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

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.