  We propose to use two-body regularized finite-range pseudopotential to
generate nuclear energy density functional (EDF) in both particle-hole and
particle-particle channels, which makes it free from self-interaction and
self-pairing, and also free from singularities when used beyond mean field. We
derive a sequence of pseudopotentials regularized up to next-to-leading order
(NLO) and next-to-next-to-leading order (N2LO), which fairly well describe
infinite-nuclear-matter properties and finite open-shell paired and/or deformed
nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large
effective mass, the obtained solutions constitute a preliminary step towards
future implementations, which will include, e.g., EDF terms generated by
three-body pseudopotentials.
