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 non-central and non-local terms in realistic interactions as well as the frequently used restriction of pairing interactions to the ${}^1S_0$ partial wave. The treatment of the center-of-mass motion and its effect on theoretical pairing gaps is assessed independently of the used interactions.