Exact expressions of the distributions of total magnetic quantum number and angular momentum in single-$j$ orbits: A general technique for any number of fermions - CEA - Commissariat à l’énergie atomique et aux énergies alternatives Accéder directement au contenu
Article Dans Une Revue Physical Review C Année : 2024

Exact expressions of the distributions of total magnetic quantum number and angular momentum in single-$j$ orbits: A general technique for any number of fermions

Résumé

A general method is proposed to obtain the distribution of the total quantum number M for a set of N identical fermions with momentum j, which is a cornerstone of the nuclear shell model. This can be performed using a recursive procedure on N, yielding closed-form expressions, which are found to be linear combinations of piecewise polynomials. We also highlight and implement in that framework two three-term recurrence relations over N, more convenient than Talmi’s five-term recurrence which has nevertheless already proved its worth in the past. In addition, the current approach allows one to consider both integer and half-integer values of j on the same footing. The technique is illustrated by detailed examples, corresponding to N = 3 to 6 fermions.
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Dates et versions

cea-04444888 , version 1 (08-02-2024)

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Michel Poirier, Jean-Christophe Pain. Exact expressions of the distributions of total magnetic quantum number and angular momentum in single-$j$ orbits: A general technique for any number of fermions. Physical Review C, 2024, 109 (2), pp.024306. ⟨10.1103/PhysRevC.109.024306⟩. ⟨cea-04444888⟩
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