Using Continuum Level Density in the Pairing Hamiltonian: BCS and Exact Solutions

Abstract

Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant pairing Hamiltonian and to make a comparison between the approximate BCS and the exact Richardson solutions. The continuum is introduced by using the continuum single particle level density. It is shown that the continuum makes an important contribution to the pairing parameter even in those case when the continuum is weakly populated. It is shown that while the approximate BCS solution depends on the model space the exact Richardson solution does not.

15 pages, 5 figures, accepted in Nucl. Phys. A

References in corpus (2)

• Shell Model in the Complex Energy Plane
• Study of the transition from pairing vibrational to pairing rotational regimes between magic numbers N=50 and N=82, with two-nucleon transfer

Cited by in corpus (8)

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• Cooper pairs in the Borromean nuclei ${}^6$He and ${}^{11}$Li using continuum single particle level density
• Pairing in the BCS and LN approximations using continuum single particle level density
• Richardson's solutions in the real- and complex-energy spectrum
• Continuum discretized BCS approach for weakly bound nuclei
• Pairing versus quarteting coherence length
• Estimate of the location of the neutron drip line for calcium isotopes from an exact Hamiltonian with continuum pair correlations
• Exact solutions for pairing interactions