# Extracting free-space observables from trapped interacting clusters

## TL;DR

This paper develops an improved formula for relating trapped two-particle energy spectra to free-space scattering phase shifts, enabling more accurate extraction of nuclear scattering information from finite trap calculations.

## Contribution

It introduces a systematically improved formula for low-energy dynamics in finite traps, facilitating the extraction of nuclear scattering phase shifts from ab initio calculations.

## Key findings

- Provides a new formula valid for finite traps
- Enables extraction of nuclear phase shifts from many-body calculations
- Establishes effective field theory as a useful framework

## Abstract

The energy spectrum of two short-range interacting particles in a harmonic potential trap has previously been related to free-space scattering phase shifts. But the existing formula for this purpose is exact only in the limit of an infinitely shallow trap. Here we provide a systematically improved formula---describing the low-energy dynamics---that enables the use of finite traps. This paves the way for extracting nuclear scattering phase shifts from {\it ab initio} nuclear many-body structure calculations, a long-sought goal in nuclear physics. The derivation establishes effective field theory as a powerful framework for studying the connection between structure information of a trapped system (with two or more sub-clusters) and continuum physics in the fields of both nuclear and condensed-matter physics.