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Figure 2 shows the number of states in the truncated
particle spaces as functions of the SVD cutoff for various
cutoff energies . For large or , these numbers are
close to the numbers of quasiparticle states (shown by dotted lines);
however, for small , 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).

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Jacek Dobaczewski
2005-01-23