Nuclear Physics :535 (1991) 94-106North-Holland

0v u DUMIT E C

NUCLEAR REACTION" N(polarized p, a), E =T

metry. C60 leve

1. Introduction

Rived 13 May 1 .9-0 1(Revised 26 June 1991)

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e parity=- and partially isospiaa-forbidden a,-decay from `0* (J'=2-,T=I; E,,=86 MeV) to 1 °C(g.s .) hasbeen thoroughlyinvestigated theoretically. Consideringvarious strong

and weak interaction models, the longitudinal AC _ and the irregular transverse At, analyzing powersof the reaction "N(p, a,,)i9C have been calculated in the energy range around the 2- resonancein "0*. The isospin impurity due to the coupling with 2- , E,, =12.53 MeV excited level in `0*,which has mainly a T = 0 component, have been considered in the calculations . Energy anomaliesfor the expected interference effects, relevant for the experiments, have been found to be AL_2.0x 1 ¬)- ' and A,,= 0.4 x 10- '.

0.898 MeV, calculated longitudinal asym-1 deduced parity nonconserving longitudinal, transverse analyzing powers,a-decay width weak pion-nucleon coupling constant ranges .

With the discovery in 1973 [ref. ' )] of neutral currents, the standard SU(2)OU(1)model 2-7 ) stood out as a strong candidate for a theory of electroweak interactions .In the years following these investigations great progress has been made in under-standing the weak NN interactions, especially after the experimental detection 8,9)

of the `V' and Z° bosons, mediators of the weak force . The weak interactionsbetween the nucleons and especially those components with dominant contributionof the neutral currents can be studied only when the strong and electromagneticinteractions between the nucleons are forbidden by a symmetry principle, such asflavour (i.e . strangeness (S) or charm (C)) conservation . According to the standardtheory, neutral current contribution to ®S =1 and ®C = 1 weak processes are stronglysuppressed '°'") and, therefore, the neutral-current weak interaction between quarkscan only be studied in flavour-conserving processes which we meet in low-energynuclear physics only r2-22 ) .

' Permanent address : Department ofTheoretical Physics, Institute of Physics and Nuclear Engineering,Institute of Atomic Physics, P.O . Box MG-6, Magure1c, Bucharest R-76900, Romania .

Here, however, favoura ,le cases should be selected and these are the parity mixeddoublets (PMD) for which:

(i)measurementof parity nonconserving (PNC) observables which, in conjunc-tion with known lifetimes, energy splitting, branching ratios (partial widths) etc.determine a well-defined PNC matrix element (

PNC)-(ii)

e transition "filters" (if all the quantum numbers of the excited states areknown) specific components of PNC weak interaction . This happens because onlytwo levels are involved in the parity mixing.

(iii)

e members of PMD have different decay (formation) amplitudes, and thisis why the PNC observables

n be significantly enhanced.In a recent work of Kniest et at. "), an application of a general non-parity-

conserving theory of resonance nuclear reactions, developed in refs. '9"'' ), to thepolarized-proton-induced PNC resonance nuclear reaction has been done.

In ref. ' s ) the authors assumed that the 2 - , E,=12.9686 MeV level mend. -=- edabove has, within a very good approximation, a good isospin quantum number( T =1). Furthermore, the parity-mixed doublet (PMD), formed by this level withthe 2+0, EY =13,02 MeV level in `60* was considered in ref. ' 8 ) to be of the isovectorparity-mixed type . If so, the PNC observable can give us necessary informationabout the contribution of the neutral currents, mediated by the heavy bosons - r,to the weak interactions . Such a judgement is realistic in the case when the pion-nucleon (7rN) component dominates the PNC - hamiltonian involved in the con-sidered process (i.e . if the values predicted by the Weinberg-Saiam plus the quarkpicture of Desplanques et A'3) or Dubovik and Zenkin '6) could be taken asgranted) .

