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We have calculated ac polarizabilities of the $2 \ ^3S$ and $2 \ ^1S$ statesof both $^4$He and $^3$He in the range 318 nm to 2.5 $\mu$m and determined themagic wavelengths at which these polarizabilities are equal for either isotope.The calculations, only based on available ab initio tables of level energiesand Einstein A coefficients, do not require advanced theoretical techniques.The polarizability contribution of the continuum is calculated using a simpleextrapolation beyond the ionization limit, yet the results agree to better than1% with such advanced techniques. Several promising magic wavelengths areidentified around 320 nm with sufficient accuracy to design an appropriatelaser system. The extension of the calculations to $^3$He is complicated due tothe additional hyperfine structure, but we show that the magic wavelengthcandidates around 320 nm are predominantly shifted by the isotope shift.

Magic wavelengths for the $2 \ ^3S \to 2 \ ^1S$ transition in helium