Application of the Hylleraas-$B$-spline basis set: Nonrelativistic Bethe logarithm of helium

Abstract

In this work, we report an application of Hylleraas-$B$-spline basis set to the nonrelativistic Bethe logarithm calculation of helium. The Bethe logarithm for $n{}^{1}S$, $n$ up to 10, states of helium are calculated with a precision of 7-9 significant digits in two gauges, which greatly improves the accuracy of the traditional $B$-spline basis set. In addition, to deal with the numerical linear correlation problem in Bethe logarithm calculation, we developed a multiple-precision generalized symmetric eigenvalue problem solver (MGSEPS). This program may be very useful to precision calculations.

arXiv comment8 pages, 1 figure

References in corpus (6)

• Theoretical energies of low-lying states of light helium-like ions
• Testing fundamental interactions on the helium atom
• Calculation of the nonrelativistic Bethe logarithm in the velocity gauge
• Bethe logarithm for the helium atom
• An application of the Hylleraas-B-splines basis set: High accuracy calculations of the static dipole polarizabilities of helium
• Relativistic full-configuration-interaction calculations of magic wavelengths for the $2{}^3{S}_1\to 2{}^1{S}_0$ transition of helium isotopes

Cited by in corpus (1)

• Calculations of Bethe logarithms for Hydrogen and Helium atoms using B-splines in different gauges