Polarization of the C$_{60}$ cage by the photoelectron, interior static polarization of C$_{60}$ by the ion-remainder and atomic-core relaxation in $A$@C$_{60}$ photoionization

Abstract

Photoionization cross sections, σ nℓ , photoelectron angular-asymmetry parameters, β nℓ , and photoionization time delays, τ nℓ , for endohedral atoms, A@C60, are studied with account for both the individual and combined effects of dipole static polarization (DSP) of the C60 fullerene cage by the outgoing photoelectron, interior static polarization (ISP) of C60 by the ion-remainder, A + , and atomic-core relaxation of the encapsulated atom upon its ionization. It is unraveled by the direct calculations that the DSP effect is weak. It changes the phase of confinement-resonant oscillations in σ nℓ , β nℓ and τ nℓ without generally noticeable changes in their magnitudes, unless σ nℓ concentrates a relatively large part of oscillator strength of the continuum spectrum near threshold; then and there, the changes can be noticeable. This is counter-intuitive in view of a large dipole static polarizability of C60, α > 800 a.u.. Furthermore, it is demonstrated that the DSP effect results in the transmission of a part of oscillator strength of the continuum spectrum of A@C60 into its discrete spectrum. It is shown that the DSP effect is counteracted by ISP, thus getting partially cancelled out by the latter. Possible reasons behind the made findings are provided. Photoionization of Xe@C60, Ne@C60, H@C60 and some hypothetical C − 60 fullerene anions is chosen as a case study. For Xe@C60, the role of atomic-core relaxation of the ionized encapsuled Xe + -ion-remainder on the 4d photoionization of Xe@C60 is explored and detailed, and is revealed to be of utter significance, as in the known case of free Xe. The study is performed in the frameworks of both the random phase approximation with exchange (RPAE) and generalized RPAE (GRPAE), when needed. The C60 cage is modelled by a spherical attractive potential of a certain inner radius, thickness and depth. Its dipole static polarization potential is approximated by the Bates dipole static potential.

Role of polarizability of a C N fullerene cage in A@C N photoionization and e−–C N scattering: the size effect

“…Many theoretical results on this topic have been obtained in the framework of a model potential where the C N carbon cage is modeled either by a Dirac δ-like potential [7,8], or a U C (r) spherical attractive potential of a certain inner radius, thickness and depth [1,3,5,6,9], or the Woods-Saxon potential [10][11][12], or other potentials [13,14] (and numerous references in all the cited works above, as well as other references cited in text). A recent study [15,16] has provided the initial insight into photoionization of some A@C 60 s impacted by the polarization of a C 60 cage by the outgoing photoelectron.…”

“…With the impetus of [15,16], we study how the polarization impact by a polarized C N cage on both photoionization of A@C N and --e C N elastic electron scattering depends on the size of the cage. This is an interesting physics problem because the polarizability of a C N cage increases drastically with the increase of its size (see e. [17], a C N being the static dipole polarizability).…”