An effective field theory approach to two trapped particles

TL;DR

This paper develops an effective field theory framework for two particles in a harmonic trap, systematically improving interaction models through perturbative corrections and connecting to pseudopotential results.

Contribution

It introduces a hierarchical approach to model short-range interactions in trapped particles using effective field theory, including higher-order corrections and range effects.

Findings

Next-to-leading order interactions improve convergence

Perturbative corrections enhance accuracy in larger model spaces

Results connect to pseudopotential in the large-space limit

Abstract

We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.