Path integral calculation of the third dielectric virial coefficient of helium based on ab initio three body polarizability and dipole surfaces

We develop a surface for the electric dipole moment of three interacting helium atoms and use it with state-of-the-art potential and polarizability surfaces to compute the third dielectric virial coefficient, C_ɛ, for both ⁴He and ³He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability and are extended to the low-temperature regime by including exchange effects. In addition, the uncertainty of C_ɛ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to C_ɛ. Our results compare reasonably well with the limited experimental data. The first-principles values of C_ϵ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium.