ~olld cur~es were obtanwd using the Fr~ne~-Love interaction as modified by Stephenson ct al [15] to reproduce the lso~ecto~ 4- h a n s l t l o n m lt>O Vvhde use ot the modified interaction clearly pushes the calculations in tile right dlle~tlon, quantitative agreement is lacking Ot more concein is recent analysis of the two m-plane obserx ables for l°B, which appear to tax or calculat,ons based on a tree lnterattlon We ate cmrentlv planning measurements to extract the tyro lemamlng orthogonal m-plane spin tran~fel observables to tI3 to isolate the source of ttns discrepancy In an earher separate analysis, Baghael el al [18] ~ere al~o able to obtain reasonable agreement ,~Ith the normal-component data (rr, P, 4y, and D ~ , ) for l°B l)~ allow mg interaction tel ms to vary, emplo} mg an appIoach slgnlficantl) (hfferent from that ot Stephenson This interaction, lnodlfled specifically to reprodure the l°B obserxablea hsted abo\e, also laded to account for the m-plane data Baaed on the above successes, ~,et mmdiul oI some ob-vlOUS problems, we are presently u n d e l t a k m g several new endeavors On the experunental front, we hope to (omplete soon the m plane spin transfer measurements for all of the ~soscalar and ~sovector transitions
S W Wtssmk /Studtes of spm observables
31 c
m l°B and 2sS1 discussed above In the last month, we have also obtained data on DNN, for the 1 / 2 - --+ 9/2 + transition in 13(, which is a nearly pine neutlon state Tills wdl substantially bloaden out database fot transitions that are not pledonnndntlv Isovec tor m charactel hi our htting p r o t e d u i e s , attempt~ ~111 hI~t ])e made to lelnodu{ e simultaneously all spin observables for all ttnee 4 - transitions m 1sO, while malIltammg col>lstencv with previous isoscalal stu&es and (p,n) work Adjustment oI tile NN phas< shifts d n e c t b , rather than individual terms m t h e / - m a t r i x , will be ~tudwd Vve wdl also investigate the use of effective interactions m which medium effects ha~e been m( orporated within a relat~vlstlc tramework [19]
3
STUDIES
O F T H E (15, p'~) R E A C T I O N
For transitions induced via proton inelastic scattering to nuclear states of non-zero spin ], lnfoimatlon about the scattering a m p h t u d e is contained m the polarization ~tate of the recoil nucleus This information, which is not accessible nl (p,p') ~tudles, ma3 be determined through Investigations of the angular correlation between the scattered pIoton and the galnma-~ay e m i t t e d during the nuclear de-excitation It has been shown [21] that for transltmns such as 0 + --+ 1+, measurements of all (t~,p'7) observables combined w,th complete sets of (l~,l~') d a t a allow for a complete specification of the scattering matrix T h > would present an extremely stringent test for competing theoretical models More mtmtlvely, certain (t~, P'7) observables are sensltl~e to the ielatlve phases between the 'hn plane" and "normal" amphtudes, terms which do not appear Ill (I~, ~1) singles observables To e,(plolt this sensltlvlt3, we ha~e peflo~med simultaneous measurements of (1~, Iy ) and (t~,p"?) spin obseivables at 200 MeV for the 1+, T = I state at 15 11 MeV m 12(, At each of tour proton s( attermg angles, measurements were carried out with three BaF2 aIlax s [20] lyulg in the scattering plane, then mo~ed to 45 ° out-of-plane A tourth array, positioned (hrectly o~er the target, provided an independent determination of the observables D ~ , and P - A v , and thus served as a race consistency check Measurements In which the emitted photon lay zn the scattering plane, howe~er, are sensltl~e to amplitudes that dictate the spin dependence of knock-on exchange, At, v(E K)(cr q) and Av~, (E q)(~r K ) , which in a relatlvlstw P W I A are proportional to the composite spin-convection c u n e n t s (8 x ]} and ((7 ]}, respect,rely [21] Our analysis of tins d a t a is almost complete Preliminary d a t a is plesented Ul Figure ~I for the coetficlents B and C that characterize the in-plane p-"/ angular correlation terms which are symmetric and anti-symmetric about 0~, respechvely The statistical quaht5 ot the data, and the clear prelerence for the relatlvlstw predmtmns are apparent We }lope to obtain our final results b 5 early summer 1994
4
ACKNOWLEDGEMENTS
It is a pleasure to acknowledge tile efforts of the many people who have contllbuted to tlns work Edward Stephenson and lily students Allena Opper and SteveI1 Wells desel,,e special mention The help ot A D Bacher, G P A Berg, S M Bowyer, S Chang W Franklin, J Lm, and the ORNL collaborators is also g r e a t s appreciated This work was supported in part by the U S National Science Foundation
32c
S W Wtssmk /Studtes of spm observables
lZC 15 11 MeV, 1 +
lZC 15 11 MeV, 1 +
o4
L"'"l
oz
~C/A
oo
E-..