In ref. ") the PNC meson-nucleon vertices were investigated within the frameworkof a chiral effective lagrangian for ir-, p- and to-meson exchange and treating thenucleons as topological solitons. The weak irN coupling constant (hJ was found ")to be considerably smaller (2.0 x 10-8) than the standard quark-model results 1 .3 x10-7 [ref. '6)], both these results restrict significantly the often-used Desplanques-Donoghue-Holstein (DDH) "best values" 13) . Such a controversy stimulates us toinvestigate with greater interest experiments sensitive to h,.

Moreover, recently 23'24) the experimental measurements showed strong isospinmixing of the 2- 1, E,, =12 .9686 MeV level with the 2-0, E,, =12.53 MeV level in '60*.The aim of the present paper is to establish whether or not the above-mentioned

isospin impurity alters the magnitude of the PNC irregular analyzing powers calcu-lated in ref. 'g) . We show that the isospin mixing does not change significantly thevalues of PNC analyzing powers obtained in ref. 'x), unless the PNC pion couplingis ~ 10-7. This conclusion follows because the additional contribution to the PNCmatrix element is of the isoscalar type, this type is determined by p- and w-mesoncontributions, whose large masses as compared to the pion mass diminish themagnitude of the PNC matrix elements . On the other hand, the isospin impurity isnot dominant.

O

mitrescu / Parity and isospin nonconservation

95

96

0. Duinitrescu / Parier and içospin nonconservalion

A thorough investigation of the PNC matrix elements, both of the isovector andisoscalar type, within different strong and weak interaction models, has been per-formed by us.The paper is organized as follows. The isospin mixing in the 2-, T = 1 ; E.,

12.9686 MeV level is discussed in sect . 2. Discussions concerning the weak interactionmodels and the corresponding PNC matrix elements are given in sect . 3 . Sect. 4 isdevoted to the discussion concerning the particular behaviour of the PNC analyzingpowers. Sea. 5 will contain the conclusions .

2. lsospin mixing in the 2-, E, =12.9686 MeV level in "0

After the observation 2~) of a large isospin matrix element in '2C of (179 * 75) keV- a large interest in the study of isospin symmetry in light self-conjugate nuclei hasappeared . In "0 the T= I levels are situated in a region where the level density isnot high and T = I levels can be expected to mix with one or two nearby T= 0levels only . Under such a favourable condition, the matrix element of the charge-dependent interaction, causing the mixing of the 2- , T =1, E, =12.9686 MeV with2 - , T= 0, E, =12.30 MeV was experimentally deduced .Thus, by using ' :5 N(p, p)'5N and 4̀5N( p, a ) 2C (4.439 MeV) reactions, the proton

and a-widths of the 2 - levels have been measured in ref. 23). The absolute value ofthe charge-dependent matrix element, responsible for the isospin mixing of the two2- states, was deduced to be equal to (181 -:k 10) keV, in agreement with otherexperimental measurements 24,26,27), which use other nuclear reactions or gammadecay . The authors of ref. 23) exclude the participation of the nearest second 2 -(E, = 8.87 MeV) level in 160* to the isospin mixing.Thus, the wave functions of the isospin mixed levels may be written as follows') :

12 - , 12.9686 MeV) = a 12- , T =1) - .8 12- , T= 0) ,(1)

12 12.5300 MeV) = «12 - , T=0)+ß112-, T=1),

(2)2with a = I/v/1+E2,

EI -4+E 2 and E = 0.278 :1: 0.052 .

3. Shelf-model predictions for parity-mixing matrix element

In order to determine the range and the amplitude of the AL and .4b around theexcitation energy of the first 2 - 1 excited state in 160 (Ep = 898 keV) we have madea shell-model estimate of the

MPNC = a(2-1,12-9686 MeVJHPNC 12'0, 13 .020 MeV )

-,8(2-0,12.5300 MeVIHPNC (2+0,13 .020 MeV) .

