  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.
