Method to circumvent the neutron gas problem in the BCS treatment for nuclei far from stability

Extending the Kruppa's prescription for the continuum level density, we have recently improved the BCS method with seniority-type pairing force in such a way that the effects of discretized unbound states are properly taken into account for finite depth single-particle potentials. In this paper, it is further shown, by employing the Woods-Saxon potential, that the calculation of spatial observables like nuclear radius converges as increasing the basis size in the harmonic oscillator expansion. Namely the disastrous problem of a "particle gas" surrounding nucleus in the BCS treatment can be circumvented. In spite of its simplicity, the new treatment gives similar results to those by more elaborate Hartree-Fock-Bogoliubov calculations; e.g., it even mimics the pairing anti-halo effect. The obtained results as well as the reason of convergence in the new method are investigated by a variant of the Thomas-Fermi approximation within the limited phase space which corresponds to the harmonic oscillator basis truncation.