Elementary particle approach to neutral current processes in nuclei

2.B:2.L

NuclearPhysics A324 (1979) 365-378 © North-HollandPublishing Co., Amsterdam Not to be reproducedby photoprint or microfilmwithout written permissionfrom the publisher

ELEMENTARY PARTICLE APPROACH TO NEUTRAL CURRENT PROCESSES IN NUCLEI J. BERNABEU Department o[ Theoretical Physics, University ol: Valencia

and P. PASCUAL Department of Theoretical Physics, University o[ Barcelona Received 29 December 1978

Abstract: We study neutrino-nucleus inelastic cross sections and longitudinally polarized electronnucleus scattering in order to analyze the quantum number structure of weak neutral currents. General formulae are obtained when nuclei are treated as elementary particles by the use of global form factors. It is shown that, for 1+ transitions and to an excellent approximation, a siqgle function if(q2) controls all nuclear structure ingredients for both processes. Explicit results for tZC, 6Li and 7Li are presented.

1. Introduction T h e s t r u c t u r e of n e u t r a l c u r r e n t s is a f u n d a m e n t a l q u e s t i o n in o r d e r to fix a u n i f i e d m o d e l of w e a k a n d e l e c t r o m a g n e t i c i n t e r a c t i o n s . P r e s e n t i n f o r m a t i o n on t h e q u a n t u m n u m b e r s a n d c o u p l i n g s 1) has b e e n o b t a i n e d f r o m n e u t r i n o - h a d r o n i n t e r a c t i o n s . T h e results e x t r a c t e d f r o m t h e a v a i l a b l e inclusive, s e m i - i n c l u s i v e a n d exclusive d a t a a g r e e a m a z i n g l y well with the p r e d i c t i o n s of the s t a n d a r d W - S - G I M t h e o r y 2). It has b e e n p o i n t e d o u t b y s e v e r a l a u t h o r s 3) t h a t a clean s e p a r a t i o n of t h e different c o m p o n e n t s of t h e n e u t r a l c u r r e n t i n t e r a c t i o n w o u l d b e p o s s i b l e t h r o u g h t h e use of n u c l e a r t r a n s i t i o n s . O n e t a k e s the n u c l e u s as a g a d g e t which allows t h e filtering of t h e v a r i o u s q u a n t u m n u m b e r s . E x p l i c i t c a l c u l a t i o n s for t h e e x p e c t e d s t r e n g t h s h a v e b e e n m a d e in t h e i m p u l s e a p p r o x i m a t i o n f r a m e w o r k a n d t h e sensitivity to m o d e l s of w e a k i n t e r a c t i o n s has b e e n d i s c u s s e d 4). R e c e n t l y , s o m e tests 5) of the feasibility of i n t e r m e d i a t e e n e r g y n e u t r i n o e x p e r i m e n t s at p i o n f a c t o r i e s with b e a m s of low d u t y f a c t o r h a v e b e e n m a d e with e n c o u r a g i n g results. T h e y allow o n e , in p a r t i c u l a r , to e n v i s a g e t h e e x c i t a t i o n of t h o s e n u c l e a r levels w h i c h a r e accessible f r o m G a m o w T e l l e r t r a n s i t i o n s , t h e o n e s which h a v e a m a x i m a l strength. T h e s i t u a t i o n for the n e u t r a l c u r r e n t i n t e r a c t i o n b e t w e e n e l e c t r o n s a n d h a d r o n s is still c o n f u s e d . Its p a r i t y - v i o l a t i n g p a r t has b e e n s e a r c h e d for in t h e i n t e r f e r e n c e w i t h t h e e l e c t r o m a g n e t i c a m p l i t u d e . E x p e r i m e n t s in h e a v y a t o m s a r e p r i m a r i l y sensitive to t h e ( e l e c t r o n axial c u r r e n t ) × ( h a d r o n i c v e c t o r c u r r e n t ) p i e c e of t h e i n t e r a c t i o n . 365

