Ground-state Energy Of Helium Atom Research Articles

Symmetry-dependent analytical all-electron potential for helium atom

Electron–electron interaction is the origin of the many-body problems usually encountered in physics and chemistry. Helium atom and other two-electron systems are the simplest many-body systems in nature. The Schrödinger equation even for such simple systems cannot be solved exactly without resorting to approximate methods. In this study, we have suggested a symmetry-dependent analytical all-electron potential for helium atom derived using an alternative multipole expansion, a variational technique, and a mean-field approximation. We have calculated the non-relativistic groundstate energy for helium atom to be −2.90422284. The suggested all-electron potential has a local Coulomb potential with embedded nuclear charge screening effect in the leading term of the multipole potential. A non-local component of the potential emanates from the higher-order angular momentum terms of the multipole series expansion. The higher-order multipole interactions are fully included through the exchange correlation processes where the interacting electrons exchange their angular momenta via the operator. With the derived potential, the effects of the local long-range and non-local short-range components, and the finite nuclear mass corrections are tested. Our results are in reasonable agreement with literature values. Indeed with the finite nuclear mass correction, we obtain the groundstate energy of helium atom to be −2.90382769.

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

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.).