(3)

PNC matrix element using the OXBASH code in the Michigan State Universityversion 28-40), which includes different effective two-nucleon interactions .

O. Dumitrescu / Parity and isospin nonconservation

97

In these calculations the ZBM model space has been used. The abbreviation ZBMshould be understood as the Zucker-Buck-McGrory model space 33) in which ls,/2and lp3/2 levels are filled and the active (valence) particles are restricted to lp,/2 ,2s,/2 and ld5/2 orbits. The single-particle energies are fitted in ZBM I, as in ref. 32),

and the two-body matrix elements (TBME) are identified with Kuo and BrownG-matrix elements (the F-interaction) 32'36,37)

Within the ZBM-II we are dealing with the same model space as above. A fittingprocedure for two single-particle energies and for 30 two-body matrix elements inthe A =13-17 mass region was performed (the Z-interaction) 3-.33) .

Reehal and Wildenthal (REWIL) make a 33-parameter fit ofspectra in A =13-22mass region 35) . Zucker, Wildenthal and McGrory use two-body matrix elementscalculated with a Hamada-Johnston G-matrix 3') (ZWM) and the Oxford Avila-Aguirre-Brown 3°) interactions (ZWMO). The spurious center-of-mass componentin the wave functions have been eliminated according to the prescription given inref. 40) .

Bearing in mind that the behaviour of the shell-model wave functions at shortrelative NN distances is wrong, and taking into account that most of thecomponents '3-'`') of HPNc are short-range two-body operators, it is necessary touse the shell-model wave functions including short-range correlations (SRC) tocalculate correctly their matrix elements . The correlations were included by multiply-ing the harmonic-oscillator wave functions (with hw =14 MeV) by the factor

1- exp ( -ar2)(1- br2) ,

a =1.1 fm-2 ,

b=0.68 fm -2 ,

(4)

given by Miller and Spencer 4' ) . This procedure is consistent with results obtainedby using more elaborate treatments ofSRC such as the generalized Bethe-Goldstoneapproach ' 4'42) . By inluding SRC, the PNC pion-exchange matrix element decreasesby 50-60%, as compared with the values of the matrix elements without includingSRC, while the p(w) exchange matrix elements decrease by a factor of about 5, inagreement with the results of ref. 32

) .The nuclear structure part of the PNC matrix elements sometimes shows an overall

opposite sign if comparing two strong-interaction model results . Investigating thedirect overlaps of the same OXBASH wave functions used in those models we gota negative quantity, which tells us that in the OXBASH code the overall sign of thesame wave functions with different interactions is not defined by some phaseconvention. Nevertheless, in the energy dependence (see the next paragraph andref. ' 8)) the difference between the maximum and the minimum of the irregular PNCanalyzing power does not depend on the phase of the PNC matrix element.The PNC matrix element depends linearly on integrals containing the derivative

operator and the relative NN radial wave functions. By a careful analysis of theseintegrals we have come to realize that using Woods-Saxon-type wave functions thePNC matrix element could decrease at most by 20% as compared to our PNC matrixelements calculated with harmonic-oscillator wave functions . This result is obtained

98

O. Diitatitresca / Parity and i.sospin nonconservation

by a simple replacement of the harmonic-oscillator wave functions with Woods-Saxon ones . Such a procedure is not, however, consistent with the recipe used inthe, OXBASH code, because the fitting procedure of the strong-interaction matrixelements depends on the basis used. To estimate the above-mentioned effect wemay use a cliff`-rent procedure, namely, we may enlarge the single-particle basis byincluding higher shells, such as fp and sdg. Such a procedure leads to a factor oftwo or three smaller 4,S ) PNC matrix elements as compared to the PNC matrixelements calculated in this work. This procedure, however, implies largemodifications in the OXBASH code, which are at the moment difficult to perform .To test the standard model, one needs to calculate the weak meson-nucleon

vertices . Only a few calculations based on the quark model '"- ") exist. Thesecalculations start from the observation that there are essentially three types ofdiagrams, which can be categorized as factorization, quark-model and sum-rulecontributions . Renormalization group techniques and baryon wave functions basedon phenomenological models are needed to evaluate them. This introduces a varietyof uncertainties, which leads DDH in ref. ") to introduce a "reasonable range" forthe values of the weak meson-nucleon coupling constants. In particular, the weakpion-nucleon coupling constant (h-..) is very sensitive with respect to these uncer-tainties, for instance, the values of h- differ by a factor of 3 in refs. 13,16)

