Generalized Oscillator Strength of Endohedral Molecules

We calculate here the main characteristic of the fast electron scattering on endohedrals, namely their generalized oscillator strength (GOS), total and differential in the angle of atomic electron emission. Endohedrals are atoms A staffed inside the fullerene CN and denoted as A@CN. We take into account two major effects of CN on ionization of the atom A: the scattering of the emitted electron by the static potential of the fullerenes shell and the modification of the interaction between the fast incoming and atomic electrons due to polarization of the fullerenes shell by the incoming electron beam. We substitute the complex fullerenes shell CNby a static zero thickness potential, and express its deformation under incoming electron action via CNpolarizabilities. We perform all consideration in the frame of the random phase approximation with exchange that gave reliable results for GOSes of isolated atoms. We limit ourselves with the dipole and the biggest nondipole contributions to the differential in angle GOSes. We compare differential in angle GOSes with differential in angle photoionization cross-section as a source of information on the target electronic structure and emphasize some advantages of the fast electron scattering. The concrete objects of calculations are noble gas endohedrals Ar@C60 and Xe@C60, and the results are presented for two transferred momentum q values, q = 0.1 and 1.0. Even for small q = 0.1, in the optical limit, the deviation from photoionization case is prominent and instructive. We demonstrate impressive new features of GOSes that appear due to fullerenes shell actions—regular oscillations and very big maxima. As an interesting and very specific object, we study onion-type endohedrals A@CN1@CN2, in which the construction A@CN1 is stuffed inside CN2 with N2 >> N1. The consideration is similar to that developed in our recent article on total and differential in angle GOSes of isolated atoms (Amusia et al., Phys. Rev. 2012, A 85, 042722). © 2012 Wiley Periodicals, Inc.