Polarization effects in the reactions $ p + \,^{3}{He} \rightarrow \pi^{+} + \,^{4}{He}$, $\pi^{+} + \,^{4}{He} \rightarrow p + \,^{3}{He}$ and quantum character of spin correlations in the final $(p,\,^{3}{He})$ system

Lyuboshitz, Valery V.; Lyuboshitz, Vladimir Lvovich

doi:10.22323/1.314.0743

Abstract

The general consequences of

$T$ invariance for
the direct
and inverse binary reactions

$a + b \rightarrow c + d$ ,

$c + d \rightarrow a + b$ with spin-1/2 particles

$a$ ,

$b$
and unpolarized particles

$c$ ,

$d$ are considered.
Using the formalism of helicity amplitudes, the polarization
effects are studied in the reaction

$p + \,^{3}{He} \rightarrow \pi^{+} + \,^{4}{He}$ and in the inverse process

$\pi^{+} + \,^{4}{He}\rightarrow p + \,^{3}{He}$ . It is shown
that in the reaction

$\pi^{+} + \,^{4}{He} \rightarrow p + \,^{3}{He}$ the spins of the final proton and

$^{3}{He}$ nucleus are strongly correlated. A structural expression
through helicity amplitudes, corresponding to arbitrary emission
angles, is obtained for the correlation tensor. It is established
that in the reaction

$\pi^{+} + \,^{4}{He} \rightarrow p + \,^{3}{He}$ one of the "classical" incoherence inequalities of the
Bell type for diagonal components of the correlation tensor is
necessarily violated.