Описание стабильных химических элементов с помощью aF-диаграммы и среднеквадратичных флуктуаций

Теоретическая и математическая физика. 2019. Т. 201. № 1. С. 65–83.

Maslov V.

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a small neighborhood of zero pressure and obtain new important
parastatistical relations between the temperature and the chemical potential when a nucleon separates
from an atomic nucleus. The obtained relations allow constructing a new diagram (an aF diagram) or
isotherms of very high temperatures corresponding to nuclear matter. We mathematically prove that
the transition of particles from the domain governed by Fermi–Dirac statistics to the domain governed by
Bose–Einstein statistics near the zero pressure P occurs in the neutron uncertainty domain or halo domain.
We obtain equations for the chemical potential that allow determining the width of the uncertainty domain.
Based on the calculated values of the minimum intensivity for Bose particles, the chemical potential, the
compressibility factor, and the minimum mean square fluctuation of the chemical potential, we construct
a table of stable nuclei of chemical elements, demonstrating a monotonic relation between the nucleus
mass number and the other parameters.

Keywords: parastatistics, парастатистика, nuclear matter, mean square fluctuations, energy of neutron separation from the atomic nucleus, nucleus binding energy, neutron domain of uncertainty, энергия связи ядра, нейтронная область неопределенности, средне- квадратичные флуктуации, ядерная материя, энергия отрыва нейтрона от атомного ядра