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 pxz 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 23S − 33P transition at 413 nm.Research support by the Natural Sciences and Engineering Research Council, by SHARCnet, and by the Australian Research Council Discovery Project DP180101093 are gratefully acknowledged. P.- P. Zhang acknowledges support by the National Natural Science Foundation of China under Grant No. 11604369, and the Strategic Priority Research Program of the Chinese Academy of Sciences under Grants No. XDB21010400