Comparison of Δ-and Gogny-type Pairing Interactions

The pairing interaction plays a crucial role in the nuclear mean-field model calculations. The most frequently used pairing type is the so-called monopole pairing interaction (g=const model). More realistic residual interactions are those with state-dependent matrix elements, e.g. δand Gogny forces. Previously the Gogny-type pairing force were studied within conventional Hartree-Fock-Bogoliubov (HFB) method [1] and in fully selfconsistent Relativistic Hartree-Fock-Bogoliubov theory (RHB) [2]. Here we investigate different kinds of pairing forces using the Nilsson mean-field model and BCS approximation. Contrary to the finite-range Gogny force, the δ-interaction is the zerorange force. The zero-range nature of the pairing interaction tends to overestimate the coupling to continuum states [3]. This defect doesn’t occure when using the Gogny force which is, however, cumbersome to handle; it involves sophisticated numerical techniques while the δ-force is relatively simple for numerical calculations. The effect of the finite range for the δforce can be easily simulated by introducing an energy cutoff which plays the role of an additional parameter similarly like in the case of the monopole pairing model except that the δ-interaction is less sensitive to the cutoff. These seemingly different pairing interactions should produce in fact similar resultsthe coherence length of nucleonic Cooper pair is of the order of size of a nucleus, therefore its structure should be insensitive to the details of the interaction in the particle-particle channel [4]. The aim of this