Work

Statistics of Quantum Numbers for Non-Equivalent Fermions in Single-j Shells

Year: 2025

Type: article

Abstract: This work addresses closed-form expressions for the distributions P(M) of the magnetic quantum numbers M and Q(J) of total angular momentum J for non-equivalent fermions in single-j orbits. Such quantities play an important role in both nuclear and atomic physics, through the shell models. Using irreducible representations of the rotation group, different kinds of formulas are presented, involving multinomial coefficients, generalized Pascal triangle coefficients, or hypergeometric functions. Special cases are discussed, and the connections between P(M) (and therefore Q(J)) and mathematical functions such as elementary symmetric, cyclotomic, and Jacobi polynomials are outlined.

Source: Atoms

DOI: 10.3390/atoms13040025

Author: Jean-Christophe Pain

Institutions: Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay, CEA Paris-Saclay - Etablissement de Saclay, CEA DAM Île-de-France, Laboratoire Matière en Conditions Extrêmes

Language: English

Topic: Nuclear physics research studies

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,810

OpenAlex ID: W4408827417

FWCI: 0.945

Cites: 53

Cited by: 2

Related to: 10