Helium tune-out wavelength: Gauge invariance and retardation corrections

The problem of calculating the tune-out wavelength for an atom interacting with a plane electromagnetic wave is formulated as a zero in the Rayleigh scattering cross section, rather than a zero in the dynamic polarizability. Retardation (finite wavelength) corrections are discussed in the velocity gauge, and possible gauge transformations to a length form are investigated. For the special case of S-states, it is shown that a pure length form exists for the leading p _x z retardation correction, even though one does not exist in general. The results of high-precision calculations in Hylleraas coordinates are presented for the tune-out wavelength of helium near the 2 ³ S − 3 ³ P transition at 413 nm.