Average pairing correlation properties and effective pairing residual interactions

This paper describes a method to determine the intensities of effective pairing residual interactions, extending what has been done for the seniority force model [Phys. Rev. C 110, 024311 (2024)]. It has been tested in Hartree-Fock plus BCS calculations using residual pairing zero-range interactions. The average pair condensation energy is the key quantity connecting the determination of constant pairing matrix elements to the estimation of delta interaction intensities. From individually fitted delta pairing strengths of $28$ well and rigidly deformed nuclei whose proton number $Z$ ranges from $50$ to $82$ evaluated at the ground-state, we have determined average interaction intensities. They reproduce equally well the data on MoI as what is obtained within the seniority force ansatz with a r.m.s. deviation of about $2 \: \hbar^2 \mbox{MeV}^{-1}$. This approach provides a non-ambiguous way to determine reasonably well the strengths of pairing interactions at the ground-state of well deformed nuclei. It allows to perform, with some reasonable level of confidence, calculations for other nuclei in the corresponding nuclear region as well as beyond their ground states in particular to assess deformation properties as, e.g., to evaluate fission barriers or spectral properties of quasi-particle states.