In this work, we investigated the pairing regularization method using the s.p. Green's function in the Thomas-Fermi approximation and found it to be very suitable for a description of spherical and deformed nuclei. We checked the stability of the method with respect to the cutoff energy and found fluctuations in the total energy below 200keV. Fluctuations coming from the method itself do not exceed 50keV for the cutoff energy as low as 30MeV. However, if a still lower cutoff energy is assumed, the Thomas-Fermi approximation to the s.p. Green's function may no longer be valid.
We found that the differences between pairing renormalization and regularization procedures for volume and mixed pairing are rather small. Therefore, we conclude that physical conclusions previously obtained within the pairing renormalization scheme remain valid. Nevertheless, we believe that the theoretical motivation and simplicity of the regularization method is preferred to a phenomenological renormalization scheme.
Discussions with Aurel Bulgac are gratefully acknowledged. This work was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant DE-FG03-03NA00083; by the Polish Committee for Scientific Research (KBN) under contract N0. 1 P03B 059 27 and by the Foundation for Polish Science (FNP).