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Journal Articles Physical Review C Year : 2021

Exact expressions for the number of levels in single-j orbits for three, four, and five fermions

Abstract

We propose closed-form expressions of the distributions of magnetic quantum number M and total angular momentum J for three and four fermions in single-j orbits. The latter formulas consist of polynomials with coefficients satisfying congruence properties. Such results, derived using doubly recursive relations over j and the number of fermions, enable us to deduce explicit expressions for the total number of levels in the case of three-, four-, and five-fermion systems. We present applications of these formulas, such as sum rules for six-j and nine-j symbols, obtained from the connection with fractional-parentage coefficients, an alternative proof of the Ginocchio-Haxton relation, or cancellation properties of the number of levels with a given angular momentum.

Dates and versions

hal-03534039 , version 1 (19-01-2022)

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Michel Poirier, Jean-Christophe Pain. Exact expressions for the number of levels in single-j orbits for three, four, and five fermions. Physical Review C, 2021, 104 (6), pp.064324. ⟨10.1103/PhysRevC.104.064324⟩. ⟨hal-03534039⟩
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