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J. BERNABI~U AND P. PASCUAL

Results for atomic bismuth from the Oxford and Seattle groups 6) place an upper limit for parity violation which is roughly an order of magnitude smaller than the values predicted from the standard theory. There is a recent claim from the Novosibirsk group 7) that the effect has been observed and agrees in sign and magnitude with the W - S - G I M prediction. In order to avoid the complications in the analysis associated with atomic physics, experiments in hydrogen and deuterium 8) have been suggested. Electron scattering offers a powerful tool to look for the neutral current interaction. A parity-violating observable is constructed from helicity dependence of the cross section, which can be observed using longitudinally polarized electron beams. Recent results 9) from S L A C in deep inelastic electron scattering from deuterium are in agreement with the predictions lo) of the standard theory. A model independent analysis points out that all different pieces of the parity-violating interaction are a priori relevant. Again the use of nuclei to isolate the different q u a n t u m numbers has been advocated. Thus elastic scattering has been discussed by Feinberg 11), whereas magnetic dipole transitions have been calculated in the impulse approximation by Walecka 12) for isovector excitation, and Bernab6u and E r a m z h y a n 13) for the isoscalar case. The aim of this p a p e r is to present a unified treatment of neutral current processes in nuclei for both neutrino excitation and parity-violating electron scattering. To show that the processes can be used to extract information about the neutral current structure we analyze them in a global approach for the nuclear vertex. The couplings relevant to the q u a n t u m numbers of each transition are introduced at the f u n d a m e n tal point-like quark level and nuclear form factors describe the system without c o m m i t m e n t to any specific model. In sect. 2 we obtain the general relations of the non-polarized nuclear tensor built from two currents with the nuclear form factors. Sect. 3 discusses neutrino-nuclear scattering in terms of the relevant hadronic couplings with neutrinos. A compact result for the differential cross section is obtained in terms of the structure functions and the long wavelength limit is given. In sect. 4 the differential cross section for polarized electron-nuclear scattering is calculated by keeping the interference between the electromagnetic and neutral current parity-violating contributions. Sect. 5 gives explicit expressions for 1 + transitions. It is shown that, to a very good approximation, all nuclear ingredients are contained in a single function ~.(q2) c o m m o n for both electron and neutrino scattering. Finally we present in sect. 6 numerical calculations for 12C, 6Li and 7Li and discuss the information content of these transitions.

2. N u c l e a r structure tensor

Both for neutrino and electron scattering the nuclear ingredient can be factorized in terms of the matrix element X " of the appropriate hadronic current J " between the initial and final nuclear states. It has been proved 14) that, in the Breit reference

NEUTRAL CURRENT PROCESSES

367

system, such a matrix e l e m e n t can be written as

X " ( p 2 , pl)~ 2 = t" Z ( - 1)i2+X2Cqlj2L; )tl, -/~2, 0)AtL)(q 2) L

+ Y~ n~,-~21(- l )i2+x' +l C q l j 2 L ; "~1,

--/~2, ~1--/~2)

LI

x C ( L l l ; A1-A2, - A 1 +A2, 0)F~t'L)(q2),

(1)

w h e r e Pl,/'1, )tl(p2, ]2, A2) are the initial (final) m o m e n t u m , spin and helicity of the nucleus, q = p l - p 2 and t, n(i) is the usual tetrad of reference. F o r most situations, parity and angular m o m e n t u m selection rules imply that only a few form factors A (L~, F (t'c) contribute. F u r t h e r m o r e , they are relatively real due to t i m e - r e v e r s a l invariance. Since IA1 -Az] = 0, 1 the natural c o m b i n a t i o n s of nuclear f o r m factors are

~2 L F~L.l.m(q2)+ J_ L + I F,L_~.L, at(qZ) =-- ( 2 L + 1) v 2 ( 2 L + 1) (q2), fl

Bt(q 2)-=~]~F

(L I )

'(q

2

),

CL(q 2) _----AtL~(q2),

xfL+l FtZ+,L, • L r-(L ~ . (q2)_ ~ / 2 ~ - ~ r

DE(q2)=- V ~

1,L)/

2x

tq ).

