A theory for the isotropic Raman line shape in the condensed state

A theory for the isotropic Raman line shape (width and shift in particular) of diatomic molecules in the condensed state (liquid or solid) within the linear response formalism is presented. The prototypic system considered is that of a nitrogen argon mixture in any proportion. The two much discussed mechanisms which effect the lineshape (the vibrational modulation and the resonance transfer effects) appear naturally. The explicit concentration dependence of the width and shift is found while only the qualitative temperature dependence is determined. In particular, it is shown that the different temperature dependences of the line width in the liquid and solid states are simply related to the different types of collective modes which exist in the two states. It is also shown that the contributions to the width and shift of the above two mechanisms depend differently upon concentration and so can be separated experimentally.