American Journal of Applied Mathematics and Statistics
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American Journal of Applied Mathematics and Statistics. 2015, 3(3), 111-130
DOI: 10.12691/ajams-3-3-5
Open AccessReview Article

On Theoretical Methodology of Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. I. What Follows from the Analytical Properties of the One-channel and the Multichannel S-matrix?

V.S. Olkhovsky1,

1Institute for Nuclear Research of NASU, prospekt Nauki, 47, Kiev-03028, Ukraine

Pub. Date: June 29, 2015

Cite this paper:
V.S. Olkhovsky. On Theoretical Methodology of Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. I. What Follows from the Analytical Properties of the One-channel and the Multichannel S-matrix?. American Journal of Applied Mathematics and Statistics. 2015; 3(3):111-130. doi: 10.12691/ajams-3-3-5


Analytical structure of the non-relativistic unitary and non-unitary S-matrix are investigated for he cases of any interactions with any motion equations inside a sphere of radius a, enclosed by the 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 r > a for the particle motion and the condition of 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 investigated and the sum rules for mean compound-nucleus time delays and the density of compound-nucleus levels. Sometimes (as physical revelations of 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 manifested. Finally a scientific program of future search is presented as a clear continuation and extension of the obtained results.

S-matrix condition of completeness of external wave functions external centrifugal and rapidly decreasing potentials causality time resonances or explosions parity violation enhancement

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