P-VIOLATING

EFFECTS

IN THE POLARIZATION

OF THE y + D § N + P REACTION

PHEN0~NA

NEAR THE THRESHOLD

14. P. Rekalo

UDC 539.12

Since at the threshold the P-odd amplitude of deuteron photodisintegration (T + D + P + N) is determined by three independent multipole amplitudes (describing the E1 iSo, E1 § 3SI, and M2 § 3SI transitions), at least three different experiments on measuring the P-odd polarization characteristics of the Y + D § P + N process are needed (provided that P-odd threshold amplitudes are known) in order to determine the multipole amplitudes. A P-odd dependence of the threshold cross section on the polarizations of the colliding y-quantum and deuteron is established and P-odd contributions to the polarization vector of protons formed in the Y + D § P + N process are found. The P-odd characteristics are calculated in terms of P-even and P-odd threshold amplitudes. The importance of investigating P-odd effects in deuteron photodisintegration (T + D § N + P) and radiation neutron capture (N + P + D + y) was remarked more than 20 years ago [i, 2]. The result of measurement of P-odd circular polarization of the T-quantum in the N + P § D + T reaction [3] has hitherto not been explained theoretically [4]. The experimental estimate [5] of the P-odd asymmetry of the angular distribution of y-quanta in N + P § D + Y, formed during the capture of longitudinally polarized neutrons, is not at variance with the theoretical calculations. Recently discussions have been conducted [6] on the possibility of measuring the P-odd dependence of the Y + D § N + P cross section (near the threshold) on the circular polarization of the photons. In this paper we analyze the P-odd polarization effects in the Y + D § N + P reaction near the threshold, where the spin structure of the P-even and P-odd parts of the amplitude is particularly simple. The analysis is carried out in terms of the threshold multipole amplitudes, derived phenomenologically. We do not try to calculate these amplitudes; instead, our task is to ascertain what combinations of amplitudes determine the different P-odd characteristics of y + D + + N + P near the threshold. Besides P-odd asymmetries in Y + D * N + P, caused by the polarizations of the colliding particles, we also consider the P-odd contributions to the polarization of the protons as a function of the vector and tensor polarization of the deuteron target. This analysis makes it possible to point out the experiments in which all the P-odd threshold amplitudes can be determined. The P-odd contribution to the differential cross section of the y + D + N + P process from the polarizations of the colliding particles (summation is carried out over the nucleons formed) can be written as do/d~ = PijHij, where Pij is the y-ray density matrix, which depends on the Stokes parameters as follows [7]:

1 . (~) r~) -F el~)e~?)) + ~ [e(1)er2) -~ ~2)~(1)~

~ i,j~)j2)

~(2)~m~

+ ~ (ell)e~l) - - e_(2) i ej~).), where ~i are the Stokes parameters and e (I) and e (2) are mutually orthogonal (unit) vectors which are orthogonal to the photon three-momentum k. The hadron tensor Hi4 is determined by the product of the P-even and P-odd parts of the electromagnetic current o~ the process

~+D-~

N-~-P,

[-]ij=JiJ~-~-JiY~, where

the bar denotes

summing

over the polarizations

of the

Physicotechnical Institute, Academy of Sciences of the Ukrainian SSR, Kharkov. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 80-83, December, 1983. Original article submitted March 23, 1983.

0038-5697/83/2612-1139507.50

9 1984 Plenum Publishing

Corporation

1139

nucleons.

The P-odd hadron tensor H i j

can be written as a sum Hij + H~j) +(o

HI~ d)'~ + H~_~),~'~ where

the superscript (0) corresponds to a polarized deuteron and the superscripts (i) and (2) correspond to the absorption of a y-quantum by a deuteron with vector and tensor polarizations. For the individual contributions to Hij we can write the following general expressions, which are valid near the threshold of the y + D § N + P reaction: A

~4qq)

A

[sift tClX1 ; ~~(i) 9 i j =.~. lcgO.x.); A A A A A H(~) , , i j = [S[jltCl (Sabl~atCo) X3 -7 [SijoSubl('oX4 -?- i ($iartztCmSja A ' A

-

A , EjamtCmSia ) X 5 =

-

(i)

where x i are real constants, ~ is the polarization three-vector, Sab is the quadrupole polarization tensor of the deuteron in its rest system (sao==sba, Saa=O) , and ~ ~/]K] . It must be pointed out that x6 # 0 only for complex multipole amplitudes (near the threshold), i.e., (if saa = O) only when T-invariance is violated. By virtue of sia,n~mS]a -- s]om~mSia ~ -- si]asa,n~ m two structures in H{~) are independent (for x3 and x4); when transverse y-quanta are absorbed these structures l e ~ to one P-odd asymmetry, viz , ~%~Szz(Xs+X4 xs) (z axis along k). It is seen from Eq. (i) that only three P-odd asymmetries survive at the threshold of the y + D § N + P reaction: a) when circularly polarized y-quanta are absorbed by an unpolarized deuteron target (constant xl); b) when unpolarized y-quanta are absorbed by a target whose polarization vector is directed along k (constant x2); c) when circularly polarized y-quanta are absorbed by a target with tensor polarization Sabkak b # 0 (combination x3 + x4 -- xs). The tensor Pi.d~/dg, which (after convolution with Oi~ ) determines the dependence of the o proton polarizatio~ vector in y + D § N + P on the polarization characteristics of the initial y-quantum, has the structure Pijdo/d~ = 6ijkx7 at the threshold, i.e., at the threshold the longitudinal proton polarization is P-odd an unpolarized target).

(in this case unpolarized y-quanta are absorbed by

And, finally, the polarization of protons formed in the collision of unpolarized y-quanta with a polarized deuteron target can be represented as -

d~

A

A

A

A

A

P" dO. = g=xs + i (~ X ~)mXO+ ~m (Sa~aK~) Xi0 q- SmagaX11.

