Finite-range separable pairing interaction within the new N³LO DFT approach

For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N³LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N³LO energy functional. In the present study, we use the separable, finite-range, translationally invariant interaction given in [2] and we present the first test-case application of this pairing interaction within the code HOSPHE that is able to treat the N³LO energy density functional.