Generalized oscillator strength of endohedral molecules

Abstract

We investigate here the fast electron scattering upon endohedral atoms that present a fullerene C N staffed by an atom A, A@C N . We calculate the inelastic scattering cross-section expressing it via generalized oscillator strengths (GOS) density. We take into account two major effects of C N upon ionization of the atom A. Namely, the scattering of the electron by the static potential of the fullerenes shell and modification of the interaction between the fast incoming and atomic electrons due to polarization of the fullerenes shell by the incoming electron beam.To obtain the main features of the effect, we substitute the complex fullerenes shell C N by a static zero thickness potential, express its deformation under incoming electron action via C N polarizabilities. We perform all consideration in the frame of the so-called random phase approximation with exchange (RPAE) that gave reliable results for GOSes of isolated atoms, and expressions for absolute and differential in angle cross-sections. We limit ourselves with dipole and biggest non-dipole contributions to the differential in angle cross-section.We compare fast electron scattering with photoionization as a source of information on the target electronic structure and emphasize some advantages of fast electron scattering. As concrete objects of calculations, we choose noble gas endohedrals Ar@C 60 and Xe@C 60 . The results are presented for two transferred momentum q values: q=0.1 and 1.0. Even for small q=0.1, in the so-called optical limit, the deviation from photoionization case is prominent and instructive.As an interesting and very specific object, we study onion-type endohedrals A@C N1 @C N2 , in which the all construction A@C N1 is stuffed inside C N2 with N 2 >> N 1 .

Confinement approach to pressure effects on the dipole and the generalized oscillator strength of atomic hydrogen

“…This is a useful concept for the construction of the excitation function to account for the target energy absorption due to projectile momentum transfer [1]. This characteristic function not only pertains to ion-atom collision processes, but also to electron-atom collisions and photoionization processes [3][4][5][6]. In the limit of small momentum transfer, q → 0, the function becomes the dipole oscillator strength (DOS) to account for dipole optical transitions.…”

“…Recently, increasing attention has been focused on the study of photoionization cross sections of individual atoms inside endohedral fullerene cages for which giant resonances have been predicted [5,6,26] and observed [27]. Here, the GOSs play a major role and have been calculated through suitable confinement models.…”