....
I ....
I .... •
_
•
-02 -04
0
5
10
0~m ( d e g )
15
gO
~-. . . . [ . . . . [ . . . . I , , , 0 5 10 15 gO 0em ( d e g )
Figure 3 Comparison of the normalized m-plane angular correlation coefflcwnts B and C to predictions from DWIA (dashed) and DREX (~ohd) calculations [21]
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 1} 14 15 16 17 18 19 20 21
E BleszynsM, M BleszynsM, and C A Whltten Jr , Ph3s Rev C 26, 2063 (1982) J M Moss, Phys Rev C 26 727 (1982) L Wolfenstem, Ann Rex Nucl Scl 6, 43 (1956) S W VVl~slnk, in ,5'ptn and Iso~pu~ m Nuclear Interactzons, eds S W V~lsslnk (t al, (Plenum Press, New "~ork 1991) p 253 A K Opper et a l , s u b n n t t e d t o P h \ s Rex C (' Ohner, m AnhuucleoT~- and Nucl¢ou Nucleu~ lnteractwn~s, e,ts G E Vcalkel ~t al (Pleimm P~es~, Ne~ 3ork 1985) p 261 S ('ohen and D kurath, Nucl Phys A101, 1 (1967) E Ro~t and J R ShepaId, computer code DREX (unpubhshed) T Hatsuda and S Huong Lee, Ph3~ Re~ (' 46, R34 (1992) G E Brown and hi Rho, Ph3s Rex Lett 66, 2720 (1991) M A Franejy and W G Love, Phys Rev (' 31,488 (1985) R Machleldt, Adv Nucl Ph3s 19, 189 (1989) k Naka~ama el al, Nucl Phys A431, 419 (1984) H V yon Geramb, m Th~ Intera~hon Between Medium Eulogy Nutleon, m Nu~hl, ed H O Meyer,(A I P New 5ork, lqS}) p 44 E J Stephenson anti ] A To~texm, m ,5'pn~ and Iso~ptn ta Nu(lear Iate~a~twn~, e(ls S W Wlssmk et ul, (Plenum Press, New "~ork, 1991) p 281 J J Kelly' ~t al, Phys Re~ C 4 1 , 2 5 0 4 (1990) R S Hicks et a l , P h ~ s Rev Lett 60 905 (1988) H Baghaea et al, Ph3s Re~ Lett 69, 2054 (1992) ] I Kelly and S J Wallace, Phys Rex (' 49, 1315 (1994) M Thoennessen et al, Oak Ridge Nat'l Lab Prog Rep (1989) J Plekarewwz et al, Plus Rex (: 41, 2277 (lq90)
Nuclear Physms A577 (1994) 27c-32c North-Holland, Amsterdam
Studies of spin observables in (I~, if') and (t~, P'7) reactmns at intermediate energies S Vv Wissmk ~ ~Department of Physics, I n & a n a Unl~erslty, and Indiana Umverslty Cyclotron Eaohty, Bloomington, I n & a n a 47408, USA Recent measurements at 200 MeV of (i~,l~') spin transfer observables for exc~tatlon of discrete states show slgmficant dewatlons from theoretmal pre&ctlons based on the free NN t-matt1,: Because the nuclear structure and &stortmns for these tranmtlons are beheved to be constrmned by other data, this suggests that modifications of the ~z-med~um NN lnteractmn are needed, beyond Pauh blocking, to describe these processes As a first ~tep towards identifying the phymc41 mechanisms that underhe these modlhcatlons, several phenomenolog~(al approaches have been tried to m~prove agreement between experiment and theory The successes and hm~tatmns of these approaches will be &scussed P w l m n n a r y results flora a detailed study ot the (I~, P'7) reaction for the 1+, T = I state in t~(, at 15 11 MeV will also be presented 1
INTRODUCTION
AND
OVERVIEW
OF PROGRAM
The inelastic scattering of nucleons fiom nuclei remains one of inn lwhest sources of information on nucleaI structure, the l n - m e d m m effective interaction, and the reaction mechanisms involved Work at lnterme&ate energies (100-500 MeV) provides a regime m which the spin-orbit and tensor terms of the underlying nucleon-nucleon (NN) interaction are enhanced relative to the usually dominant central term, and in which the relatmnshlp between the nucleon-nucleus (NA) and NN interaction may be made transparent through use of the mlpulse approxHnatmn O~er the past few years, the high count rate and hlgh-resolutmn (25 keV) capablhtles ot the I U ( ' F K600 spectrometer and its associated focal-plane p o l a n m e t e r have made possible detaded inveqtlgatmns of several specific nuclear tranmtlons, where the selectlvlt 3 of the q u a n t u m numbers ln~ol~ed can be exploited to xsolate or enhance specific terms in the effective NN interaction To m~e~tlgate the spin-dependence of these terms, we ha~e concentrated on unnatural pant> transitions (_XS = 1), choosing state~ for which the nu( lear stlucture is understood oi talrly simple, such as the "stretched" states m l°B, 1('O, and 28S1 We have stu&ed both low- and tngh-spm transitions, to map out the q dependence of the mtel action, and, when possible, have looked at ~eta of states for which the nuclem stlucture is beheved to be similar, but winch differ in lsospm ( T = 0 vs T = I ) To the extent that the mapulse apWoxlnaatlon 1~ valid, a complete set of spin transfer ~oe~clent~, {D,3}, serxes to constrain the in-medium effective Interaction in nmch the same way that NN spin observables help to determine the scattering amplitudes for the tlee lntetactmn The relationship between the nucleon-nucleus (NA) obseivables and 0375-9474/94/$07 00 © 1994 - Elsewer Science B V All nghts reserved SSDI 0375-9474(94)00342-4
28c
S W Wtssmk / Stu&es of spm observables
those that parametenze nucleon-nucleon (NN) scattering can be shown expllcltl2 ~ t h m tile framework of the plane-~ave impulse approxunatlon (PW IA) [1,2] In tins case the amphtude for excitation of a 0+ target nucleus to a J~ final state takes the form
M(q) = ( l,u[ ~ Mt(q)e-'~'~'~lO}
(1)
t
where 3It is tile (free) amphtude for scattering of the incident proton from the t th target nucleon All polarlzatmn transfer coefficients can now be ngowusly defined in terms oI M(q) and the nucleon spin, using, for example, tile conventions of ~ o l i e n s t e l n [3] IoD,, =- ~ T r [ M c ~ , ~ l % ]
(e)
whele or, (o-a) IS the Pauh spin matrix for tile ,t~ (3th) component ot tile incident (s(attered) nucleon polarization, and whine I0 is the unpolanzed &fferentlal cross section More lntmt~vel~¢, we see that D,~ ielates the zth component of the ln(~dent proton polarization to the ./th component of the scattered proton polarization General descnptmns of the experimental facilities a~adable at IUCF, the K600 spectrometer and ~ts associated polanmeter, and the anal vs~s techmques we have employed to extract reformation on these spin observables are prowded elsewhere [4] 2
EFFECTIVE
INTERACTION
STUDIES
For our fit~t set ot d,,ta we me,~sured the three normal-conlponent spin observables and Ay at 200 Me~ for the 1+, T = 0 (12 71 Me\') and T = I (15 11 MeV) states m 12(, and fm the ~trong 4- T = 0 (17 79 and lq 80 MeV) and T = I (18 98 M e \ ) states In 1~O [5] The measurements were performed at the same angles at which the m-plane spin transfel obselvables had been determined previousl 3 for these tranmtlons [6] Tile mare conclusions reached from these measurements have been reported plexmusl? [4,5] The D?v~,~,results foI the lso~ector transltlons exhibited the most interesting behavior, and ~re presented m Figure 1 Foi the 12(, 1+ state, we sho~ fore DVVlA calculations, each of ~hlch lIse', ('ohen-Ixmath waxe tim( tlons [7] and tile same d~btolted wa~es Also *hown > a calculation ha~ed on the lelatlxlstlc nnpul~e approxllnatlon code DREX [8] Fol the 4- ~tate m 160 the wa~e functmn > a @/ep.7/12configuration and is assumed to he putel,¢ >ovectol The DWIA calculations are described m the fi~me captmn Although no single