(2)

W h e n nuclear polarizations are not o b s e r v e d the relevant quantities for cross section calculations are the following:

B"V(P2, Pl)

=

~'. 2 ~ ( p 2 , Pl)XI[ x2 X ~'(P2, P,)]~]*,

(3)

A.IA2

w h e r e ~('~ d e n o t e s the matrix e l e m e n t of a nuclear current J~" which can be equal or different to J " . O n L o r e n t z covariance and t i m e - r e v e r s a l invariance grounds one can write B "v in t e r m s of five structure functions Wi(q2), even in the case of two different • • t currents• T h e conventional d e c o m p o s t t l o n is

B~(p2, pl)=-

g""

q"q_~ Wa(q2)+ q

p'¢----y-q

1 .~+ - . . t 2e.~t3pl~qj3W3(q2 ) + 1--Tq . ~q W4(q 2)----7(Plq

zml

ml

ml

- - ~q" q

q

, W2(q 2)

~ 2 qUpl)Ws(q ),

(4)

w h e r e e °123 = + 1 and m l (m2) is the initial (final) nuclear mass. * For the general tensor (3) in which two different currents may appear, the positivity restrictions are no longer valid.

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P. P A S C U A L

Taking into account that this tensor should be contracted with leptonic currents, the terms which contain q " a n d / o r q" will not contribute since they give zero or are proportional to the electron mass which can always be neglected for our purposes. By substituting (1) in (3) and comparing with (4) written in the Breit system we can identify the interesting structure functions Wl(q 2) = AA +/~B, 2

d

A

_

A

D

q 2 Wl(q2)' AZ--q

2M ,/~[AB +tiA],

W3(q 2) =

(5)

if A/M, -q2/4M2<< 1, which turns out to be true in all practical situations, 1 where A = r n a - rn~ and M = ~ ( m l +m2). The quantities appearing in eq. (5) are defined as , 2,)R Ltq , 2x), SR-----E Ltq

(9)

L

where S, R = A, B, C, D. From parity selection rules one has that, for a given L, the functions AL, CL, DL are all coming from the vector current, whereas BL receives contributions from the axial current or vice versa. From relation (6) it follows that Wl(q 2) and W2(q 2) contain vector ® vector plus axial ® axial contributions and W3(q 2) contains only the vector ® axial interference contribution.

3. Neutrino-nucleus scattering We start from the most general effective neutrino-quark Lagrangian 15) = - 4~- G , ; ~ , " (1 + J•

-

vs),J.,

1

= O'y.(~a73+½y)O+

1 1 Q, Oy.y5 (~/3r3 + ~6)

(7)

where c~,/3, T, 6 are the couplings associated with isovector vector, isovector axial, isoscalar vector and isoscalar axial neutral currents, respectively, and Q stands for the up and down quark field doublet. In the standard W - S - G I M (ref. 2) theory the couplings are a = 1 - 2 sin 2 0w,

/3 = 1,

Y = _ 2 sin 2 0w,

~ = 0,

(8)

with 0w being the mixing (unification) angle. Using well-known techniques, a straightforward calculation gives for the

NEUTRAL CURRENT PROCESSES

369

differential cross section do" G2 dq 2 - 4~r(2jl + 1)(s - m21)2 W w ( S , q2), Ww(s, q2) = _ q2 W, (q2) + 2__~1[(S

_

m 21)(s - rn 2) + sq2] W2(q2)

2 - 4m2112s q _m~_mZ+qZ]W3(q2),

(9)

where s = (pl + p~)2 is the usual Mandelstam variable. For antineutrino scattering the sign of the third term of Ww(s, q2) must be changed. In the forward direction all the contribution comes from W2(q2-- 0) only, while this structure function does not a p p e a r in the backward direction. Notice that in the case of neutrino scattering one has J , ~ J~, and, as a consequence,/?L = RL and SR = I~S =-SR. The subindex in Ww is an indication that only weak currents are involved. In our definition of the current J~ the strengths of the quark couplings are included, so that

