*International Journal of Physics*.

**2014**, 2(2), 41-75

DOI: 10.12691/ijp-2-2-4

### On Mathematical Foundations of Quantum Collisions and Nuclear Reactions and Outcome of Certain Physical Phenomena from Them

**V.S. Olkhovsky**^{1, }

^{1}Institute for Nuclear Research of NASU, prospekt Nauki, Kiev, Ukraine

**Cite this paper:**

V.S. Olkhovsky. On Mathematical Foundations of Quantum Collisions and Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. *International Journal of Physics*. 2014; 2(2):41-75. doi: 10.12691/ijp-2-2-4

### Abstract

I. Analytical structure of the non-relativistic unitary and non-unitary*S*-matrix is reviewed for the cases of any interactions with any motion equations inside a sphere of radius

*a*, enclosed by centrifugal and rapidly decreasing (exponentially or by the Yukawian law or by the more rapidly decreasing) potentials. Some kinds of the symmetry conditions are imposed. The Schroedinger equation for the particle motion in the external region where

*r > a*and the completeness of the correspondent wave functions are assumed. The connection of the obtained results with the causality is examined. Partially some analytical properties for the multi-channel

*S*-matrix are reviewed and the sum rules for mean compound-nucleus time delays and the density of compound-nucleus levels. Sometimes (as physical manifestations of the profound general methodic and in very good consistent accordance with the experiment) observable physical effects, such as parity violation enhancement and time resonances or explosions, are appeared. Finally a scientific program of future search is presented as a clear continuation and extension of the obtained results. II. It is already known the appearance of time advance (due to distortion by the non-resonant background) instead of the expected time delay in the region of a compound-nucleus resonance in the center-of-mass (C-) system. Here at the same conditions we study cross sections and durations of the neutron-nucleus scattering in the laboratory (L-) system. Here it is shown that such time advance is a virtual paradox but in the L-system the time-advance phenomenon does not occur and only the trivial time delay is observed. At the same time the transformations from C-system into the L-system appeared to be different from the standard kinematical transformations because in the C-system the motion of a compound nucleus is absent but it is present in the L-system. We analyze the initial wave-packet motion (after the collision origin) and the cross section in the laboratory (L-) system. Also here (as physical revelations of profound general methodic and in very good consistent accordance with the experiment) several results of the calculated cross sections for the neutron-nucleus in comparison with the experimental data in the L-system at the range of one or two overlapped compound resonances are presented. It is shown in the space-time approach that the standard kinematical transformations of cross sections from the C-system to the L-system are not valid because it is necessary to consider the center-of-mass motion in the L-system. Finally on a correct self-consistent base of the space-time description of the nuclear processes in the laboratory system with 3 particles in the final channel, it is shown the validity of the former approach, obtained for the space-time description of the nuclear processes with 2-particle channels earlier.

**Keywords:**(I) S-matrix condition of completeness of external wave functions external centrifugal and rapidly decreasing potentials causality time resonances or explosions parity violation enhancement; (II) space-time approach to nuclear collision time delay time advance transformations of cross sections from the C-system to the L-system interference phenomena

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