Absorption Spectrum of Na Atoms Attached to Helium Nanodroplets

We present an analysis of the electronic 3 p ←3 s excitation of Na atoms attached to 3 He and 4 He droplets. Once the ground state structure of the doped drops has been obtained within finite-range density functional theory, we determine the time-correlation function of the Na atom evolving in the full three-dimensional 2 Π 1/2 , 2 Π 3/2 and 2 Σ 1/2 potentials generated by its pairwise interaction with the helium atoms. The Fourier analysis of the time-correlation function determines the absorption spectrum of Na, which is compared with the experimental spectrum. We show that the existence of a redshifted shoulder in the absorption line of Na@ 4 He N , absent in Na@ 3 He N , is due to the wider vibrational motion of the dopant atom in the dimple it causes on the surface of the droplet.