, whereash,,,,.,,, are more stable . By using a nonlinear chiral effective lagrangian which includes

p- and ca-mesons, and treating nucleons as topological solitons, Kaiser andMeisner °') obtained different values for strong and weak meson-hadron couplingconstants as compared to other results "-'6 ) .

For comparison we inserted in the calculations of the PNC matrix element thecoupling constants of the weak meson-nucleon vertices h,-,, h,, and hw calculatedwithin different models of weak interactions and summarized in table 1 . The firstcolumn contains h,,,~T ' obtained by Kaiser and Meissner (KM) ") using the modelparameters as follows: the pion decay constant f, = 93 MeV, the "gauge" coupling

TAHL F. 1

Weak meson-nucleon coupling constants calculated within differentweak-interaction models (in units of a0-7 ) . The abbreviations are :KM = Kaiser and Meissner "), DDH = Desplanques, Donoghue andHolstein ")p AH = Adelberger and llaxton -"-) and DZ = Dubovik and

Zenkir R16) .

h meson KM DDH AH DZ

h!, 0.19 4.54 2.09 1.30h`P -3.70 -11 .40 -5.77 -8.30h P -0.10 -0.19 -0.22 0.39h2ho -3.30 -9.50 -7.06 -6.70hp, -2.20 0.00 0.00 0.00h~, -1 .40 -1.90 -4.97 -3.90h. -1 .00 -1 .10 -2 .39 -2 .20

constant gp.,, = 6, the pion mass m,, =138 MeV and three pseudo-scalar-vectorcoupling constants (g,,O =1 .9, h = 0.4 and k = 2) (see table 1) . The second columncontains the often-used Desplanques-Donoghue-Holstein (DDH) 13 ) "best" valuesobtained within a quark plus Weinberg-Salam model. In the third column are :~istedthe values of h (T) fitted from experiments by Adelberger and Haxton 22). In thelast column are included the values obtained by Dubovik and Zenkin (DZ) '6) withina more sophisticated quark plus Weinberg-Salam (SU(2)OU(1)0SU(3)C-) model.We consider these values as more "realistic", taking into account that they aresustained by comparison with the experimental data, given in the comprehensivereview of Adelberger and Haxton (AH ) 22) . However, the extraction 22), of the h_..- coupling constant from the experimental data uses the analogy of the 7rN PNCoperator [see eq. (19)] with that of the .8-decay and also the assumption that thepion-nucleon component of HPNC- is dominant 13 ). If considering the Kaiser-Meissner results "), these assumptions may not be true . There are two types ofcontributions to the PNC matrix element: one is coming from the two-body transitiondensities, if all four orbitals entering the two-body matrix elements are in the valencespace 32) ; another one arises from the one-body transition densities if two orbitalsare in the core and the other two belong to the valence space :

The total

PNC matrix element, mentioned in this section, is =0.1 eV, but ranges from 0.03to 0.7 eV (see sect . 4) .

Results for all the models, given in the tables 1 and 2, can be obtained by astraightforward multiplication .

In the vicinity of the 2- 1 narrow rsonance the PNC longitudinal (A L ) andtransverse (At,) analyzing powers have the following simple expression 8"9)

where

and

O. Dumitrescu / Parity and isospin nonconservation

99

((1s,/2)4(1P3i2)"(2s, /2)IHPNC-I(1Pl/2)(1P3i2) 8(ls,i2)4) .

