Three-body Forces in Oscillator Bases Expansion

TL;DR

This paper extends the oscillator bases expansion method to include three-body forces for three identical particles, maintaining computational efficiency and validating accuracy against established methods.

Contribution

It introduces a generalization of the oscillator bases expansion to incorporate three-body forces without increasing computational cost.

Findings

The method accurately models three-body forces in oscillator bases.

Validation shows comparable results to Lagrange mesh and hyperspherical harmonic methods.

Extension to larger systems is discussed.

Abstract

The oscillator bases expansion stands as an efficient approximation method for the time-independent Schr\"odinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such parameters. It handles both non- and semi-relativistic kinematics with generic two-body interactions. In the current work, focusing on systems of three identical bodies, the method is generalised to include the management of a given class of three-body forces. The computational cost of this generalisation proves to not exceed the one for two-body interactions. The accuracy of the generalisation is assessed by comparing with results from Lagrange mesh method and hyperspherical harmonic expansions. Extensions for systems of $N$ identical bodies and for systems of two identical particles and one distinct are also discussed.