New Mechanism for the Enhancement ofsdDominance in Interacting Boson Models

Abstract

We introduce an exactly solvable model for interacting bosons that extend up to high spin and interact through a repulsive pairing force. The model exhibits a phase transition to a state with almost complete sd dominance. The repulsive pairing interaction that underlies the model has a natural microscopic origin in the Pauli exclusion principle between constituent nucleons. As such, repulsive pairing between bosons seems to provide a new mechanism for the enhancement of sd dominance, giving further support for the validity of the sd interacting boson model.

Solving the Richardson equations for fermions

“…However, it turned out that in the Fermion case the solutions exhibit singularities which are hard to treat numerically [3,4]. Recently, exactly solvable pairing models have gained new attention [5], with applications to nanometalic grains [6] (for a review see [7]), Bose Einstein Condensates [8] and nuclear physics [9]. It was first shown that the pairing model was integrable by finding the complete set of commuting integrals of motions [10], and subsequently, three new families of fully integrable and exactly solvable models [11] giving rise to a large class of pairing Hamiltonians with non-uniform matrix elements [12] were presented.…”

Scalar two-level boson model to study the interacting boson model phase diagram in the Casten triangle

“…The Hamiltonian describing this transition is a repulsive boson pairing Hamiltonian that has the particularity of being exactly solvable allowing the study of very large systems. The boson pairing model was first solved by Richardson [6] and more recently applied to the IBM [7][8][9]. However, this is the only integrable line in the phase diagram of the IBM often described with the Q-consistent Hamiltonian (QCH) [10] and pictorially represented by the Casten triangle.…”

Meaning ofS−Ddominance

“…The Hilbert space of N particles moving in shells k, l, m, ....p can be classified in terms of the product of groups SU (1,1) …”

“…The reason why it is interesting to consider this hamiltonian is that the repulsive pairing interaction between the bosons mucks up the influence of the Pauli principle between the quasibosons built on fermion pair (see Appendix 1 for a description of this relation in the single j-shell case). In a recent letter [1] a renormalized pairing interaction as well as a set of single bosons energies more related to the nuclear case yields that the S and D states are the only ones that have large occupations numbers. In Ref.…”