In this study, the variation after particle-number projection is discussed in the context of the nuclear density functional theory. Specifically, we implement for the first time the self-consistent Skyrme HFB+VAPNP formalism. We demonstrate that the particle-number conserving HFB equations with Skyrme functionals can be simply obtained from the standard Skyrme HFB equations in coordinate space by replacing the intrinsic densities and currents by their gauge-angle-dependent counterparts.
The calculations are carried for the Ca and Sn isotope chains. The VAPNP results are compared with those obtained with the LN and PLN methods. We demonstrate that the pathological behavior of LN and PLN methods around closed-shell nuclei can be partly cured by performing particle-number projection from neighboring open-shell systems. This result is important in the context of large-scale microscopic mass calculations, such as those of Ref. [22].
The restoration of broken symmetries in the density functional theory causes a number of fundamental questions, mainly related to the density dependence of the underlying interaction and to the different treatment of particle-hole and particle-particle channels [26,41]. These questions and problems will be discussed in detail in a forthcoming paper.
This work was supported in part by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through the U.S. Department of Energy Research Grant DE-FG03-03NA00083; 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), DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research), DE-FG02-00ER41132 (Institute for Nuclear Theory); by the Polish Committee for Scientific Research (KBN) under Contract No. 1 P03B 059 27; and by the Foundation for Polish Science (FNP).