RL(qa)=aR~V,,~(q2)+/jR~A,,)(q2)+yRkV,m ( q2) + 6 R Ltam ' (q2),

(10)

for any form factor combination RL(q2). Due to space-time and isospin invariance properties only one or two of these four terms will contribute in a definite situation. In specific cases we will omit the super-indices when no confusion is possible. In the long wavelength approximation (qR)2 << 1 the only non-vanishing 14) form factors are Aml(q 2 ~ 0) and Fm'~(q 2 ~ 0). For inelastic transitions CVC requires that they vanish in this limit. T h e r e f o r e they remain only for the axial case: A/m induces parity change and F m'l~ no parity change. The G a m o w - T e l l e r transitions are determined from this non-vanishing form factor Fm'l~(q2~0) and they are the dominant ones at low energies. By integration of the angular distribution (9) when Fm'l)(q 2) ~ Fm'l~(q 2 = 0) and neglecting all the other form factors we get

o'=

(GE'~) 2 1 F{O.l) 2 4~ 2 j , + ~ --M-- '

(11)

where E'v = E~ - ,:1 is the final neutrino energy. For the case of an isovector transition with an analogue inverse /J-decay, eq. (11) can be written in the following form: 2212+ 1 In 2 2 ,2 o-=~r 2/1+1 mT-r--/2/jefrl E . ,

(12)

This formula is expected to be valid for light nuclei up to energies E~ of the order of 50 M e V with an estimated error <~ 20%.

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J. B E R N A B I ~ U

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P. P A S C U A L

4. Polarized electron-nucleus scattering Here we are interested in the interference between the electromagnetic and weak neutral current amplitudes. A signal of this interference is provided by its parityviolating piece. The most general parity-violating effective Lagrangian for the electron-quark neutral current interaction is ~Opv =

]" - Ix -~/~G{ey yseV, +~y~'eA~,},

=

= 0%,7s(~r3 + ~(3)0,

(13)

with the couplings defined as before. If the neutral current electron-hadron interaction were mediated by the same intermediate vector boson Z responsible for the sectors of neutrino physics one would have the following factorization relations 16): = 2 GAO(,

33= 2 GAy,

K

13 = 2 Gv~,

K

g = 2 Gv6,

K

(14)

K

where GA, G v are the couplings as determined from neutrino-electron scattering and K is the neutrino-neutrino coupling. In the standard theory 2) one has K = 1,

GA-- --2,

Gv =

+ 2 sin 2 0w.

(15)

The quantity to be measured using longitudinally polarized electron beams is

R(s, q2) = do-+- do-do'+ + do'_'

(1 6)

where the subindex denotes the incident electron helicity. To calculate this observable we maintain the dominant parity conserving part of do-/dq2[xe, which is given by the square of the one photon exchange contribution, and the helicity dependent dominant part which is determined by the interference between the electromagnetic and neutral current parity-violating contributions. A straightforward calculation gives dd~

+do-= + dq 2

do do" ~q2 +--~q2_ =

4rr 1 ce2. We.m.(S, q2) ' (s-m~)22/'1+l q

"f2 1 af.s.G (s_m21)z2]]+l q2 We..... (s, q2),

(17a)

(17b)

w h e r e oLf.s, is the fine structure constant. The We.re. function, defined as in eq. (9),

receives contributions only from the e.m. currents and therefore W3(q 2) vanishes identically. The function We ..... originates from the interference of e.m. and weak currents and the corresponding structure functions receive contributions from the

NEUTRAL CURRENT PROCESSES

371

vector h a d r o n i c neutral current for W1 and W2 and f r o m the axial hadronic neutral current for W3. As a c o n s e q u e n c e only o n e of the two t e r m s a p p e a r i n g in the expressions for Wl(q 2) and Wa(q 2) given in eq. (5) will remain. For the case of elastic scattering f r o m a 0 + nuclear state only the vector f o r m factor Am)(q 2) contributes. This a p p e a r s in the structure function W2(q 2) for W e . r a and We ...... which contain b o t h isoscalar and isovector pieces with different couplings. In the interesting case of an isoscalar transition the vector neutral current coincides, up to a factor ~, with the isoscalar e.m. one and hence ,awA(°)~q2")=oy, a~m.~q"---m) , 2,). O n e r e p r o d u c e s i m m e d i a t e l y F e i n b e r g ' s result H) G 23. R ( q 2) = 2~.af~.x/2(-q ) y.

