Theoretical determination of the polarizability dispersion and the refractive index of helium

The refractive index n of gaseous helium can be measured by optical interferometry so accurately that it can be used to establish a pressure standard which is expected to be superior to the current standard based on the height of a mercury column. The new standard requires knowledge of the dynamic polarizability of helium atom with accuracy significantly higher than obtainable in the best experiments, but possible to achieve computationally. Calculations of this quantity are presented at relativistic and quantum electrodynamics levels of theory including relativistic nuclear recoil effects. The uncertainties of the results are carefully estimated. Our recommended value of the dynamic polarizability at the He-Ne laser wavelength of 6329.908 {}, equal 1.39181197(14) a.u., has uncertainty at least two orders of magnitude smaller than that of recent measurements and is sufficiently accurate to establish a new pressure standard. Purely ab initio values of the refraction coefficient n are computed using our polarizability, literature values of magnetic susceptibility, and dielectric virial coefficients. It is shown that n-1 can be predicted by theory as a function of density and temperature with uncertainty of 1 ppm for pressures up to 3 MPa.