Nuclear Physics A577 (1994) 387c-392c North-Holland, Amsterdam

N U C L E A R PHYSICS A

Induced Terms of Weak Nucleon Curren ts in Light Nuclei

M M o r i t a a , R M o r l t a b a n d K KoshlgmC

aJosai Internat ional University, 1 Gumyo, Togane, Chiba 283, Japan

bWomen's Junior College, Josm University, Sakado, Sa l tama 350-02, Japan

CDepartment of Physms, Osaka Kyoiku University, Kashlwara, Osaka 582, Japan

Vector and axial vector currents of the weak interactions in hght nuclei are reviewed Induced terms of the nucleon currents are discussed Our recent analysis of the new experimental da t a on the be ta - ray angular dis tr ibut ion in the aligned 12B and l~N given by the Osaka group finds a new limit for the induced tensor current and a slightly larger value of the axml charge y This brings the strength of the induced pseudoscalar current very close to the PCAC value in the muon capture on 12C

1. I N T R O D U C T I O N

In order to investigate the weak interactions in nuclei, we assume the current-current type interact ion based on the s tandard model The vector and axial vector currents are given by the following forms, which changes the neutron s tate to the proton s ta te for be ta decay

v~ = ~;p(fvT~ + fw~x,k, + ~fsk~)~..

A:, = Cp75(fAT:, + f'ra.~oko + zfpka)¢n,

(1)

(2)

with

k = k , - k . , o ~ = [ -~ , -r~] /2 , (3)

Six terms In (1) and (2) are called the main vector, weak magnetism, induced scalar, main axial vector, induced tensor, and induced pseudoscalar currents, respectively The effects of these currents can be studied with various physical observables mostly an nuclear be ta decays Only the induced pseudoscalar current is not well known as the others, al though it can be s tudied m muon capture reactions We shall show a new value of fp which has been obtained from the s tudy of muon capture in 12C

Before going to discuss the detail of the results of our latest Investigation, we shall summarize recent s tatus of f , 's Firs t of all the magni tude of fv is well established by the Investigation on the super allowed 0 + - 0 + transit ions [1,2] Numerically [1], we have

f v / ( h c ) 3 = (1 14927 + 0 00065) × 10 -5 GeV -2 (4)

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388c M Mortta et al / Induced terms of weak nucleon currents

Agreement of this couphng constant m eight positron decays 1s a strong support of the CVC hypothesis at the level of 4 × 10 -4 A shghtly different value of fv as obtained from the da ta on lifetime and be ta- ray angular distr ibution of the neutron decay [1,3],

f v / ( h c ) a = (1 1580 + 0 0024) x 10 -s GeV -2 (5)

There are, at least, two ways for solving this dmcrepancy The one is to assume a further investigation of the Coulomb and radiatave corrections together with improved precision experament of the neutron The other is to introduce some addit ional interactions beyond s tandard model A V + A right-hand current is considered, e g , in [4], where the da ta on neutron, lONe, and others hmlt the boson mass in a region 207 < M2 < 369 GeV/c 2

The strength of the main axial vector is derived also from the be ta- ray asymmetry in the polarized neutron decay as

f a / f v = - 1 257 + 0 003 (6)

The strong support of the CVC theory brings the following relatmns for the induced scalar te rm and weak magnet ism

fs = 0 and f w = - ( # p - #,~)/2M = - 3 706/2M (r)

Here #v and #~ are anomalous magnetic moments of the proton and neutron, respectively M is the nucleon mass Existence of fw term was directly observed by, e g , an extra energy dependence of the electron in the allowed beta-ray spectra, in good agreement with the above relation

The induced tensor can be studied preferably in the mirror be ta decays, since the effect changes its sign for different charges of the electron From number of experiments on the lifetime and be ta- ray angular distr ibution in oriented nuclei, it is known that the magni tude of JeT is also vamshingly small, see, e g , [5] Since new experimental da ta on the be ta - lay angular distr ibutions in aligned 12B and 12N have been given by the Osaka group with a high precision [6], we have made an analysis of these da ta with our formalism It gives a new limit for fT and a revised value of the axial charge y in Sec 2 Since this y value plays an impor tant role for determining the pseudoscalar coupling constant, we shall see at In Sec 3

2 B E T A - R A Y A N G U L A R D I S T R I B U T I O N I N A L I G N E D mB A N D 12N

Beta-ray angular dl~trlbutlon an aligned 12B and 12N 1s given by

N ( E ) = Bo(E) + B2(E),,4P2(cosO), (8)

where .4 lS the degree of nuclear ahgnment The full formula is given elsewhere [7,8] In the lowest approximat ion, the difference of the anasotropy coefficients, B 2 ( E ) / B o ( E ) E , for the electron and positron gwes { [ ( f v / 2 M ) - fw] + fT } / fh , whale the sum for those gives y, which is the ratio of the t ime component of the main axial vector current to its space component ,

