$${T}$$-Invariance Conditions for Differential Cross Sections for Binary Nuclear Reactions Involving Spin-Oriented Particles and Nuclei

Abstract

By employing the $$T$$ -invariance condition for the amplitudes describing arbitrary binary nuclear reactions that involve spin-oriented particles and the respective time-reversed reactions, a relation between the differential cross sections for these reactions is obtained for the first time. These cross sections are determined with the aid of sets of potentials simulating the interaction between particles of the initial and final reaction channels and not including any of spin–orbit interactions. The resulting relation covers the case corresponding to the implementation of the previously known detailed-balance principle. This relation is used to derive equalities between the components appearing in the cross sections under analysis via a unified mechanism and possessing identical $$P$$ and $$T$$ parities. These equalities make it possible to prove the existence of a number of components in the cross section that vanish upon taking into account $$T$$ invariance, and this opens new possibilities in studying $$T$$ -noninvariant interactions in nuclear reactions.