Angular correlation of radiations with parallel angular momenta

Abstract

The discovery (1) cf par i ty non-conservat ion in the dis integrat ion of ~°Co has a t t r ac ted a t ten t ion to the chain of emission processes which s tar ts f rom 6'~Co wi th spin j'o 5 and yields: 6~Ni with j l = 0 , an electron with Je---~-, a neutr ino wi th j~=1⁄2, and two y-rays wi th i v = 2 , so t h a t ja:jl--je-~-j,~-2]V. Such a chain of emission processes, wi th (~ paral lel angular momen ta ~), is by no means unusual because radiat ion emission wi th least angular m o m e n t u m is general ly favored by selection rules. In this special but in teres t ing case, the theory of angular correlat ion and dis t r ibut ion of radiat ion simplifies considerably, as not iced by Cox and ToLnoEx (~). The simplification m a y be expressed as a theorem which is a lmost obvious when s ta ted in terms of the vector model. Consider the angular correlat ion be tween two radiat ions emi t t ed with angular momen ta j~ and j2 anywhere along a chain of emission processes. The quan tum number J corresponding to the resul tant J = j ~ d-jo. has a single possible value, namely J=]~+]2, if j~ and j2 are ~ parallel i>. Under th is condit ion, the angular correlat ion depends on the quan tum numbers ix, J2, and J , and on no other angular momen tum. One may then calculate the correlat ions as though there were only an unor iented part ic le wi th spin J which dis integrates into two radiat ions and leaves no residue. The correlat ion be tween the or ienta t ion of the ini t ial nuclear spin Ja and any successive radia t ion wi th angular m o m e n t u m j~ d e , ends similarly on ]~, J'l and on J = []a -Jl [, as though the radia t ion were emi t t ed direct ly by the nucleus in its ini t ial s tate, leaving i t wi th a residual spin J = j ~ j 1 . The actual order of emissions is immater ia l , p rovided only tha t the paral lel ism of angular m o m e n t a fixes the value of the quan tum number J unambiguously . These s ta tements are proved, when the theory is formula ted in te rms of Racah