We have experimentally studied the electronic $3pleftarrow 3s$ excitation of Na atoms attached to $^3$He droplets by means of laser-induced fluorescence as well as beam depletion spectroscopy. From the similarities of the spectra (width/shift of absorption lines) with these of Na on $^4$He droplets, we conclude that sodium atoms reside in a ``dimple on the droplet surface. The experimental results are supported by Density Functional calculations at zero temperature, which confirm the surface location of sodium on $^3$He droplets, and provide a microscopic description of the ``dimple structure.
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