calculatmn fits the 12(, data over the whole range oI q, most follo~ the general trend of the data, at least over the first lobe ot the foim factor The sltuatum is qmte dlffeient for the 18 98 MeV state in 160 m that all of the calculations are quite similar to each other over the range ot q coxered bx the data but all pull awax from the nea>zero ;alue of the data foI m o m e n t u m transfms aboxe 200 MeV/c Because one expects an u n n a t m a l pant3, lsovector transltmn to be driven p n m a t d y bs the tensol term m the effective mteractmn, winch m turn is me&ated by the mte~pla} bet,~een 7c and p meson exchange, the s3stematlc d~sclepanc~es observed ,~re of particular mterebt, m that they may lend support to ~ecent QCD-based ple&ctlons [q,10] for the mod~flcatmu ot meson masses and couphng constants m the nuclear medium Motivated b3 the abo~e concerns Stephen~on [15] cmrled out a DVvBA anMvs~s m winch the central and tensor terms of the Franev-Love/-matrix Ill] ~ere allo~ed to xarv
DNN,, P,
29c
S W Wtssmk I Studtes of spm observables
laC 15 11 MeV, 1 +
160 18 9 8 MeV, 4 -
10
-''"l .... DNN,
I ....
I':t
05
00
-05
-10
,,,I 0
100
EO0
q (MeV/e)
300
0
........ 400 q (MeV/e)
200
I, 600
Figure 1 Values of DXN, for the lSO'vector states m & c a t e d The calculations shown are the Frane3-Lo~e [11] (solid) and free Bonn [12] (short-dashed), density-dependent Bonn [1 ~] (long-dashed) and P a n s [14] (dotted) and the RIA code DREX [8] (dot-dashed)
m order to mlprove agreement between theory and experiment foi the 4 - , T = I , t a t e at 18 98 MeV m 160 The results [15] were encouraging, m that the quaht~ of fit to a large number ot spin observable d a t a increased sigmflcantly Moreover, because the changes to the interaction were assumed to xary llnearlx with density, it was possible to e x t r a p o l a t e the changes to full nuclear density Comparison of the full-denmt 3 results for the tensor interaction to those predicted in a boson-exchange potential model m wlnch the p mass had been reduced by 20% showed excellent agreement for q < 2 t"111-1, favoring a reduced attraction in the lsovector tensor channel Despite such successes, however, there are severe llmltatmns to this approach At large momentum transfer, where the deviations ot theory from the d a t a are most pronounced, excltatmn of the 4 - states contains large knock-on exchange conttlbut~ons, for which changes to elthel the lsovector or lSOscalar interaction affects both T = 0 and T = 1 trans> tlonq via lsospln couphng A t t e m p t s to leproduce spin observables for the two lSOScalar 4 - states in 1~O, howexer, have had hmlted success While it is tempting to sunplv in crease the number of adjustable parameters in the fitting procedure, the physics content of these modifications tends to become ambiguous at best, unless there is a corresponding m t t e a s e 111 the d a t a b a s e used to constrain the interaction Improved "second-generation" phenomenologlcal fits should not only a c c o m m o d a t e ad&tlonal (i3,13') data, but must remare consistent with results from other studms (e g , Ref [16]) that are more sensitive to pieces of the lntmactlon only weakly probed m our A,g = 1 measmements such as the central teHn, To augment the e×mtlng (t3,1~') database, particularly at tngh momentum transfer, we ha~e begun detaded investigations of the t+ --+ 0 + (1 74 MeV, T = I ) U a u s m o n In 1°B and
30c
S W Wtssmk / Studtes of spm observables
2BS~ 14 36 MeV, 6-
~°B 1 74 MeV, 0 +
t DNN,
0
-~.