(2- 12.9686 McVIHPNC-I2+ 13.02 MeV) .

4. Longitudinal and irregular transverse analyzing powers for the 'N@,&o)'ZC

resonance reaction

AL(h) - DL(h) Re {;r2- (E - E'`-+ i;r2- ) - ' exp [i(~L(h)+OPNC')]I 9

(6)

DL(h) =2(F2-)-1

I(2 1IHPNC_I2+0)I

r2 12r2+ ICL(Ij

(7)

_

,~,

_s1 P`(cos B) E

b~~~~~(L(b))( ta~*~ tâ i~~)CL(h )l - ICI-(h)l exP (~~f'L(hl) ®

I

~.

'

(g)E1 PI(cos 0 )

nui Q~nn~n~~ ~~

Nuclear-structure part of the PNC-NN matrix element (in MeV) as defined in eq . (KX ) in the text . Theabbreviations 3re: ZBM0= Zucker, Buck and McGrory (F-interaction) 33 ), ZBMÖK= Zucker, Buck andMcGmmry (Z-interaction ) ^z ) . 0KEWÖL=the interaction given im Reehml and WildemmhaÖ -15 ), ZWM andZWMO=te interactions given im McGmmry and WildenthmX In talic parentheses the matrix elementsnithoou SRC are presemxedthe first two rows present the single-particle contributions to the Mi,,,, thesecond two rows the two-particle contributions andthe last tworows - thesumofthetwoaforementionedcontributions, giving the total value of the nuclear-structure part (M&. ,) of the PNC matrix element.

0. D mmitwscu / Pmrity and ismxpin nonconservation

TABLE 1

Interaction ZBM0 ZBM00 REW0L ZWqM ZWMO

AL-1 0.2600 -0.0571 0.3131 -0.6438 0.8975

M-3573> (-0.0160) (0.4074) Y-w.8504) (Kk%633)

0. 70 -0.0305 -0.0070 -0.N095 -0.003X

M0056> (-0J0413) (0.@040) (-0.0291) (0.0066)

0~27f& -0.0076 0.3200 -0.7533 0.2006

(03729) (-0.1U74) (0.42X4) (-Ni8875) (KK2@99)

AI,,, &0145 -0.0031 0.0170 -0.0349 0.0107

MOSQO0 (-0.00J7) (0.0609) (-0.161X) (0.04Ö2)

X ~~ 0.0028 0.0012 -0.0055 0.0002

(0A164 ; (0.005Q) (0.094-3) (-0.0269) (-0.N0&3)

(0,0177 -0.0003 0.0002 -0.0404 0.010740.0744) (0.00-31) {0.0732) (-0.1000) (0.040#)

0.0070 -0.00-36 0.0190 -0.0400 0L0125

(0.0636) (-0.0D36) <0.0743) (-0X528) {0.0469)

0.0042 0.0050 0.0007 -0.0086 -0.0004

(0~ 146) (0.0Ö59) (0.0027) (-0.0232) {-0.00lX)0.0212 0.0014 0.0205 -0.0474 0.0121

(0.0702) (0D0023) (0.077Ö) (-UL1760) (( .0457)

0.0137 -0.0029 0.0160 -0.0029 0.0101

(0.0741) (-0.0158) (0.0064) (-&l779) (0.0545)0.0019 -0.0023 0.0830 -0.0050 0i0024

(#.0078) (-0.0002) (0.0106) (-0.0103) 0.80890.0156 -0.0052 0.0100 -8.0309 0.0125

(A.08l7) (-#.0250) (0.0971) (-{il962) (0.0634)

M` -0.0425 0.0152 -0.0088 -0.0191 0.0045(-O.0530) (0.0567) (-0.0253) (-0.07l3) (0.0lG8 )-0.0063 0.0030 -0.0021 -0.8027 0.0019

(-0.020l) (0.0l56) (-KO0A0) (-0.0l22) (0.0074)-0D4Q8 0.0100 -0.0009 -0.0218 0.0064(-<l073g) (0.0723) (-0lB4J) (-0.0035) (UlD72)