(2)

C l e a r l y , x7 = x8 a n d x9 = 0 (by v i r t u e o f t h e r e a l n e s s o f t h r e s h o l d m u l t i p o l e a m p l i t u d e s ) . From Eq. (2) i t f o l l o w s t h a t a l o n g i t u d i n a l P-odd polarization o f t h e p r o t o n s p r o d u c e d can arise both in the coll• of unpolar• p r o t o n s and i n t h e a b s o r p t i o n o f u n p o l a r i z e d y quanta by a deuteron target with quadrupole polarization, s u c h t h a t Szz ~ 0. The c o m p o n e n t s Px a n d Py a r e due t o . q u a d r u p o l e

polarization

such that

Sxz # 0 o r Sy z ~ 0.

I t must b e e m p h a s i z e d t h a t a t t h e t h r e s h o l d t h e q u a n t i t i e s xi are constants determined b y t h e p r o d u c t o f t h e t h r e s h o l d P - o d d and P - e v e n a m p l i t u d e s . From t h e c o n s e r v a t i o n o f a n g u l a r momentum i t f o l l o w s t h a t t h e P - e v e n a m p l i t u d e o f t h e y + D § N + P p r o c e s s a t t h e t h r e s h old is characterized by t h r e e m u l t i p o l e a m p l i t u d e s : Two o f them d e s c r i b e t h e a b s o r p t i o n o f a m a g n e t i c - d i p o l e y - q u a n t u m w i t h t h e f o r m a t i o n o f a s i n g l e t and a t r i p l e t s t a t e o f t h e NP s y s tem w h i l e a n o t h e r m u l t i p o l e a m p l i t u d e s p e c i f i e s t h e a b s o r p t i o n o f an e l e c t r i c - q u a d r u p o l e yquantum w i t h t h e f o r m a t i o n o f a t r i p l e NP s t a t e . The t h r e s h o l d P - e v e n a m p l i t u d e o f t h e y + D § N + P process can thus be written as A

A~

A

F = ig~X~x2e.U X u + g2e. U Z ~ ' ~ Z 2 + g ~ U . ~ z ~ , ez~,

(3)

w h e r e oaX2, X t , 2 X t , 2 a r e t w o - c o m p o n e n t s p i n o r s o f n u c l e o n s i n y + D § N + P, e ( O ) i s t h e polarization three-vector o f t h e y - q u a n t u m ( d e u t e r o n ) , and U • the axial vector, since the spatial parity of the deuteron is positive. The a m p l i t u d e g~ d e s c r i b e s t h e t h r e s h o l d M1 § XSo t r a n s i t i o n , t h e d i f f e r e n c e g2 -- g~ d e s c r i b e s t h e M1 + 3S~ t r a n s i t i o n , w h i l e t h e sum g2 + g3 d e s c r i b e s t h e E2 § 3S~ t r a n s i t i o n .

1140

The threshold P-odd amplitude F is also determined by three multipole amplitudes: Two describe the absorption of an electric-dipole y-quantum with the formation of a single and a triplet state of the NP system (El § iSo and E1 § 3SI) and the third multipole amplitude describes the absorption of a magnetic quadrupole y-quantum with the formation of a triplet state (M2 § 3S~). As a result, we can write the amplitude F as .

.

.

.

A~

A

= g~x~z2e. U + i g 2 z ~ . e X U ~ + i g 3 z ~ . e X gz2U .~, %

%

(4)

%

where gl, g2, and g3 are the amplitudes of the E1 § iSo, E1 § 3SI, and M2 § 3Sl transitions, respectively. Using Eqs.

(3) and (4), we can get the following expressions for the coefficients xi:

x~

- ~ ( g , g , + g ~ g , - - g393 - - g 3 g J ; x , ---- - - 4 g ~ g ~ ;

x., = 2 ( g , g ,

'

- - g~g~);

x~ = - - 2 ( g , g l + g2g', + 2g3g=,), 4-

.

.

.

.

X 7 ---- x~ = - ~ (g~g2 + g..,g, + g~g2 + gag:~);

9,o = 4 I(~, + g~)~, + (g., + g j ( - Z;, + ~._,+ x,, : ~ / [ - (g, + g~)(g~ + }~) + g~ (g,

~,)];

+ ~)].

From this we see that the seven different experiments considered above for the measurement of P-odd characteristics of the y + D § N + P process at the threshold (determined by the quantities x i) present many possibilities for indicating those independent measurements which make it possible to establish all three P-odd threshold amplitudes (if the P-odd amplitudes are known). We point out that the P-odd asymmetries are linked by one relation 4xi -- x3 = 2x2, irrespective of the value of the P-even and P-odd amplitudes. The search for the correlations of x6 and x9 could serve as a verification of T-invariance. The large selection of P-odd experiments is due to the richness of the spin structure of the y § D § N + P process at the threshold. LITERATURE i. 2. 3. 4. 5. 6. 7.

CITED

R. J. Blin-Stoyle, Phys. Rev., 120, 181 (1960). R. J. Blin-Stoyle and F. Feschbach, Nucl. Phys., 27, 395 (1961). V. H. Lobashov, D. M. Kaminker, G. I. Kharkevich, et al., Nucl. Phys., 197, 241 (1972)o B. Desplangues, Nucl. Phys., A335, 147 (1980). J. F. Cavaignac and R. Vignon, Phys. Lett., 67B, 148 (1977). H. Co Lee, Phys. Rev. Lett., 41, 843 (1978). V. V. Berestetskii, E. M. Lifshits, and L. P. Pitaevskii, Relativistic Quantum Theory [in Russian], Part I, Nauka, Moscow (1968), pp~ 39-45.

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