0
200 400 600 q (MeV/e)
800
-I
,,,I,,,,I,,,,I,,, 0
200
400
600
800
q (MeV/~)
Figure 2 Values of D~N, fo, the lsovector states indicated The dashed (urv( ubes the Franev-Love interaction [11] The sohd curve ~s explained m the text
the two dominant 0 + --+ 6- (11 58 MeV, T = 0 , and 14 36 Me\ r, T = I ) transitions m ebS1 The l°B state, being a "stretched" 0h~o transition oI low excltahon energy, lb ot partwula, interest m that the form factor for this transition has been measured m (e,e') studies [17] out to about 4 f i n - ' The 6- states m 28S1 have a more conventional lhw stretched structure, similar to that of 160 Extracted values oi DNN, tor the two lsovector transitions are shown In F'lgure 2, P, 4y, and two linear combinations of the tour m-plane D,j's have also been measured Fol b01h transitions, D,,~, is (lose to zero at all m o m e n t m n t~ansiets and ~b m malke(l dlbagleement with theoretical pied1( tlons that emt)loy the tree NN lnterac)lon (dashed curves m figure), e(homg the 1~O results discussed above The ~olld cur~es were obtanwd using the Fr~ne~-Love interaction as modified by Stephenson ct al [15] to reproduce the lso~ecto~ 4- h a n s l t l o n m lt>O Vvhde use ot the modified interaction clearly pushes the calculations in tile right dlle~tlon, quantitative agreement is lacking Ot more concein is recent analysis of the two m-plane obserx ables for l°B, which appear to tax or calculat,ons based on a tree lnterattlon We ate cmrentlv planning measurements to extract the tyro lemamlng orthogonal m-plane spin tran~fel observables to tI3 to isolate the source of ttns discrepancy In an earher separate analysis, Baghael el al [18] ~ere al~o able to obtain reasonable agreement ,~Ith the normal-component data (rr, P, 4y, and D ~ , ) for l°B l)~ allow mg interaction tel ms to vary, emplo} mg an appIoach slgnlficantl) (hfferent from that ot Stephenson This interaction, lnodlfled specifically to reprodure the l°B obserxablea hsted abo\e, also laded to account for the m-plane data Baaed on the above successes, ~,et mmdiul oI some ob-vlOUS problems, we are presently u n d e l t a k m g several new endeavors On the experunental front, we hope to (omplete soon the m plane spin transfer measurements for all of the ~soscalar and ~sovector transitions
S W Wtssmk /Studtes of spm observables
31 c
m l°B and 2sS1 discussed above In the last month, we have also obtained data on DNN, for the 1 / 2 - --+ 9/2 + transition in 13(, which is a nearly pine neutlon state Tills wdl substantially bloaden out database fot transitions that are not pledonnndntlv Isovec tor m charactel hi our htting p r o t e d u i e s , attempt~ ~111 hI~t ])e made to lelnodu{ e simultaneously all spin observables for all ttnee 4 - transitions m 1sO, while malIltammg col>lstencv with previous isoscalal stu&es and (p,n) work Adjustment oI tile NN phas< shifts d n e c t b , rather than individual terms m t h e / - m a t r i x , will be ~tudwd Vve wdl also investigate the use of effective interactions m which medium effects ha~e been m( orporated within a relat~vlstlc tramework [19]
3
STUDIES
O F T H E (15, p'~) R E A C T I O N
For transitions induced via proton inelastic scattering to nuclear states of non-zero spin ], lnfoimatlon about the scattering a m p h t u d e is contained m the polarization ~tate of the recoil nucleus This information, which is not accessible nl (p,p') ~tudles, ma3 be determined through Investigations of the angular correlation between the scattered pIoton and the galnma-~ay e m i t t e d during the nuclear de-excitation It has been shown [21] that for transltmns such as 0 + --+ 1+, measurements of all (t~,p'7) observables combined w,th complete sets of (l~,l~') d a t a allow for a complete specification of the