On the non-Unitarity of the Bogoliubov Transformation due to the Quasiparticle Space Truncation
J. Dobaczewski$^{1-4}$, P.J. Borycki$^{2,5}$, W. Nazarewicz$^{1,2,4}$ and M. Stoitsov$^{2-4,6}$
$^1$Institute of Theoretical Physics, University of Warsaw, ul. Hoza 69, PL 00681 Warsaw, Poland
$^2$Department of Physics, University of Tennessee, Knoxville, Tennessee 37996, USA
$^3$Joint Institute for Heavy Ion Research, Oak Ridge, Tennessee 37831, USA
$^4$Physics Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831, USA
$^5$Institute of Physics, Warsaw University of Technology, ul. Koszykowa 75, PL 00662 Warsaw, Poland
$^6$Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Science, Sofia-1784, Bulgaria

Abstract

We show that due to the energy cutoff in the Hartree-Fock-Bogoliubov quasiparticle space, the Bogoliubov transformation becomes non-unitary. We propose a method of restoring the unitarity by introducing a truncated single-particle Hilbert space, in which the HFB equations are to be solved.

PACS 21.30.Fe, 21.60.Jz, 24.30.Cz