Separable pole expansions in four-nucleon bound state calculations

Abstract

We compare the utility of the generalized unitary pole expansion and the energy-dependent pole expansion for the three-body subsystem amplitudes in four-body bound state calculations for a variety of separable and local nucleon-nucleon interactions. It is found that with the energy-dependent pole expansion the four-body binding energy is well reproduced with only two terms each for the (2 + 2) and the (3 + 1) subsystems, respectively, while the generalized unitary pole expansion requires three terms for the (3 + 1) channel and four terms for the (2 + 2) channel. We thus conclude that pole dominance is of greater importance for the generalized unitary pole expansion than for the energy-dependent pole expansion, which works equally well for both types of subsystems. It is found that both methods, in particular the energy-dependent pole expansion, converge more rapidly with increasing repulsion in the two-body interaction, i.e., the more realistic the interaction becomes. Both expansions require similar computing times for a converged calculation and are about 15-20 times faster than the widely used Hilbert-Schmidt expansion. The respective merits of the two pole expansions are discussed and compared with the Hilbert-Schmidt expansion.NUCLEAR STRUCTURE Four-body bound state calculations for various nucleon-nucleon interactions. Comparison of the generalized unitary pole expansion and energy-dependent pole expansion.