Absorption Spectrum of Na Atoms Attached to Helium Nanodroplets

We present an analysis of the electronic 3p <- 3s 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)Pi(1/2), (2)Pi(3/2) and (2)Sigma(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.