Science Record

32

express the effect of eliminated fields by equivalent direct interactions between hyperons, nucleons and x-mesons. ‘These equivalent interactions, usually of the non-local type, may depend on the higher derivatives of the field quan‘tities. As a first step, let us examine the simplest direct equivalent interaction which does not depend on the derivatives of the field quantities.

It is assumed that the interaction Hamiltonian which leads to the decay process

My pt + x7 , (3) is of the following form: HP = ghp(Ei + ¥s)Pa-@ + ghar — 75) 09", (4)

where ¢a, ¢ and @ represent the field operators of A, p and 7 respectively. It is assumed here that the A particle is a spin 4 particle and obeys the Dirac equation. g and &, are real numbers. If we are not interested in the spin of the proton in the final state, then we obtain the following matrix which determines the angular distribution of protons:

0,=1+ 4,62), 6)

where @ is the Pauli matrices, @ the unit vector in the direction of the - momentum of the proton and @, the asymmetry parametre,

ee : nea Dee. ©

where m represents the mass of the proton, E, the energy of the proton and p the absolute value of the momentum of the proton. If @ is to be made equal to 1, then the value of & must be taken equal to 0.05. Thus the coupling constant of the parity non-conserving term must be very much smaller than that of the parity conserving term, if it is assumed that the A particle and the nucleon are of the same parity.

We assume next that the interaction Hamiltonian density contains the first derivative of the m-meson field quantity, ie.,

= Diy eee ep ee

HP = bey u(E + Ys)a-S aX.

“

Doa(Es + ¥s)brPut(Er + ¥5) 05 (7)

| we

where », represents the unit vector in the direction of the normal of the space-like curved surface. From the Hamiltonian HY, we obtain the following matrix which determines the angular distribution: