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TMF, 2019, Volume 201, Number 1, Pages 65–83 (Mi tmf9754)  

Description of stable chemical elements by an $aF$ diagram and mean square fluctuations

V. P. Maslov

Moscow Institute of Electronics and Mathematics — National Research University "Higher School of Mathematics", Moscow, Russia

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.

Keywords: energy of neutron separation from the atomic nucleus, nucleus binding energy, neutron domain of uncertainty, parastatistics (Gentile statistics), mean square fluctuations of energy and chemical potential, nuclear matter.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation АААА-А17-117021310377-1
This research was supported by the Federal Target Program (Government Registration Number AAAA-A17-117021310377-1).


DOI: https://doi.org/10.4213/tmf9754

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English version:
Theoretical and Mathematical Physics, 2019, 201:1, 1468–1483

Bibliographic databases:

Received: 22.05.2019
Revised: 19.06.2019

Citation: V. P. Maslov, “Description of stable chemical elements by an $aF$ diagram and mean square fluctuations”, TMF, 201:1 (2019), 65–83; Theoret. and Math. Phys., 201:1 (2019), 1468–1483

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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