  We present first-principles theoretical determination of the three-body
polarizability and the third dielectric virial coefficient of helium.
Coupled-cluster theory and the full configuration interaction procedure were
used to perform required electronic structure calculations. The mean absolute
relative uncertainty of the trace of the three-body polarizability tensor,
resulting from the incompleteness of orbital basis set, was determined using
extrapolation techniques. Additional uncertainty due to approximate treatment
of triple and the neglect of higher excitations was estimated using full
configuration interaction calculations. An analytic function was developed to
describe the behavior of the polarizability and its asymptotic decay to
three-atomic and atom-diatom fragmentation channels. We also developed an
analytic function describing the local behavior of the total uncertainty of our
calculations. Using both fits we calculated the third dielectric virial
coefficient and its uncertainty using the classical and semiclassical
Feynman-Hibbs approaches. The results of our calculations were compared with
available experimental data and with recent Path-Integral Monte Carlo (PIMC)
calculations employing the so-called superposition approximation of the
three-body polarizability. For temperatures above 200 K we observed significant
discrepancy between the classical results obtained using either the
superposition approximation or the ab initio computed polarizability. The
theoretical data reported in this work eliminate the main accuracy bottleneck
of the development of optical pressure standard and are expected to facilitate
further progress in the field of quantum thermal metrology

Chemical Physics