Angle-angular-momentum entropic bounds and optimal entropies for quantum scattering of spinless particles

In this paper the angle-angular-momentum entropic lower and upper bounds are proved by using Tsallis-like entropies, the Riesz theorem, and the Lagrange multiplier method for the quantum scattering of the spinless particles. A connection between optimal states and the most stringent entropic bounds on Tsallis-like entropies in the quantum scattering is established. The results of experimental tests of the state-independent angle-angular-momentum entropic bounds as well as of the stringent entropic optimal bounds in pion-nucleus scattering are obtained by calculations of the scattering entropies from the experimental available pion-nucleus phase shifts. Comparisons of these results with predictions of the principle of minimum distance in the space of states are presented. Then it is shown that experimental pion-nucleus entropies are well described by optimal entropies, and that the experimental data are consistent with the principle of minimum distance in the space of scattering states.