Review of fundamental nuclear-geophysical researches in OSENU: i. standard beta decay theory elements and new cooperative electron-β-nuclear spectroscopy

This paper opens a series of publications, devoted to review of new results of the original nuclear-geophysical researches at the OSENU mathematics department and its laboratories (computational and quantum mathematics and mechanics, environmental radioactivity, nuclear geophysics). Primarily the first material will focus on fundamental issues that constitute the theoretical basis of the further applied nuclear-geophysical research. It is shortly presented a modern approach to computing the key parameters of the beta decay processes. There are discussed the cooperative electron β-nuclear processes in atoms and molecules, including the excitation, ionization, electronic rearrangement, induced by the nuclear reactions and β-decay. A few factors are taken into account: changing the integration limits in the Fermi function integral, energy corrections for different chemical substances, and the possibility of the bound β-decay or other exotic decay channels.

Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media

We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.