# Estimated values of the kinetic energy for liquid $^3$He

## TL;DR

This paper estimates the ground-state kinetic energy of liquid $^3$He using a variational path integral quantum Monte Carlo method, resolving previous discrepancies between experimental and theoretical values.

## Contribution

It applies an extended fermionic path integral Monte Carlo approach with a fixed-node approximation to accurately compute kinetic energy and other properties of liquid $^3$He.

## Key findings

- Estimated kinetic energy: 10.16±0.05 K/atom.
- Results agree with most experimental data.
- Method effectively reduces approximation errors.

## Abstract

The kinetic energy is estimated for the ground-state of liquid $^3$He at equilibrium density. The obtained value for this quantity, $10.16\pm0.05$ K/atom at density $0.0163~\mbox{\AA}$, is in agreement with most of the experimental data found in the literature. This result resolves a long-standing controversy between experimental and theoretical values of this quantity. The variational path integral method, an "exact" quantum Monte Carlo method extended for fermionic systems, is applied in the calculations. The results obtained are subjected only to the restrictions imposed by a chosen nodal structure without any further approximation, even for quantities that do not commute with the Hamiltonian. The required fixed-node approximation entails an implementation that allows a more effective estimation of the quantities of interest. Total and potential energies together with the radial distribution function are also computed.