# Virial relations for ultracold trapped Fermi gases with finite range interactions through the BCS-BEC crossover

## TL;DR

This paper investigates virial relations in ultracold two-component Fermi gases with finite-range interactions across the BCS-BEC crossover, providing numerical verification and insights into the energy derivatives at unitarity.

## Contribution

It introduces a detailed analysis of virial relations considering finite-range interactions and verifies these relations numerically throughout the BCS-BEC crossover.

## Key findings

- Virial relations hold for finite-range interactions in ultracold Fermi gases.
- Partial derivatives of energy show extremal behavior at unitarity.
- Virial relations serve as a check for the quality of variational wave functions.

## Abstract

We study the virial relations for ultracold trapped two component Fermi gases in the case of short finite range interactions. Numerical verifications for such relations are reported through the BCS-BEC crossover. As an intermediate step, it is necessary to evaluate the partial derivatives of the many body energy with respect to the inverse of the scattering length and with respect to the interaction range. They are found to have extreme values at the unitary limit. The virial results are used to check the quality of the variational wave function involved in the calculations.