M5v -O.U02l 0.0007 0.0003 0.0000 0.0002(-0.O00l) (-0.0003) (0.0000) (0.0002) (0.000l)-0.U0l2 -0.0041 0.0020 0.0040 -0.0012(-0.0U51) (-0.0l0n) (0.0U06) (U.0220) (-0.U045)-0.0033 -0.0034 0.0023 0.0057 -0.0010(-0.0053) (-0.0l0l) (U.0006) (-U.0222) (-0.0044)

M/° 0.0136 -0.0029 0.0159 -0.0327 0.0100

(0.07l6) (-0.0152) (0.08J5) (-O.]78l) (0.0527)0.0030 0.0026 0.0011 -0.0052 0.0002

(0.0l5V) (0.0l54) (U.004l) (-O.026U) (-0,0003)0.0166 -0.0003 0.0170 -0.0479 0.0102

(O.00?5 ) (U .000l) (0.08?6) (-Klg79) (0.05J4)

O. Dumitrescu / Parity and isospin nonconservation

101

TABLE 2-continued

where '8,'9)

tj = T,,g = ToOO,p l

t2 = T'-0'P01

t3- Ta 10,p21

t4= TâO,pl 1

are four PC reaction matrix elements .

T, = Ta20,p2O

T2 = Tâiô,p2l 9

(10)are two PNC reaction matrix elements, which participate in the reaction process.The subscripts are channel, a, la , s,, ; proton, lp , sp , and the superscripts are thetotal angular momentum j and parities . Here for L: a = 0, for b : a =1, 74 =

t4 exp (i(ep2l -e,, � )) [see refs .

The coefficients b �̀;'� (L(b)) and a"' (L(b)) aresimple specific values of the geometrical coefficients [see refs . '8,'9)] for the case weare investigating now.

Defining by 4AL(h) the distance between the minimum and the maximum of thePNC analyzing powers as a function of energy we find that this quantity is equalto the quantity DL(h) defined in eq. (7) and does not depend on the PNC matrixelement phase (OPNO and PC quantity phase ($L(h)) .

interaction ZBMI ZBMII REWIL ZWM ZWMO

0.0161 -0.0034 0.0188 -0.0387 0.0119(0.6l8) (-0.0132) (0.072l) (-0.1484) (0.0455)0.0040 0.0047 0.0007 -0.0063 -0.0004(0.0l42) (0.l54) (0.0027) (-0.0225) (-0.0011)0.0201 0.0013 0.0195 -0.0450 0.0115(0.0759) (0.0022) (0.0748) (-0.1709) (0.0444)

43. 0.0128 -0.0027 0.0150 -0.0308 0.0095(0.07l6) (-0.0152) (0.0835) (-0.1719) (0.0526)0.0018 -0.0021 0.0028 -0.0046 0.0022(0.0074) (-0.0089) (0.0l02) (-0.0176) (0.0086)0.0146 -0.0048 0.0178 -0.0354 0.2017(0.0790) (-0.0241) (0.0937) (-0.1895) (0.0612)

M6. -0.0134 0.0048 -0.0021 -0.0060 0.0014(-0.0174) (00.0184) (-0.0082) (-0.0231) (0.0054)-0.0038 -0.0003 0.0002 0.0027 0.0005(-0.0108) (-0.0032) (00.0010) (00.0083) (0.0009)-0.0072 0.00045 -0.0019 -0.0033 0.00019(-0.0282) (00.0152) (-0.0072) (-0.0147) (0.0064)

M,. -0.0221 0.0079 -0.0035 -0.0099 0.0-23(-0.0402) (00.0429) (-0.0190) (-0.0537) (0.0125)-0.0026 0.00013 -0.0011 -0.0014 0.00009(-0.0147) (0.0066) (-0.0050) (-0.0048) (0.0047)-0.0247 0.00092 -0.0046 -0.0113 0.00032(-0.0549) (00.0495) (-0.0240) (-0.0585) (0.0172)

