Optical properties of helium including relativistic corrections

We have obtained very accurately calculated nonrelativistic values of the index of refraction and the Verdet constant of helium gas. We have used the Breit-Pauli operator to obtain corrections of order ${\alpha }^2$ to the same optical quantities. This required us to analyze the scattering of light by helium atoms correct up to third order: second order in the electromagnetic field and first order in the Breit-Pauli operator. We compare these results with experimental values and find some significant discrepancies.