Effective Hamiltonian for doubly excited Helium states based on four dimensional Harmonic Oscillator

TL;DR

This paper develops an effective Hamiltonian model based on a four-dimensional harmonic oscillator to describe doubly excited helium states, providing insights into electron correlation and a unified atomic state description.

Contribution

It introduces a revised effective Hamiltonian using approximate O(4) symmetry and new quantum numbers for helium states with both electrons in the n=2 shell.

Findings

Hamiltonian optimized with non-linear least squares

Results interpreted in terms of electron correlation

Potential unified description of two-electron intrashell states

Abstract

Effective Hamiltonians for doubly excited Heliums states based on approximate O(4) symmetry are revised. New quantum numbers for a 4D Harmonic Oscillator are assigned to Helium states with both electrons in the n=2 shell. An effective Hamiltonian operator is constructed and optimzed by means of non-linear least-square fits to the energy levels of the Helium isoelectronic series. The results are interpreted in terms of electron correlation and a possible unified description of two-electron atom intrashell states.