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In this Letter, we investigate the time delay of photoelectrons by fullerenes shell in endohedrals. We present general formulas in the frame of the random phase approximation with exchange (RPAE) applied to endohedrals A@CN that consist of an atom A located inside of a fullerenes shell constructed of N carbon atoms C. We calculate the time delay of electrons that leave the inner atom A in course of A@CN photoionization. Our aim is to clarify the role that is played by CN shell. As concrete examples of A we have considered Ne, Fr, Kr and Xe, and as fullerene we consider C60. The presence of the C60 shell manifests itself in powerful oscillations of the time delay of an electron that is ionized from a given subshell nl by a photon with energy. Calculations are performed for outer, subvalent and d-subshells.
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We have calculated photoionization cross-section of endohedral atoms A@CN. We took into account the polarizability of the fullerene electron shell CN that modifies the incoming photon beam and the one-electron wave functions of the caged atom A. We employ simplifi
We concentrate here on photon absorption as well as electron and positron scattering upon endohedrals that consist of a fullerenes shell and an inner atom A. The aim is to understand the effect of fullerene electron shell in formation of corresponding cross-section. We consider the problem substituting the action of a complex multiatomic fullerenes shell by a combination of static pseudopotential and dynamic polarization potential. The electron correlations in the atom A are taken into account in the frame of the random phase approximation with exchange (RPAE). We demonstrate that the fullerenes shell strongly affects the cross-sections, bringing in a number of peculiarities, such as confinement resonances and giant-endohedral resonances and partial wave Ramsauer-type minima. Numerical data are obtained for endohedrals A@C60 and A@C60@C240, where A are noble gas atoms He, Ar and Xe.
We discuss the temporal picture of electron collisions with fullerene. Within the framework of a Dirac bubble potential model for the fullerene shell, we calculate the time delay in slow-electron elastic scattering by it. It appeared that the time of transmission of an electron wave packet through the Dirac bubble potential sphere that simulates a real potential of the C60 reaches up to 104 attoseconds. Resonances in the time delays are due to the temporary trapping of electron into quasi-bound states before it leaves the interaction region. As concrete targets we choose almost ideally spherical endohedrals C20, C60, C72, and C80. We present dependences of time-delay upon collision energy.
We demonstrate that the angular distribution of photoelectrons from a strongly polarizable target exposed to a laser field can deviate noticeably from the prediction of conventional theory. Even within the dipole-photon approximation the profile of distribution is modified due to the action of the field of alternating dipole moment induced at the residue by the laser field. This effect, being quite sensitive to the dynamic polarizability of the residue and to its geometry, depends also on the intensity and frequency of the laser field. Numerical results, presented for sodium cluster anions, demonstrate that dramatic changes to the profile occur for the photon energies in vicinities of the plasmon resonances, where the effect is enhanced due to the increase in the residue polarizability. Strong modifications of the characteristics of a single-photon ionization process can be achieved by applying laser fields of comparatively low intensities $I_0 sim10^{10}-10^{11}$ W/cm$^2$.
Within the framework of a Dirac bubble potential model for the C60 fullerene shell, we calculated the time delay in slow-electron elastic scattering by C60. It appeared that the time of transmission of an electron wave packet through the Dirac bubble potential sphere that simulates a real potential of the C60 cage exceeds by more than an order of magnitude the transmission time via a single atomic core. Resonances in the time delays are due to the temporary trapping of electron into quasi-bound states before it leaves the interaction region.
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