# Two-electron atom with a screened interaction

## TL;DR

This paper provides analytical solutions for a modified helium-like atom model with screened and regularized electron-electron interactions, revealing exactly solvable ground states that include electron correlation effects.

## Contribution

It introduces a new exactly solvable model for a two-electron atom with screened interactions, expanding understanding of correlated quantum systems.

## Key findings

- Exact ground state solutions found for specific parameters.
- Electron correlation explicitly included in the solutions.
- Model demonstrates how screening affects atomic interactions.

## Abstract

We present analytical solutions to a quantum-mechanical three-body problem in three dimensions, which describes a helium-like two-electron atom. Similarly to Hooke's atom, the Coulombic electron-nucleus interaction potentials are replaced by harmonic potentials. The electron-electron interaction potential is taken to be both screened (decaying faster than the inverse of the interparticle separation) and regularized (in the limit of zero separation). We reveal the exactly solvable few-electron ground state, which explicitly includes electron correlation, for certain values of the harmonic containment.