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.

Zeros of 6-jsymbols: Atoms, nuclei, and bosons

“…This work can be regarded as an extension of previous work on companion problems [10]. In the previous contributions we showed how similar expressions have consequences on different physical problems and different branches of physics e.g.…”

“…In the previous contributions we showed how similar expressions have consequences on different physical problems and different branches of physics e.g. how isospin can be used to get the same results as quasispin [10,16]. We find such such associations fascinating.…”

New relations for coefficients of fractional parentage—The Redmond recursion formula with seniority

“…The present authors have presented an alternative derivation of the above two results by using an m scheme [12]. A recent preprint by Talmi also uses the m scheme to go beyond the above two examples and to prove many conjectures of Zhao and Arima [13].…”

“…This leads to the fact that the values of the wave-function components for T = T max are two-particle coefficients of fractional parentage [16,17] …”

Alternate proof of the Rowe-Rosensteel proposition and seniority conservation

“…(Introductions to the quasispin scheme can also be found in Talmi's book [2] and recent publications [18].) * chongq@kth.se They proposed a matrix that can project the eigenvectors to two quasispin subspaces and stated that the eigenvalues of the matrix must equal to 2 or −1.…”