Date of Award
Doctor of Philosophy
Elbio Dagotto, David Dean, Thomas Papenbrock, Lawrence Townsend
In this work we show how to regularize the ultraviolet divergences appearing in the local pairing term of the energy density functional. Our approach, entirely rooted in the framework of the Density Functional Theory, is based on the regularization of local densities and currents and can be applied to various classes of energy density functionals. We demonstrated, that for the particular choice of the pairing term of energy density functional, our procedure gives the same regularization scheme to the one obtained earlier by the means of the pairing gap regularization.
We also investigated the non-unitarity of the Bogoliubov tranformation due to the energy cutoff in the quasiparticle space. We developed and tested the method of restoring the unitarity of the Bogoliubov transformation. We demonstrated that by applying this method one can perform HFB calculations for significantly lower cutoff energies, without losing accuracy.
Borycki, Piotr Jerzy, "Regularization of the Particle-Particle Interaction in the Nuclear Density Functional Theory. " PhD diss., University of Tennessee, 2006.