(18)

T h e origin of the factor 3 in the w e a k - e . m , connection c o m e s f r o m the use of an isoscalar quark coupling. 5. T h e 1 ÷ t r a n s i t i o n s

In this section we would like to specify our general f o r m u l a e to transitions with spin-parity 1 ÷ q u a n t u m n u m b e r s , b e c a u s e they allow us to give closed results for 0 ÷ ~ 1 + processes which are particularly interesting experimentally. In this case the only n o n - z e r o f o r m factors are F (I'1),

vector,

F (°'I),

A ('),

F ~2'I),

axial,

(19)

and therefore A l(q 2) =

~/~[F""" + ,/½F'2"],

Bl(q 2) = ~/~F ('''t, Cl(q 2) = A ~'1,

(20)

Da(q 2) = __ x/31--[F
F2.1, (q2) = [ /3 ;o7 , ' /F(1,1 . . . . (q2),

for A T = {10}.

(21)

T h e structure function W3(q2) only contains the cross t e r m B .... Aw, so that the function R (s, q2) has all nuclear structure information contained in st(q2)

Al(q2) ----~-V3

,/-2F'°'l)+~/~F(2.1) ~

.

(22)

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J. BERNABEU AND P. PASCUAL

Explicitely we find

R(Ee, q2) = G ( - q 2) { g~ } [ ¢~ ] 2(E~ Ee)lql ~, 2,-1 2~a~.. ~/2 3") -'13g~(E~+E'~)2+lq[ 2~tq )J ~

+

'

(23)

where Ee(E'e = Ee- A) is the incoming (outgoing) electron energy in the laboratory system. The kinematical factor present in the second term has been obtained by neglecting the electron energy as compared to the nuclear mass. It is 1 in the backward direction and of the order of 1 at other angles. Since ((q2) behaves as [ql-lMp, one expects an important enhancement of the second term at low values of [q]. Detailed results for some specific cases will be given below. We turn now our attention to inelastic neutrino scattering. We would like to discuss an approximation valid for these 1 ÷ transitions which works extraordinarily well. Eq. (5) for W2(q 2) shows that the D~ contribution is only important for low values of ( _ q 2 ) where D~ ~ - A 1 as seen in eq. (20). This implies

Wz(qe)~A~

2 A 2q_ q 2 B 2 + C 2 + 2 4 U A q~CIA1.

(24)

In practice the third and fourth terms are always negligible whereas the second term is negligible at low (_q2) and given by ~ +B~ at higher (_q2). The final relation is thus W2(q 2) ~ Wl(q 2)

(25)

in all cases for which a non-vanishing dominant axial contribution A1z exists. This allows us to present a closed form expression in terms of Al(q 2) and Bl(q2), i.e. the same combinations present in the electron scattering observable (22). The differential cross section is given by do" G(E'~,) 2 l + s i n 2 ~10 F(O1)~ _~q 2,,2 ) /32 d-~ v - 8 ~ r ~ 1) 3 × 1

4(E~+E'~) sin2½0 1 a 1 ce2~ Iq[ 1+sin210~r(q2)/3 ~ ( ( q 2 ) 2 ~ j ,

(26)

for the case of a pure isovector transition. For the isoscalar case, one must replace a by 3 y and fl by 3& It is apparent that the neutrino cross section is mainly sensitive to 2

In order to obtain the total strength of the transition a knowledge of the q dependence of the nuclear form factor is necessary. It will be discussed below for some explicit examples. In particular; for energies low enough one reproduces easily eq. (12).

NEUTRAL CURRENT PROCESSES

373

6. Examples 6.1. THE TRANSITION ~2C(0*; T=0)~12C*(1+, 15.11 MeV; T= 1) A recent determination of the nuclear form factors for this transition using experimental information from the e.m. decay, electron scattering,/3-decay rate and asymmetries gives 17)

F"~'l)(q 2 = 0) = - 1.75 M,

GCl"l~(q2 = 0) = 33.3 M,

(27)

where F (°'1) is the weighted average of the two charged weak branches and F(l'l~(q 2) = ([q]/M)G(~'l)(q=). Notice that our form factors differ by a factor ~/2 from the ones given in ref. 17). The q2 dependence of the G(l'l)(q 2) form factor has been extracted from Chertok et al. 18) and we have used the parametrization given in their eq. ( l l c ) . In ref. 17) the suggestion is made of using the same q2 dependence for A l ( q 2) than for G(l'l)(q2). This implies that the function ~.(q2) is simply given by

