# An application of the Hylleraas-B-splines basis set: High accuracy calculations of the static dipole polarizabilities of helium

## TL;DR

This paper introduces the Hylleraas-B-splines basis set, significantly improving convergence for helium calculations, enabling high-precision static dipole polarizability values with at least eight-digit accuracy.

## Contribution

The paper presents a novel Hylleraas-B-splines basis set that enhances convergence and accuracy in calculating helium's static dipole polarizabilities compared to traditional methods.

## Key findings

- Achieved high-precision polarizability values with at least eight significant digits.
- Demonstrated improved convergence rates over traditional B-splines.
- Validated results in both length and velocity gauges.

## 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.