  We applied the finite-size scaling method using the B-splines basis set to
construct the stability diagram for two-electron atoms with a screened Coulomb
potential. The results of this method for two electron atoms are very accurate
in comparison with previous calculations based on Gaussian, Hylleraas, and
finite-element basis sets. The stability diagram for the screened two-electron
atoms shows three distinct regions: a two-electron region, a one-electron
region, and a zero-electron region, which correspond to stable, ionized and
double ionized atoms. In previous studies, it was difficult to extend the
finite size scaling calculations to large molecules and extended systems
because of the computational cost and the lack of a simple way to increase the
number of Gaussian basis elements in a systematic way. Motivated by recent
studies showing how one can use B-splines to solve Hartree-Fock and Kohn-Sham
equations, this combined finite size scaling using the B-splines basis set,
might provide an effective systematic way to treat criticality of large
molecules and extended systems. As benchmark calculations, the two-electron
systems show the feasibility of this combined approach and provide an accurate
reference for comparison.
