A Bethe theory for the directional dependence of stopping by molecules

We derive a Bethe formula for the stopping of swift ions by target molecules oriented with respect to the beam. The theory is characterized by a directional mean excitation energy formed from transition energies and dipole matrix elements. The expression for the mean excitation energy is similar to the one for an isotropic sample but the dipole matrix elements corresponding to the various transition moment directions carry unequal weights which depend on the orientation of the molecule with respect to the beam. For a large class of molecules, the logarithm of the mean excitation energy is linear in sin ² θ, where θ denotes the angle between the beam and the principal molecular axis. We illustrate the properties of the theory in the simple case of a diatomic molecule.