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arXiv:nucl-th/0702059 · Physical Review C

Spectra and symmetry in nuclear pairing

A. B. Balantekin, J. H. de Jesus, Yamaç Pehlivan

Published Jun 4, 2007• 16 citations
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Abstract

We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there are degeneracies between the states corresponding to less than and more than half full shell. We also provide a technique to solve the equations of Bethe ansatz.

DOI
10.1103/physrevc.75.064304

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Quantum invariants of the orbit dependent pairing problem are identified in the limit where the orbits become degenerate. These quantum invariants are simultaneously diagonalized with the help of the Bethe ansatz method and a symmetry in their spectra relating the eigenvalues corresponding to different number of pairs is discussed. These quantum invariants are analogous to the well known rational Gaudin magnet Hamiltonians which play the same role in the reduced pairing case (i.e., orbit independent pairing with non degenerate energy levels). It is pointed out that although the reduced pairing and the degenerate cases are opposite of each other, the Bethe ansatz diagonalization of the invariant operators in both cases are based on the same algebraic structure described by the rational Gaudin algebra.