.i/2 M 0(0'1'(0) ;(q2) = V 3 ~ ~

"

(28)

Numerical integration of eq. (26) with this input gives the cross section plotted in fig. 1 1. The standard theory with sin 2 0w = z would give the results corresponding to/? = 1, c¢ =1. They are similar to the results found by other authors 3) in the impulse approximation framework. The low energy limit given in eq. (12) corresponds to the broken line. The high energy plateau is very sensitive to the mean square transition radius. F r o m eq. (26) and considering the small contribution of the last term, for typical values of a/13, one sees that the antineutrino cross section can be obtained by subtracting from the curve ~//3 = 0 what has been added to it to obtain the neutrino cross section. For the polarized electron process we plot in fig. 2 the results of R (Ee, q2) for the experimentally interesting case of backward scattering. For the most interesting region of energies, around 100 M e V where the cross section is still large, the parity-violating effects are of the order of few 10 -s and they are not very sensitive to the value of dfffi. The second term in eq. (23) gives an effective linear Ee dependence for R(Ee, cos = - 1 ) , whereas the first term would originate a quadratic dependence. This behavior is apparent in fig. 2. 6.2. THE TRANSITION 6Li(1 +, T = 0)~ 6Li*(0 ÷, 3.56 MeV; T = 1) Using the e.m. decay width of the excited state 19) as well as the frl/2 value of the analogue ground state of 6He we obtain F(°'l)(q2 = 0) = - 3.93 M,

G(1"11(q2=O)=40.2M.

(29)

The q2 dependence of G(l'l)(q 2) used here is the one given by H u t c h e o n etal. 20). The results obtained are similar to the ones calculated using the set A of Bergstrom et

374

J. BERNABEU AND P. PASCUAL Ct" 1041cm2/2

1

LJ

±

L

I00

200

3O0

E (MeV)

Fig. 1. Neutrino induced cross section for the transition to 12C(1+; 15.11 MeV), as a function of the incident energy. Results are given (full lines) for a ratio a/fl of isovector vector and axial couplings equal to 0 and ½. The broken line indicates the low energy limit.

al. 21) T h e i n t e g r a t i o n of eq. (26) gives t h e results p l o t t e d in fig. 3 for the n e u t r i n o cross section. T h e y a r e s i m i l a r to the o n e s o b t a i n e d in t h e i m p u l s e a p p r o x i m a t i o n b y o t h e r a u t h o r s 3). T h e low e n e r g y limit is given by t h e b r o k e n line a n d it is a g o o d a p p r o x i m a t i o n u p to e n e r g i e s of 40 M e V . F o r the e l e c t r o n s c a t t e r i n g p o l a r i z a t i o n a s y m m e t r y at b a c k w a r d angles w e give in fig. 4 t h e results as f u n c t i o n of t h e e n e r g y . A s b e f o r e , o n e r e a l i z e s that for e n e r g i e s of a b o u t 100 M e V , R(Ee, cos = - 1) is m a i n l y sensitive to/~. A t h i g h e r e n e r g i e s , the q u a d r a t i c Ee d e p e n d e n c e of t h e t e r m with ~ is n o t i c e a b l e . 6.3. THE TRANSITION 7Li(3-; T = ½)-~7Li*(½ , 0.478 MeV; T = ~) T h e t r a n s i t i o n is p a r t i c u l a r l y f a v o r a b l e for n e u t r i n o r e a c t o r e x p e r i m e n t s . W e a r e going to discuss it in t h e low e n e r g y limit. T h e p r e s e n c e of b o t h i s o v e c t o r a n d isoscalar t r a n s i t i o n f o r m factors allows us to w r i t e eq. (11) in t h e f o l l o w i n g f o r m : o.(E,,) = ½7r2 I n 2

~2t i

36 /_~

F~s°'1)'2 ET. p~7"-"

(30)

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NEUTRAL CURRENT PROCESSES R 105/~"

F;Z

5

~2 12 C .~o,C ( I+~15.11)

l Io0

l 200

L 300 Ee(MeV)

Fig. 2. Polarization assymmetry for longitudinally polarized electron scattering to the azC(l+; 15.11 MeV) level. Results are given for a ratio d/j9 of isovector vector and axial effective couplings equal to 0 and ½.