M01 0.00170 -0.0036 0.00198 -0.0408 0.00125(00.0636) (-0.0136) (00.0743) (-0.1548) (00.0469)0.00015 -0.0024 0.00019 -0.0035 0.00017

(00.0055) (-0.0076) (00.0071) (-0.0127) (0.0062)0.00185 -0.0060 0.00217 -0.0443 0.00142

(00.0691) (-0.212) (00.0814) (-0.1655) (00.531)

re

in which

with

l~aaaaaïr~~~sraa / ï'~a~ïre° ~aatf ïsra~~ïaa aac)aac°caaacera.'~tï(,a

rt~ain resu~t of the present papereould be con ense in the foilowïng formuia:

where ~.~N~- (

) (gin e~) are +d~ erent meson contributions to the total P~tCshe 'mo e

atria us ent :

i ._ ,~.?~,u~

~d ~~~(49 rJA .~~ ®(~ ~°

aa )

(1?)

(13)

C1 )

(15)

(16)

(lï)

® (2 1 ~,1~,~ ~ 2~®) (1~)

(19)N

1(20)

1

M~(P9_ $Ta_)l(y XQ,)èl(r, s) s_ _ (21)

~ 1(22)

N

.Î~,s1

= (Te ' z~)i(W X vr~~u(r, ms) , (23)N

f~, .,1

= (T v ' T,)(~, -~~)v(r, m.~) , (24)MN

MN

1(2b)

u(r, m.s)1

_ (P~ - PZ)~ exp ( - m~r) (27)47rr

v(r, m.s ) 1_ (p~ - Pz) ~ exp ( -m,,r) . (28)4~rr

Here

O. Dumitrescu / Parity and isospin nonconserration

103

g~ = 13.45,

gn =2.79,

gv,=8.37,

r=ri -r,,

iz, =3.7,

p,=-0.12 .

The nuclear-structure part of the PNC matrix elements (see

, quantities (18)from eqs. (12)-(17)) calculated by using the models included in the OXBASH codeare given in table 2. Presented in detail are: single-particle an two-particle

nttions and their sum, respectively, calculated with and without inshort-range correlations within different strong-interaction models.

r

this tablewe can conclude how much the SRC suppress the PNC rnatrix elements anfact that the single-particle contribution dominates the

C matrix element-

erelative signs of different contributions are also given. However, it

n happen thatfor instance for two different interactions for the same matrix element Mt,, the signsare opposite. In this case we have calculated the direct overlap of the

e wavefunction produced by the corresponding interactions obtaining a neg tive quantity .Such information corresponds to the fact that the ®ABASH code does not fix thesign of the wave function .The eq. (11) differs from the corresponding result ofref. "). It contains in addition

the PNC isoscalar term according to the isospin-mixing treatment (see sect. 3). Thisdifference, however, does not modify the magnitude of the PNC matrix elementand hence, nor the magnitudes of the irregular (PNC) analyzing powers, calculatedin ref.The quantity D'O'

(in eV-' )

5. Conclusions

D""b) = 2(r2-)-l

rP1CL(b)

~ 2F2+ I

L(b)1

(29)P

has

the

following

values

for

0,...=90",

DO=1 .121 x 10-5 eV- '

and

Do=0.92 x 10-5 eV- ' while for ®,,.R ,_ =150°, D, =1 .4 x 10-5 eV- 'and Db= 0.25 x 10-5 eV- ' .

Finally gathering the numbers from the tables 1 and 2 we find that [see eqs .(11)-(28)] the energy PNC anomalies for the expected interference effects, relevantfor the experiments, have been found to be in average : AL= 2.0 x 10-5 [(0.6-- AL14) x 10-5] and Ab = 0.4 x 10-5 [(0.12-~ A,,-z ;z-: 2.8) x 10-5], i.e ., the analyzing powerskeep their -values obtained in ref. '') .

