带有任意自旋粒子衰变产物的角分布

本文研究了具有任意自旋的粒子衰变为一个自旋为零,另一个自旋为1/2的粒子的角分布。给出了球谐函数展开式系数的表式。发现偶次球谐函数项的系数是和引起衰变的相互作用哈密顿量具体形式无关的。但是在球谐函数展开式的奇次项的系数却和一个参变数α有关,而α的值却反映了宇称守恒的相互作用和宇称不守恒的相互作用之间干涉作用的大小。我们给出了这些系数的极大值,发现凡是偶次项系数的极大值是随着衰变粒子自旋的增加而增加的,而奇次项系数的极大值却随着衰变粒子自旋的增加而减小。本文还给出了衰变着的粒子的密度矩阵作为展开式的系数的函数的表式。当这些展开式系数已经知道以后,用这些函数就能决定衰变前的粒子的极化状态,决定宇称守恒相互作用和宇称不守恒相互作用之间的干涉的程度。

ON THE ANGULAR DISTRIBUTION OF THE DECAY PRODUCTS OF PARTICLE OF ARBITRARY SPIN

The angular distribution of the decay products of particle of arbitrary spin decaying into a particle of spin zero and a particle of spin 1/2 is investigated. The expressions for the expansion coefficients are derived. It is found that coeffieients of terms of even order spherical harmonics are independent of the detailed form of the interaction Hamiltonian inducing the decay process. But the expansion coefficients of terms of odd order spherical harmonics depend on a parameter α, which is a measure of the interference between the parity conserving and the parity nonconserving interaction. The maximum values which can be taken by the various coefficients are given. It is found that the maximum values of the even coefficients increase with the value of the spin of the initial particle, while those of the odd coefficients decrease correspondingly. The expression for the density matrix of the initial particle as a function of these expansion coefficients is also given which can be used to determine the state of polarization of the initial particle and the interference between the parity conserving and parity nonconserving interactions, when the expansion coefficients are known.