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The zero crossing of the dynamic differential scalar polarizability of the$S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be$459.1614(28)\,$THz. Together with previously determined matrix elements andbranching ratios, this tightly constrains the dynamic differential scalarpolarizability of the clock transition over a large wavelength range ($\gtrsim700\,$nm). In particular it allows an estimate of the blackbody radiation shiftof the clock transition at room temperature.

Magic wavelength of the $^{138}$Ba$^+$ $6s\;{}^2S_{1/2}-5d\;{}^2D_{5/2}$ clock transition