Compact variational wave functions for bound states in three-electron atomic systems

TL;DR

This paper develops a variational method using six-dimensional gaussoids to construct compact, accurate wave functions for three-electron atoms and ions, enabling precise calculations of energies and properties.

Contribution

It introduces a novel variational approach with optimized basis functions for three-electron systems, improving accuracy in bound state calculations.

Findings

Accurate energies for ground states of various three-electron systems.

Determination of hyperfine structure splittings and field shifts.

Explicit formulas for total energies using $Q^{-1}$ expansion.

Abstract

The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional gaussoids written in the relative four-body coordinates $r_{12}, r_{13}, r_{23}, r_{14}, r_{24}$ and $r_{34}$. The non-linear parameters in each basis function have been optimized carefully. By using these variational wave functions we have determined the energies and other bound state properties are determined for the ground $1^2S$-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithium-like ions: Be$^+$, B$^{2+}$, C$^{3+}, ...$Na$^{8+}$ and Mg$^{9+}$. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the $Q^{-1}$ expansion are derived for the total energies of these three-electron systems.