$${T}$$ -Invariance Conditions for Differential Cross Sections for Binary Nuclear Reactions Involving Spin-Oriented Part
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CLEI Theory
T -Invariance Conditions for Differential Cross Sections for Binary Nuclear Reactions Involving Spin-Oriented Particles and Nuclei S. G. Kadmensky1)* , P. V. Kostryukov1), and D. E. Lyubashevsky1) Received December 25, 2019; revised December 25, 2019; accepted December 25, 2019
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. DOI: 10.1134/S1063778820040134
1. INTRODUCTION An analysis of the effect of time-reversal invariance (T invariance) of quantum systems [1–5] on the behavior of such systems is one of the pressing tasks with which nuclear physics has to deal. Of particular interest is the problem of taking into account such an effect on the relation between the differential cross section dσβ,α /dΩkβ for the α → β binary nuclear reaction and the differential cross section dσα, ¯α ¯ β¯/dΩk for the β¯ → α ¯ reaction, where α ¯ and β¯ are the timereversed states of the particles in, respectively, the initial, α, and the final, β, channel of the original reaction. Further, the initial and final channels of the α → β reaction involve components oriented in the spins of pairs formed by particles a and A and by particles b and B (they may include various atomic nuclei and elementary particles). Unfortunately, only in two relatively simple cases was this effect taken into account. By employing the T -invariance conditions for the amplitudes describing the reactions in question, it was shown in [5–8] that the differential cross sections dσβ,α /dΩkβ and dσα, ¯ α are in di¯ β¯/dΩk rect proportion to each other in the case of fully spinunoriented particles in the α initial channel of the α → β original reaction and in the β¯ initial channel of the β¯ → α ¯ time-reversed reaction. This proportionality of the above cross sections reflects the detailed-balance principle well known in nuclear-reaction physics [5]. 1) *
Voronezh State University, Voronezh, Russia. E-mail: [email protected]
Finally, the S-matrix theory of nuclear reactions [2– 5, 9, 10] was used in [11, 12] to show, with the aid of the T -invariance condition f
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