scattering matrix T h > would present an extremely stringent test for competing theoretical models More mtmtlvely, certain (t~, P'7) observables are sensltl~e to the ielatlve phases between the 'hn plane" and "normal" amphtudes, terms which do not appear Ill (I~, ~1) singles observables To e,(plolt this sensltlvlt3, we ha~e peflo~med simultaneous measurements of (1~, Iy ) and (t~,p"?) spin obseivables at 200 MeV for the 1+, T = I state at 15 11 MeV m 12(, At each of tour proton s( attermg angles, measurements were carried out with three BaF2 aIlax s [20] lyulg in the scattering plane, then mo~ed to 45 ° out-of-plane A tourth array, positioned (hrectly o~er the target, provided an independent determination of the observables D ~ , and P - A v , and thus served as a race consistency check Measurements In which the emitted photon lay zn the scattering plane, howe~er, are sensltl~e to amplitudes that dictate the spin dependence of knock-on exchange, At, v(E K)(cr q) and Av~, (E q)(~r K ) , which in a relatlvlstw P W I A are proportional to the composite spin-convection c u n e n t s (8 x ]} and ((7 ]}, respect,rely [21] Our analysis of tins d a t a is almost complete Preliminary d a t a is plesented Ul Figure ~I for the coetficlents B and C that characterize the in-plane p-"/ angular correlation terms which are symmetric and anti-symmetric about 0~, respechvely The statistical quaht5 ot the data, and the clear prelerence for the relatlvlstw predmtmns are apparent We }lope to obtain our final results b 5 early summer 1994
4
ACKNOWLEDGEMENTS
It is a pleasure to acknowledge tile efforts of the many people who have contllbuted to tlns work Edward Stephenson and lily students Allena Opper and SteveI1 Wells desel,,e special mention The help ot A D Bacher, G P A Berg, S M Bowyer, S Chang W Franklin, J Lm, and the ORNL collaborators is also g r e a t s appreciated This work was supported in part by the U S National Science Foundation
32c
S W Wtssmk /Studtes of spm observables
lZC 15 11 MeV, 1 +
lZC 15 11 MeV, 1 +
o4
L"'"l
oz
~C/A
oo
E-..
....
I ....
I .... •
_
•
-02 -04
0
5
10
0~m ( d e g )
15
gO
~-. . . . [ . . . . [ . . . . I , , , 0 5 10 15 gO 0em ( d e g )
Figure 3 Comparison of the normalized m-plane angular correlation coefflcwnts B and C to predictions from DWIA (dashed) and DREX (~ohd) calculations [21]
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 1} 14 15 16 17 18 19 20 21
E BleszynsM, M BleszynsM, and C A Whltten Jr , Ph3s Rev C 26, 2063 (1982) J M Moss, Phys Rev C 26 727 (1982) L Wolfenstem, Ann Rex Nucl Scl 6, 43 (1956) S W VVl~slnk, in ,5'ptn and Iso~pu~ m Nuclear Interactzons, eds S W V~lsslnk (t al, (Plenum Press, New "~ork 1991) p 253 A K Opper et a l , s u b n n t t e d t o P h \ s Rex C (' Ohner, m AnhuucleoT~- and Nucl¢ou Nucleu~ lnteractwn~s, e,ts G E Vcalkel ~t al (Pleimm P~es~, Ne~ 3ork 1985) p 261 S ('ohen and D kurath, Nucl Phys A101, 1 (1967) E Ro~t and J R ShepaId, computer code DREX (unpubhshed) T Hatsuda and S Huong Lee, Ph3~ Re~ (' 46, R34 (1992) G E Brown and hi Rho, Ph3s Rex Lett 66, 2720 (1991) M A Franejy and W G Love, Phys Rev (' 31,488 (1985) R Machleldt, Adv Nucl Ph3s 19, 189 (1989) k Naka~ama el al, Nucl Phys A431, 419 (1984) H V yon Geramb, m Th~ Intera~hon Between Medium Eulogy Nutleon, m Nu~hl, ed H O Meyer,(A I P New 5ork, lqS}) p 44 E J Stephenson anti ] A To~texm, m ,5'pn~ and Iso~ptn ta Nu(lear Iate~a~twn~, e(ls S W Wlssmk et ul, (Plenum Press, New "~ork, 1991) p 281 J J Kelly' ~t al, Phys Re~ C 4 1 , 2 5 0 4 (1990) R S Hicks et a l , P h ~ s Rev Lett 60 905 (1988) H Baghaea et al, Ph3s Re~ Lett 69, 2054 (1992) ] I Kelly and S J Wallace, Phys Rex (' 49, 1315 (1994) M Thoennessen et al, Oak Ridge Nat'l Lab Prog Rep (1989) J Plekarewwz et al, Plus Rex (: 41, 2277 (lq90)