Magic wavelength for the hydrogen 1S-2S transition: Contribution of the continuum and the reduced-mass correction

Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this paper, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. The magic wavelength, at which the lowest-order ac Stark shifts of the 1S and 2S states are equal, is found to be equal to 514.6 nm. The ac Stark shift at the magic wavelength is -221.6 Hz / (kW/cm^2), and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is -0.2157 Hz/ (GHz kW/cm^2).