Absorption spectrum of atomic impurities in isotopic mixtures of liquid helium

We theoretically describe the absorption spectrum of atomic impurities in isotopic mixtures of liquid helium within a zero-temperature density functional approach. Two situations are considered. In the first one, the absorption spectrum of Na atoms attached to He-4(1000)-(HeN3)-He-3 droplets with N-3 values from 100 to 3000 is presented as a case study of an impurity that does not dissolve into helium droplets. In the second one, the absorption spectrum of Mg atoms in liquid He-3-He-4 mixtures is presented as a case study of an impurity dissolved into liquid helium. We have found that the absorption spectrum of the impurity is rather insensitive to the isotopic composition because the line shift is mostly affected by the total He density around the impurity, not by its actual composition. For bulk liquid mixtures, results are presented as a function of pressure at selected values of the He-3 concentration. The results for isotopically pure He-3 and He-4 liquids doped with Mg are compared with available experimental data.