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 $1{}^{1}S-5{}^{1}S$, $2{}^{3}S-6{}^{3}S$ 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.

arXiv comment7 pages, 1 figure and 6 tables

References in corpus (5)

• Variational calculations of dispersion coefficients for interactions between H, He, and Li atoms
• Experiment and Theory in Computations of the He Atom Ground State
• Fine structure of helium-like ions and determination of the fine structure constant
• Precision Measurement for Metastable Helium Atoms of the 413 nm Tune-Out Wavelength at Which the Atomic Polarizability Vanishes
• The higher-order black-body radiation shift of atomic energy-levels

Cited by in corpus (4)

• Relativistic full-configuration-interaction calculations of magic wavelengths for the $2{}^3{S}_1\to 2{}^1{S}_0$ transition of helium isotopes
• Application of the Hylleraas-$B$-spline basis set: Nonrelativistic Bethe logarithm of helium
• Static-field ionization model of He-like ions for diagnostics of light field intensity
• Calculations of Bethe logarithms for Hydrogen and Helium atoms using B-splines in different gauges