The spin-dipole resonance and parity mixing in compound nuclear states

Nuclear Physms A577 (1994) 443c-448c North-Holland, Amsterdam

NUCLEAR PHYSICS A

The Spm-Dspole Resonance and Panty Ivlmng m Compound Nuclear States N Auerbach Raymond and Beverly Sackler Faculty o f Exact Sciences, School o f Physscs and Astronomy, Tel Aviv Umversity, Tel Avlv 69978, Israel

We examane the role of the grant spm-
I. I N T R O D U C T I O N Since the chscovery o f panty v~olataon m the weak mteractaon by Lee and Yang st has become clear that the nucleon-nucleon force contains a panty vsolatmg component Subsequently a number of experiments have revealed the exastence of panty viulatmg effects m nuclei [1] The I~as~c parity violating lnteractaon should be described m terms o f the exchange o f the W and Z bosom, the mechators of the weak interaction Due to the large masses o f these bosons (~ 90 GeV) the range o f the interaction ts o f the order o f 0 002 f m well inside the s ~ e o f the nucleon In order to describe the effects o f parity vlolataon m a nucleus one needs to take into account the "long range" part of the parity nonconservmg (PNC) force Tlus can be accomphshed to a certmn degree by introducing a theory o f "effective" interactions revolving the exchange o f the hghter mesons (x, p, ere) To first order m the weak mteractaon couphng constant the PNC force is described by the exchange o f such a meson between two mteractang nucleons so that one o f the vertices m the process involves the weak couphng constant wlule the other the strong mteractaon coupling Such approach to the PNC force was accomphshed ts several works one of the best known is the work by Desplanques, Donoghue and Holstein [2], here referred to as DDH It ts not the purpose o f th~ talk to elaborate on that aspect o f the theory o f PNC m nucle~ We just wtsh to set the scale and state that the smgle-partacle PNC matrtx elements calculated with a DDH lnteractaon are o f the order o f a few (1-3) eV in light nuclei ( A < 16) In the last decade a new class of parity vlolatton expermaents m nuclei has been proposed [3,4] that involved the compound nucleus The idea ts to scatter polarLzed eplthermal neutrons on unpolanzed mechum or heavy mass nuclear targets In such experunents one ts able to excite only the s and p - wave resonances Higher e's are lundered due to the lack of penetrabdlty caused by the centrifugal barrier When a polarized epithermal neutron - n ts scattered by a nucleus - A the excitataon energy m the compound system (A+ n)* ~s about 4-6 MeV depending on the target At such exmtation energ0es m heavy mass nuclei the density o f states ts lugh and the spacing between the J = 1/2 + or J ffi 1/2- compound resonances ts o f the order o f 10 - 20 eV and the w~dth o f such resonances are a small fractaon o f an eV (1/10 - 1/100 eV) In recent years the experimental techmques were improved due greatly to the operation of the LANSCE In the experiments performed at the Los-Alamos facihty one was able to measure PNC effects for several p - wave resonances m the same compound nucleus [5] Tlus enabled one to provide a stattstacal analysts o f the quantaties measured. The bas~c observable m these experiments ts the long~tuchnal asymmetry 0375-9474/94/$07 00 © 1994 - Elsevmr Science B V All rights reserved SSDI 0375-9474(94)00410-2

N Auerbach I The spm-dtpole resonance and partty mtxmg

444c

P~

(1)

a+ 0,) + a_(~)

where a+ (#) and a_(p) are the p - wave resonance cross-sections for neutrons with hehcity +

and 2 ENHANCEMENTS OF THE PNC EFFECTS IN THE CO MPO U N D NUCLEUS In the early work it was pointed out that the above asymmetry wall be strongly enhanced when measured for J = 1 / 2 - states that are in the regime o f the compound nucleus The enhancement ts twofold, a) "lonemaUc", b) "dyualmC" The lonematlC enhancement o f P~, has to do with the fact that when a neutron forms a J = 1/2- resonance ~t then may exit m a panty vmlatmg translUon through the e = 0 achmxture gaming a factor o f l / k R m penetrahday; (k IS the neutron wave number and R the nuclear rachus) For 1 eV neutrons and for a heavy nucleus ttns factor IS about l0 s The second enhancement, the dynarmcal one IS more interesting. It stems from the fact that the PNC trans~tmn occurs in the compound nucleus where the density o f states IS very lugh Each state when expanded m shell-model conf~gurat~ous has close to l0 s "prmcapal" components, i e components that have comparable amphtudes each o f the order o f 10 -s It IS beheved that for such very complicated states the stage o f "chaos" IS reached and statIStical arguements should apply Theory mchcates that the most important term that contributes to the asymmetry m eq (1) IS o f the forn~

