Path-integral calculation of the second and third density virial coefficients of 4He

We present a comprehensive study of the second and third density virial coefficients, B(T) and C(T), of 4He across an extended temperature range from 1 K to 10 000 K utilizing the path-integral Monte Carlo (PIMC) method and most accurate interaction potentials. This work reports the first complete determination of B(T) within the PIMC framework, demonstrating excellent agreement and comparable uncertainties with results from the established phase-shift method, thus providing crucial cross-method validation. We generate a significantly extended and high-accuracy dataset for C(T), complementing existing literature values. A comprehensive uncertainty analysis quantifies contributions from both two-body and three-body potentials. The results reveal subtle differences from previous work for C(T) below 5 K, while reducing the uncertainty by approximately a factor of two in this low-temperature regime. This study provides crucial reference data to enhance the accuracy of primary standards for both temperature and pressure based on 4He.