Equation of State of a Strongly Interacting many-Boson System from an Effective Interaction

TL;DR

This study uses Quantum Monte Carlo methods with an effective contact potential to accurately determine the equation of state and microscopic properties of a strongly interacting $^4$He boson system, matching results from more complex potentials.

Contribution

Introduces a simplified effective contact interaction model that reproduces both macroscopic and microscopic properties of $^4$He, validated through Quantum Monte Carlo calculations.

Findings

Energy and saturation density are accurately reproduced.

Pair distribution functions converge to exact results as cutoff increases.

Effective interaction simplifies complex potential calculations.

Abstract

A contact potential describing an effective interaction between atomic $^4$He reproducing the results obtained with the HFDHE2 potential by Aziz et al. is employed to study the resulting equation of state by means of Quantum Monte Carlo calculations. \cblack The energy per particle and the pair distribution functions were investigated as a function of the ultraviolet cutoff $\Lambda$. The results suggest that not only the mean field properties of the system, such as the energy and the saturation density, are correctly reproduced, but also very microscopic quantities such as the pair distribution function are seen to converge towards the exact results when extrapolating for $\Lambda\rightarrow\infty$.