~q P~' ffi E

(E~ - Eq)

'7~

(2)

q where [q> are J ffi 1/2 + states, V p N c IS a PNC mteractmn and '~q and '~/j are neutron escape amphtudes from states [q> and [/~> (l e J ffi 1/2 + and J = 1/2-) The dynarmcal enhancement IS due to the fact that m the compound nucleus the ratio /(E~ - Eq) ~ v ~ where n IS the density of states wluch for a nucleus as heavy as 2SSTh at the above energies IS about 10 5 - 10 e and therefore, the dynamical enhancement gives as another factor o f 10s It IS easy to see how flus enhancement emerges [6] We define a PNC spreachng w~dtl~

r~No = 2,'l<~lVe.c lq>l ~ b

(3)

where we introduced a mean square ( m s ) PNC matrL~ element and an average spacing b One expects P., to be fluctuatmg in s~gn for varmus/~ and have an average P~ = 0 Define the root m s o f ( D j , ~ l / 2 In tlus case

(~)~n

tz~b j

(4)

N Auerbach / The spm-dtpole resonance and partty mtxmg

445c

It ts known that spreading widths do not (or depend weakly) on the density o f states Since ~ l / n we Lmmediately obtain that ( ~ ) 1 / 2 ~ V~ The "dynamical" enhancement ts a result of the fact that m a "chaoUc" system ( m a system o f complete rnLxang) l

- ~

(5)

(Ic> and [c'> are states describing such "chaotic" states), V ts a one or two-body mteractmn 1 As already menUoned the spacing o f levels E c - Ec, - ~, thus one obtains



(6)

~

E c - E c, Tins behaviour was recently confn'med [7] numerically by performmg large - space extended shellcalculatmns [The factor ?fq/'1~ ~ l / k R m eq (2) ts the source of the kmematscal enhancement discussed above] Altogether the two factors produce an enhancement of about 10e for P~, Indeed the experiments [4,5] have measured asymmetries of the order of several percent From these expernnents one finds that the r m s P N C matrix element for a compound J = I/2- ts of the order

of I0 -s e V and r~pNc

--~6 x I0 -7 eV m 2SSTh for example

3. T H E S P I N - D I P O L E AS T H E D O O R W A Y F O R P A R I T Y M I X I N G

We will now go somewhat beyond the statsstlcal model and describe some work m wlach one attempts to calculate the PNC spreachng width It ts natural to start the conslderataons with a onebody PNC potential The simplest parity--odd, tame reversal-even interactton ts one o f the form [8] 1

V p N c = ~ 10 -v ~ E {f(r,,r~)~, ~, c}

(7)

where ~ ts the nucleon spin, ~ = -sh~ m the nucleon m o m e n t u m operator and f(r~,r~)ts a radial functson and a funchon of tsospm Since the weak mteracUon does not conserve tsospm one may have an tsoscalarand tsovector components f(r,r) = f o ( r ) + r s f l ( r )

(8)

m eq (7) ~s a parameter that designates the strength o f the mteracuon Let us now perform a simple demonstratton [6, 9] If we restrict ourselves to a single - parUcle panty c o m e r w n g Hanultoman H o and use a PNC potentml o f the form

vx,~ = go(l + ~,~)~ ~"

(9)

where go and a are constants, then to order g~ The soluUon of

H=

H o+ VpN o

ts gsven by"

(10)

446c

N Auerbach / The spin-dipole resonanee and partty mtxmg

]~>ffi If+ flVlgo(l+ ar.)~ll@> where [@> IS the solutmn Ho[@> = adrmxtures lCpNo>0 = o* ~

(ll) FA@> and M the nuclear mass

Note that the parity

I¢>

(12a)

