Companion problems in quasispin and isospin

Abstract

We note that the same mathematical results apply to problems involving quasispin and isospin, but the problems per se are different. In the quasispin case, one deals with a system of identical fermions (e.g. neutrons) and address the problem of how many seniority conserving interactions there are. In the isospin case, one deals with a system of both neutrons and protons and the problem in question is the number of neutron-proton pairs with a given total angular momentum. Other companion problems are also discussed.

12 pages, Latex; some additions in section II and a brief summary at the end

References in corpus (5)

• General pairing interactions and pair truncation approximations for fermions in a single-j shell
• Number of states with fixed angular momentum for identical fermions and bosons
• Classification of states of single-$j$ fermions with $J$-pairing interaction
• Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
• Degeneracies when T=0 Two Body Interacting Matrix Elements are Set Equal to Zero : Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle

Cited by in corpus (8)

• Alternate proof of the Rowe-Rosensteel proposition and seniority conservation
• Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]
• $J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
• Isospin relations for four nucleons in a single j shell
• New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority
• Exact expressions for the number of levels in single-\textit{j} orbits for three, four and five fermions
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell
• Zeros of 6j Symbols:Atoms:Nuclei and Bosons