In this paper it was shown that if 1h,1 r Z x 10-' the isospin impurity of the 2- ,T = 0, E,, =12 .53 MeV into the 2-, T =1, E,, =12.9686 MeV level does not changesignificantly the results of ref. ''), i.e . the PNC analyzing powers keep their values(A L - (2.0) x 10-5 and Ab - (0.4) x 10 -5) .As in ref. ' s ), it was shown here that the 2- , T =1, EX = 12.9685 MeV and 2+,

T = 0, E,, =13 .02 MeV form a parity-mixed doublet . The parity mixing betweenmembers of the above-mentioned doublet is of a particular interest because :

1

0 Duanitrescu / Parity and isospin nonconservation

(i)

e mixing is sensitive to the AT= 1 components of HPNC and especially tothe part describing the weak pion exchange, if assuming the quark model picture.In this case we may have quantitative informations about neutral current contribu-tions to HPNC . At present, there is only one experiment ") sensitive only to theAT= 1 component of the PNC-NN weak interaction and which leads to the finala-channel - the

o-decay of 13.452 MeV 1 } l state in 2®Ne populated by polarizedprotons . It gives an upper limit for the PNC longitudinal analyzing power a valueof (1 .5 :1- 0.76)';%, 10"

(ii)

e obse ables

Uh) provide a precise way to measure the PNC matrixelements . Besides the 50 keV energy difference between the levels involved in thementioned doublet, the energy anomaly in the PNC analyzing powers (AL and Ab)is magnified also by nuclear structure effects . The magnification arises because ofcoherent contribution of proton and a-channels. The quantity CL(h) is essentially aratio between the

T-matrix contribution to the PNC analyzing powers and thecross section for the (p, a) reaction induced by an unpol"arized proton beam. Thevalue of this ratio in the resonance region is about 4.1, which indicates this coherenteffect .

e total width of the ?A resonance level is quite small (1 .6 keV) and actsas an enhancement factor. The ratio

JT-~ with the value close to unity playsalso the role of an enhancement factor as elsewhere °"' g-'') . Similar ratios ofunnatural to natural parity-level widths are of the order of 1(1- `' [see e.g. ref. ")).

(iii) The cross section is smaller at back angles as compared to the elastic-scattering cross section '' '3i ), but larger than that at forward angles . However, thea-channel can select the transition more clearly . The normal PC analyzing poweris negligibly small ") in this energy region for backward angles . Thus the experimentcan be considered free of errors from measurements .

(iv) The PNC av transition can be studied via ' sN(p, ao)"C resonance reaction

with two different observables independently, namely the PNC longitudinal AL andPNC transverse Ab analyzing powers. which sometimes show diferent energyanomaly as functions of the scattering angle.

(v) The theoretical models included in the OXBASH code are reasonably good.

The author would like to express his gratitude to Professor Pier Giorgio Bizzeti fora permanent encouragement, helpful criticism and the warm hospitality at the INFN,Firenze, where a large part ~)f this work has been done. He is grateful to ProfessorsPietro Sona and Gheorghe Stratan for many stimulating discussions . He also thanksDrs. Roberto Cecchini and Andreea Perego for tie help in implementing theOXBAS I c3de on the Vax computer in Firenze. The author would like to thankProfessors Carlo Bosio, Cristian Stanescu, Claudio Cioih degli Atti and GianniSalme for the warm hospitality at IN FN, Sanita, Roma, where part ofthe calculationspresented in this paper have been done. The author would like to express hisgratitude to Professor Luciano Fonda from ICTP, Trieste for permanent encourage-ment and criticism . The author would like to thank Professor Abdus Salam, the

O. Dumitrescu / Parity and isospin nonconseruation

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105

International Atomic Energy Agency and UNESCO for hospitality at the Inter-national Centre for Theoretical Physics, Trieste, where the last part of this workhas been done.

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