(12b) are the J = 0- components o f the ISoscalar and ISovector spm- Tlus model can be generahzed [6] by the conjecture that when the nuclear Hanultoman contains two-body, m adchtaon to one-body parts, also then the spin - d~pole states bruit on the compound state [/~> are the doorways for panty nuxing m [/~> The movector spm-chpole resonances were stuched quite extensively m several types o f nuclear reactions Such resonances were observed m (p,n) [10] and (n,p) [11] as well as m (SHe, t) (For references see [10]) Theoretacally it was also stuched m several works [10,12] The features o f tlus resonance (excltat~on energies, widths, general strength chsmbut~on, eollecnvlty) are snndar to the usual S ffi 0 elecmc chpole The difference however, ts that m the ease o f the spm-chpole we have three possible spins with J ffi 0-, 1-, 2- Theory [12] prechcts that the J ffi 0- component IS the lughest and carries a substantml part (about 1/3) o f the total spin - chpole strength As for the ISoscalar spin - chpole not much IS known experimentally It Is o f nnportance for flus problem of panty rmxmg to try and locate experimentally such moscalar spm-d~pole strength

4. T H E P N C R.M.S. M A T R I X E L E M E N T . Having ldentafled the doorway and using the doorway state approach one can try and estunate the PNC matrLx element In the doorway state approach one may write [6] the following expression for the spreading w~dth r~PNC

I<~[VpN° ld>12 r~d r~PNC ffi (E/j -Ed) 2 + r~ /4

(13)

where Id> des~guates the doorway state, E d IS the energy and r t d and r d the spreachng and total widths of the doorway These are "macroscopic" quantaUes m the sense that each one IS of the order o f a few MeV For the grant ISovector spm-chpole r d and r i d are o f the order o f 3 - 5 MeV and E u - E d -~ 10 MeV m a heavy nucleus The ISoscalar m expected to be at the same energy or maybe somewhat lower For the sake o f a rather crude estmmte we use here rJ.d ~' r d ~ 3 MeV and Eu - E d -~ 7 MeV Using the measured value for the r~pNO m 2SSTh we deduce nnmechately that:

"~ 3 e V

(14)

Note that tlus matrLx element Is o f collectave nature because of the collectav~ty o f the spin - &pole doorway In order to convert flus to a single -particle value we have to count the number of part~cle-hole components Nph that make up the spin - dipole m flus region and chvide the above matrix element by the factor o f N v ~ hp A reasonable number m Nph "-' 100 and therefore, the

N Auerbach / The ~pm-dtpole resonance and partty mtxtng

447c

single-particle PNC r m s matrtx element ts estmmted from eq (14) to be around 0 3 eV Tim m good accord wtth what the DDH mteractton would give for a nucleus with mass number A -~ 230 We again stress that tim zs only a rough estmmte but ~t does m(hcate that the ~dea that the spin - (hpole is the doorway m panty mixing of compound states ~s a reasonable one We should maybe add that t i ~ mechamsm of panty mLxmg and the role played by the spm(hpole resonance ts analogous to Coulomb (or tsospm) n~xmg m nuclei and the role played by the tsoveetor monopole resonance m such mtxmg [15]

5. SIGN C O R R E L A T I O N S IN 2SSTh One o f the large surprzses occurred when all seven measured P~ values that were staUsttcally significant m 2SSTh were all positive [5] In fact the average t'~ -~ 8% This fact m(hcated that unless this ts a staUstical fluctuaUon (and the chances for that happemng ts about 1 5%) there must be some interesting correlations m the compound nucleus The doorway approach because ~t deals w~th only a few specml states does revolve the poss~bd~ttes of producing asymmetries This was known already from the study o f tsobartc analog resonances [16] In ref [17] the above doorway state approach was apphed m the calculaUon o f the average P~ The result o f this work was that one needs a PNC matrix element o f the order o f 75 eV to explain an 8% average P~, Th~s matrix element ts much too large and contra(hcts the values one obtains from the DDH force Saying ~t (hfferently, a reasonable s p PNC matrtx element o f about l e V or less accounts for only 1% o f the effect measured m 2SSTh as far as the average P~ ts concerned. Tiros conclusion was reached m several other works [18] One cannot rely on a suggesUon that maybe m a nuclear me(hum the PNC force ts strongly renormahzed so that indeed the PNC m el turns out to be very large compared w~th me(hum free matrix elements In refs [17] it was f~rst pointed out that such a strong renormahzatton ts m contra(hctton wtth the PNC matrix elements deduced from the analysis when apphed to PNC sprea(hng width, described m the previous section We are therefore, faced with w~th an internal contra(hctmn m the case of 2SSTh We should emphaszze that flus contra(hctton ts not a stmple matter The fact that one needs a large PNC m el to reproduce a large non - zero P~, ts due to the fact that when evaluating the average o f P~ one looses the dynanncal enhancement But the dynarmcal enhancement ts the reason why such large asymmetries P~ (of the order of a few percent) are observed.

