Rayleigh scattering formalism for the tune-out wavelength: Application to the 2 ³S state of helium

The tune-out wavelength for an atom interacting with an incident laser beam is reformulated as a zero in the Rayleigh scattering cross section instead of the dynamic polarizability (or AC Stark shift). The two pictures are equivalent in lowest order, but not when higher-order retardation effects are taken into account. Detailed high-precision calculations in Hylleraas coordinates will be presented for the tune-out wavelength of helium at 413 nm near the 2 ³S – 3³ P optical transition, including D-wave retardation corrections, and compared with recent high-precision measurements.