Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Pairing functionals are often local, i.e., they can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational scheme diverges with the increasing single-particle space, and results depend on weakly occupied states. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this talk, I will introduce our method to fold the pair density with a Gaussian. I will also show that a folding width of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications. In addition, I will discuss the effects of folding the pair density on optimization of functionals.