Scaling properties of the pairing problem in the strong coupling limit

Abstract

We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling $G$ and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius $G_{\mathrm{sing}}$ of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore $G_{\mathrm{sing}}$ is not related to the critical values of the coupling $G_{\mathrm{crit}}$, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points.

28 pages, 5 figures

References in corpus (5)

• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Solutions of Nuclear Pairing
• Analysis of the Strong Coupling Limit of the Richardson Hamiltonian using the Dyson Mapping
• The multilevel pairing Hamiltonian versus the degenerate case
• The many levels pairing Hamiltonian for two pairs