M Mortta et al / Induced terms of weak nucleon currents 389c

By measuring the slopes of the experimental data of B2(E)/Bo(E) m F,gure 1 [6], we can derive numerical values of fT / fA and y approxamately In thas approxamatlon, fT / fA as derived almost nuclear-model independently, and y is derived almost couphng-constant independently

Smce we have receaved the new data of the Osaka group m Fagure 1, we extended our prevaous work [9] We adopt our formahsm of beta-ray angular dastrlbutmn [7,8], whach has the effect of higher order partml waves of leptons, Coulomb corrections of the fimte- sine nucleus, and radmtive correctmns We have made a cha-square fit to the data wath the parameters fT / fA and 6y, where ~y as defined as y = YIA(1 + 6u) + YEC YIA is given in the ampulse approximation with the Hauge-Manpuu wave functmns and YEc as the effect of the exchange currents The other matrix elements are also calculated m a sarmlar way From prevmus works we know that the core polarlzatmn effects (CP) are Important particularly for y Therefore, 6u represents CP and some other effects, whach we have not expllcatly taken into account here

Finally we had the following results

2MfT/ fA = 0 2 1 + 0 1 4 (--0 14 4-0 10) (10)

y = 5 1 0 + 0 1 6 (4 8 8 + 0 1 3 ) , (11)

-1

O 3

-4

t 12 B . . . . . . . . . . . . .

~ ~ - -

IA EC . . . . ~ f i t ~

1 , , , i , , , i I i i i i I i i

0 5 10 15

E (MeV)

Figure 1 Beta-ray angular distribution m ahgned 12B and I~N

with the 1992 data [6], and those m 1985 [10] in paren- theses, respectively In Figure 1, the dotted, dash-dotted and sohd hnes represent the impulse approximation, exchange cur- rent included and best fit, re- spectwely Notice that fT has a small nonzero value, but with a different sign m 1992 from 1985 data

If we assume fT = 0 from the beginning, this work becomes a check of the weak magnetmm fw m (7) In this case, the nu- merical value of (10) enhances (or reduces) the absolute value of fw by the same amount

390c M Mortta et al / Induced terms of weak nucleon currents

3. R E C O I L P O L A R I Z A T I O N O F T H E D A U G H T E R N U C L E U S I N M U O N C A P T U R E R E A C T I O N I N 12C

Muon capture in hydrogen is free from the nuclear physics and is Ideal for deriving mfor- tuit ion on the pseudoscalar coupling constant fe There is a relation given by Goldberger and Treiman based on PCAC,

m . f p / . fA = ge/gA = 2Mm~,/(m~ + q2) (12)

Here the symbol, ge/gA, is frequently used in the muon capture physics Numerically gP/gn is 6 8 m hydrogen, while the world average of the latest experimental results is 7 0 :[: 1 5 in good agreement with the PCAC value, although individual data have large uncertainties There are a number of experimental data on various physical quantltms in the ordinary as well as radiative muon capture reactions and theoretical works to derive gP/gh from those experimental data We have, however, no space left for introducing those We simply present our latest analysis of the ratio of the average polarization of the daughter nucleus to the longitudinal polarization in the muon capture on 12C The reason to do this is that this ratio is insensitive to the nuclear structure and it is less dependent on systematic enors in experiment

Experimental data of this ratio is given in [11], R -- - 0 516 -4- 0 041 After subtracting the effect of the muon capture leading to the excited states of the daughter nucleus, we have R(1 +) = - 0 510 :[: 0 032, which is the ratio R due to the partial transition to the ground state of 12B Here we made an average for the effect of two different values of branching ratios to the excited states of a2B [12,13] Using this value of R(1 +) and the full formula of R in our formahsm[14], we solve ge/gn numerically We again use the Hauge-Maripuu wave functions, exchange current effects and y In (11) Finally we have gP/gA = 7 3 :[: 1 3 in good agreement with the PCAC value 7 2 We also mention that the lifetime of beta decays in the A = 12 system can be understood in our framework of nuclear model with exchange current effects [9] Therefore, the weak currents in the A = 12 system are very close to those of nucleons In this section, we have assumed fT to be z e r o

We would like to express our hearty thanks to Professor T Mmamisono for providing us their experimental data [6] before publication This work is partly supported by Grant- in-Aid for Scientific Research, The Ministry of Education, Science and Culture

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