Classification of states in proton–neutron pairing model

Abstract

Isoscalar (T = 0) plus isovector (T = 1) pairing hamiltonian in LS-coupling, which is important for heavy N=Z nuclei, is solvable in terms of a O(8) algebra for some special values of the mixing parameter that measures the competition between T = 0 and T = 1 pairing. The O(8) algebra is generated, amongst others, by the S = 1, T = 0 and S = 0, T = 1 pair creation and annihilation operators . Shell model algebras, with only number conserving operators, that are complementary to theThe problem of classification of states for a given number of

Interrelations between the pairing and quadrupole interactions in the microscopic Shell Model

“…(20) in Ref. [9] where a complete classification of the states in the SO (8) proton-neutron pairing model has been done.…”

Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems

“…In the BEGOE(1+2)-S1 space, it is possible to identify two different pairing algebras (each defining a particular type of pairing) and they follow from the results in [11,14,24].…”

On the calculation of inner products of Schur functions

“…These irreps are then coupled such that the total wave functions are completely antisymmetric (if we have fermion systems) or symmetric (if we have boson systems) under permutation of all particles. For recent applications of group theoretical models to fermion and boson systems, see [1,2]. Therefore, one needs to know how to reduce the Kronecker product of two S n irreps into S n irreps and this gives the Clebsch-Gordon series for the symmetric groups [3].…”

“…≥ λ n ≥ 0 and ∑ n i=1 λ i = n. Our purpose in this paper is to give methods for evaluating the Kronecker products of S n irreps with n up to 20 and beyond. Before going further it is useful to mention that the spectrum generating groups G of interest are general linear groups GL(N), unitary groups U(N) and so on [1,2,6].…”

“…However this formula is difficult to use in practice for larger integer values n. The three operations, outer product, inner product and plethysm are connected among themselves by relations known in the literature and exploiting this, we will give in this paper two methods for the calculation of inner products for irreps for large n values. One of the methods discussed ahead is developed following a recent study of the SO (8) proton-neutron pairing model of atomic nuclei [1]. In [5] tables for inner products are given for n ≤ 9 only and the methods presented in the present paper allow one to go up to n = 20 and beyond.…”