In the standard W - S - G I M neutral current theory /3 = 1 and 6 = 0, so that the neutrino cross section would be fixed by the fr]/2 value 19) of electron capture from 7Be(3-; T = ½) to the excited 7Li* considered. We have seen that the transitions discussed above for 12C and 6Li are mainly sensitive to/3 and, to much lesser extent, a. Eq. (30) shows that this transition in 7Li would be a very clean test of the absence (or presence) of an axial isoscalar c o m p o n e n t in the neutral current sector. The isolation of this c o m p o n e n t has been suggested from parity violating electron scattering 13) to isoscalar levels or form neutrino induced reactions 3) to these isoscalar levels, such as the one present i n ZZc*(I+, 12.71 MeV; T = 0). However, this ]2C level does not decay by y-emission but strongly and for the neutrino experiment, where a very large target is planned, these facts constitute a very strong drawback 5). It seems better to use the transition in 7Li to look for the presence of the axial isoscalar piece of the neutral current. The calculation of the cross section has been made by Donnelly and Peccei 4). We present here an independent estimate of eq. (30) in order to show the relative importance of the isovector and isoscalar contributions.

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J. B E R N A B I ~ U A N D P. P A S C U A L n-l04 cmZ//~ SLi

6 L i

~ ( 0"¢'i 3 . 5 6 )

I I I I

6 --

I

l I

5--

p 2

~-~-=0

P

IO0

200

500 E (MeV) • •

o

.

+

Fig. 3. As fig. 1, but for the neutrino induced translhon to LI(0 ; 3.56 MeV). 1U.(0,1)/L~(0,1)

We are going to control the ratio i s /1 v in eq. (30) by using a connection of the weak form factors with the electromagnetic ones. Under the well known fact that the isovector magnetic dipole transitions are dominated by spin current one has, in the impulse approximation, F(O,i)

- - ~ F(v°,1)

/.tp - I-t n

g O G(1,1,

(31) /d.p -1-/.in -- ~ g A

where/z is the total magnetic m o m e n t of the nucleon, g a is the axial coupling of the nucleon and G (1"1) is the nuclear electromagnetic form factor for the transition of interest. The isoscalar Gs and isovector G v form factors, including their relative sign, can be determined from the electromagnetic decay widths 19) of the excited levels of 7Li and 7Be. Using Iavl > IGsl, we obtain G s(1'1)

F s( ° m

/qA\°

G~,I ) - - 0.0403 -->F v ' ~ ~

\gA/

(32) "

The prediction at low energies for the neutrino cross section of the 7Li transition is thus t2

/~v ~2 o'(E~) = 0.84 x 10 -44 cm 2M---~/J

[6 = 0],

(33)

NEUTRAL CURRENT PROCESSES

377

RI051~

21~

eli~6Li'l' 0+~3.56)

[ I00

[ 200

I 300 Ee(MeV)

Fig. 4. As fig. 2, but for the polarization asymmetry in the 6Li transition to 6Li(0+; 3.56 MeV).

for the case of absence of an axial isoscalar piece, as in the standard W - S - G I M theory. If ~ ~ 0, there is a modification to eq. (33) given by 1

3 ~, +0.87 1 /-5 g g l 0,2

We conclude that the presence of an axial isoscalar neutral current (3 # O) would have noticeable effects in the neutrino cross section for the transition in 7Li. We are indebted to J. Duclos, E. Fiorini and R. Peccei for stimulating discussions about the topics discussed in this work.

References 1) R.M. Barnett, Invited talk presented at the Int. Conf. on neutrino physics-neutrinos 1978, Lafayette, I N.-SLAC-PUB-2131 (1978)

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J. BERNABI~U AND P. PASCUAL

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