Pairing in the framework of the unitary correlation operator method (UCOM): Hartree-Fock-Bogoliubov calculations

In this first in a series of articles, we apply effective interactions derived by the unitary correlation operator method (UCOM) to the description of open-shell nuclei, using a self-consistent Hartree-Fock-Bogoliubov framework to account for pairing correlations. To disentangle the particle-hole and particle-particle channels and assess the pairing properties of VUCOM, we consider hybrid calculations using the phenomenological Gogny D1S interaction to derive the particle-hole mean field. In the main part of this article, we perform calculations of the tin isotopic chain using VUCOM in both the particle-hole and particle-particle channels. We study the interplay of both channels and discuss the impact of noncentral and nonlocal terms in realistic interactions as well as the frequently used restriction of pairing interactions to the ¹S₀ partial wave. The treatment of the center-of-mass motion and its effect on theoretical pairing gaps is assessed independently of the used interactions.