6 RECENT DEVELOPMENTS. Is tim constancy o f sign of P~ umversal9 Are large P~, observed everywhere9 An answer to these questtons was prowded last summer (1993) m a series o f measurements performed at LANSCE [19] Measurements w~th h-nproved stattsttcs were performed for several targets The result ts that the constancy of s~gn ~s not found m all the other targets and the averge P~ ts small However, m 2SSTh two more resonances were found that show pos~ttve Pp m ad(ht~on to the seven observed before So the case o f 2SSTh is specml On the theoreUcal side new terms for the Pj, were derived m a recent work [14] Among these terms worth noting ts the so called "(hrect" term which is g~ven by"

448c

N Auerbach / The spm-dlpole resonance and partty mzxtng

Re(ff~ ,~/~ (PNC)) PmDm = 2

]%,12

(15)

where

ff/.~(PNC) _ <¢s(-) [VpN C [~>

(16)

ts the &rect neutron decay of the J ffi 1/2-, I/~> resonance into an J ffi 1/2 + continuum vaa a PNC mteraenon A numerical evaluataon of tlus term [4] gives contnbuttons that are about 1/5 of the compound term described by eq (2) The term suggested m the work of Lewenkopf and Weldenmfiller [18] was recalculated and found to contribute about 1/3 of the compound contnbutmn The conclaslon of the work m ref [14] m that all the newly derived adchttonal terms that contribute to P~ are small and cannot resolve the chscrepancy that exasts m the 2SSTh case The ~SSTh nucleus and nearby nuclei are specml In (n,f) experiments very pronounced mtermechate structure was found and attributed to the exastence of fms~on ~somermm m these nuclei [20] The above nuclei are pear shaped having large octupole deformations Tlus m turn lmphes the exastence of closely spaced parry doublets [21 ] wluch rmght influence the parry nnxmg mechans~m In R is possible that the compound states observed m the PNC expermaents m 2SSTh are influenced by the above effects Research m th~ &rectmn ts presently m progress [21]

ACKNOWLEDGEMENTS We wmh to thank D J Bowman and V Spevak fo helpful dascusslons We also thank N V Cna~ and D Vautherm for thew hospltahty at IPN Orsay where tlus work was completed. Tbas work ts supported by the US-Israel Blnat~onal Semnce Foundataon REFERENCES E G Adelberger andW C Haxton, Ann Rev Nucl Sol 35 (1985)501 B Desplanques, J F Donoghue, andB 1L Holstein, Ann Phys ( N Y ) 124 (1980) 449 V V F l a m b a u m a n d O P Sushkov, Nucl Phys A412(1984)13 V P A l f a n e n k o v e t a l , Nucl Phys A398 (1983)93 J D Bowman et a l , Phys Rev Lett 65 (1990) 1192, C M Franlde et a l , Phys Rev Lett 67 (1991) 564 N Auerbach, Phys Rev C45 (1992) R514 N Auerbach and B A Brown, to be pubhshed. F C Michel, Phys Rev 133 (1964) B329 1L J Bhn-Stoyle, Fundamental Interactions and the Nucleus (North Holland, Amsterdam 1973) F Osterfeld, Rev Mod. Phys 64 (1992) 491 10 M Momester et a l , Phys Lett B 230 (1989) 41 11 N Auerbach and A Klein, Phys Rev C30 (1984) 1032 12 N Auerbach, J Hufner, A K. Kerman, a n d C M Shakm, Rev Mod. Phys 44 (1972) 48 13 14 N Auerbach and V Spevak, to be published. N Auerbach, Phys Rep 98 (1983) 274 15 A K. Kerman and A F R. de Toledo Plza, Ann Phys (N Y ) 48 (1968) 173 16 N Auerbachand J D Bowman, Phys Rev C46 (1992)2582 17 J D Bowman et a l , Phys Rev Lett 68 (1992)780, S E Koomn, C W Johnson, a n d P 18 Vogel, Phys Rev Lett 69(1992)1163, C H L e w e n k o p f a n d H A Weldenmfiller, Phys Rev C46 (1992) 2601 J D Bowman, private commumcanon 19 See for example A Bohr and B Mottelson, Nuclear Structure, (Ben.lamm, New York, 20 1975) Vol 2 N Auerl~ch, to be published. 21