Title: An application of the Hylleraas-B-splines basis set: High accuracy calculations of the static dipole polarizabilities of helium,
Abstract: The Hylleraas-B-splines basis set is introduced in this paper, which can be
used to obtain the eigenvalues and eigenstates of helium-like system's
Hamiltonian. Comparing with traditional B-splines basis, the rate of
convergence of our results has been significantly improved. Through combine
this method and pseudo-states sum over scheme, we obtained the high precision
values of static dipole porlarizabilities of the $1{}^1S-5{}^1S$,
$2{}^3S-6{}^3S$ states of helium in length and velocity gauges respectively,
and the results get good agreements. The final extrapolate results of
porlarizabilities in different quantum states arrived eight significant digits
at least, which fully illustrates the advantage and convenience of this method
in the problems involving continuous states.