Description of Stable Chemical Elements by an aF Diagram and Mean Square Fluctuations

Abstract

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.