Helium atom in strong magnetic fields: An application of the configuration-interaction method with Hylleraas-Gaussian basis

Abstract

In this work, we apply approximate expansions of Gaussian-type geminals of ${r}_{12}$ to replace the integer and half-integer powers of ${r}_{12}$ in Hylleraas-Gaussian basis, and use a full configuration-interaction method to calculate the energies of ${^{1}0}^{+}$, ${^{1}(\ensuremath{-}1)}^{+}$, and ${^{1}(\ensuremath{-}2)}^{+}$ states for helium atom in magnetic fields between 0 and 100 a.u. Compared to the configuration-interaction method with Gaussian basis, at least $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ improvement in the precision of energies has been made when calculated mean value of ${r}_{12}$ is less than 5.67 a.u. and more than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ improvement in precision of results has been achieved when calculated mean value of ${r}_{12}$ is less than 2.41 a.u. The ground-state energy of helium atom in our calculation is $\ensuremath{-}2.903\text{ }715\text{ }5$ in the absence of magnetic field. This work presents a general method which can attain high precise ground and low-lying states energies in the whole field regime and is hopeful to be extended to more complex atomic and molecular systems (lithium, beryllium, and ${\text{H}}_{2}$, etc.).