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

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## 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## Preview

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## Notes

### Acknowledgments

The author is deeply grateful to E. I. Nikulin, who recently listened to a course of lectures by I. A. Kvasnikov, for the help in representing some of his ideas underlying this paper.

**Conflicts of interest.** The author declares no conflicts of interest.

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