# The Momentum Distribution of Liquid $^4$He

## TL;DR

This study uses neutron scattering and quantum calculations to analyze the momentum distribution and Bose condensate fraction in liquid helium-4, confirming quantum predictions and Bose symmetry breaking in superfluidity.

## Contribution

It provides the first high-resolution measurements of the momentum distribution in liquid helium-4 that agree with ab initio quantum Monte Carlo predictions.

## Key findings

- Bose condensate fraction is zero in the normal fluid
- Condensate fraction rapidly increases below the superfluid transition
- Empirical estimates of kinetic energy and condensate fraction match theoretical predictions

## Abstract

We report high-resolution neutron Compton scattering measurements of liquid $^4$He under saturated vapor pressure. There is excellent agreement between the observed scattering and ab initio predictions of its lineshape. Quantum Monte Carlo calculations predict that the Bose condensate fraction is zero in the normal fluid, builds up rapidly just below the superfluid transition temperature, and reaches a value of approximately $7.5\%$ below 1 K. We also used model fit functions to obtain from the scattering data empirical estimates for the average atomic kinetic energy and Bose condensate fraction. These quantities are also in excellent agreement with ab initio calculations. The convergence between the scattering data and Quantum Monte Carlo calculations is strong evidence for a Bose broken symmetry in superfluid $^4$He.