Results

Figure 2 shows the number of states in the truncated particle spaces as functions of the SVD cutoff $v_c$ for various cutoff energies $E_c$. For large $v_c$ or $E_c$, these numbers are close to the numbers of quasiparticle states (shown by dotted lines); however, for small $v_c$, additional particle states are necessary to properly represent the kept quasiparticle states. Total energies obtained by solving the HFB equations in the truncated particle spaces are shown in Fig. 1. For cutoff energies above 30MeV, the total energy is stable up to about 200keV. For any fixed cutoff energy, the method is also very stable ($<$100keV) with respect to the SVD cutoff. Therefore, our method allows us to perform the HFB calculations with satisfying precision for relatively small cutoff energies and dimensions of the particle space. While the two-step character of the method, and necessity to refit the pairing strength, makes the method significantly more computationally extensive than the standard HFB approach, the procedure allows for usual interpretation in terms of Bogoliubov product states. In order to implement the pairing readjustments, one could use the Green-function regularization methods [5], which will be considered in future work.

Acknowledgement

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).