Non-dipole angular anisotropy parameters of semi-filled shell atoms

We present the results of calculations of outer shell non-dipole angular anisotropy parameters for semi-filled shell atoms in the Hartree-Fock (HF) one-electron approximation and with account of inter-electron correlations in the frame of the Spin Polarized Random Phase Approximation with Exchange (SP RPAE). We demonstrate for the first time that this characteristic of photoionization process is essentially sensitive to the fact whether the photoelectron has the same or opposite spin orientation to that of the semi-filled shell.Comment: 15 pages, 8 figure

Angular distributions of secondary electrons in fast particle-atom scattering

We present the angular distribution of electrons knocked out from an atom in a fast charge particle collision at small momentum transfer. It is determined not only by dipole but also by quadrupole transitions, the contribution of which can be considerably enhanced as compared to the case of photoionization. There the non-dipole parameters are suppressed as compared to the dipole ones by the parameter \omega R/c << 1, where is the photon energy, R is the ionized shell radius and c is the speed of light. This suppression in fast electron-atom collisions can be considerably reduced: the corresponding expansion parameter \omega R/ \nu << 1 is much bigger than in photoionization, since the speed of the incoming electron is much smaller than c. In formation of the angular distribution it is decisively important that the ionizing field in collision process is longitudinal, while in photoionization - it is transversal. We illustrate the general formulas by concrete results for outer s-, p-, and some nd-subshells of multi-electron noble gas atoms Ar, Kr and Xe, at several transferred momentum values: q=0.0, 0.1, 1.1, 2.1. Even for very small transferred momentum q, i.e. in the so-called optical limit, the deviations from the photoionization case are prominent.Comment: arXiv admin note: substantial text overlap with arXiv:1012.5465 and arXiv:1108.101

Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms

In this work we have calculated excitation energies and photoionization cross sections of Be and Ne in the exact-exchange (EXX) approximation of time-dependent density functional theory (TDDFT). The main focus has been on the frequency dependence of the EXX kernel and on how it affects the spectrum as compared to the corresponding adiabatic approximation. We show that for some discrete excitation energies the frequency dependence is essential to reproduce the results of time-dependent Hartree-Fock theory. Unfortunately, we have found that the EXX approximation breaks down completely at higher energies, producing a response function with the wrong analytic structure and making inner-shell excitations disappear from the calculated spectra. We have traced this failure to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting response function. Based on the adiabatic TDDFT formalism we propose a new way of deriving the Fano parameters of autoionizing resonances.Comment: 14 pages, 7 figure

On the photoionization of the outer electrons in noble gas endohedral atoms

We demonstrate the prominent modification of the outer shell photoionization cross-section in noble gas (NG) endohedral atoms NG@F under the action of the fullerene F electron shell. This shell leads to two important effects, namely to strong enhancement of the cross-section due to fullerenes shell polarization under the action of the incoming electromagnetic wave and to prominent oscillation of this cross-section due to the reflection of the photoelectron from NG by the F shell. All but He noble gas atoms are considered. The polarization of the fullerene shell is expressed via the total photoabsorption cross-section of F. The reflection of the photoelectron is taken into account in the frame of the so-called bubble potential that is a spherical zero --thickness potential. It is assumed in the derivations that NG is centrally located in the fullerene. It is assumed also, in accord with the existing experimental data, that the fullerenes radius R is much bigger than the atomic radius and the thickness of the fullerenes shell . These assumptions permit, as it was demonstrated recently, to present the NG@F photoionization cross-section as a product of the NG cross-section and two well defined calculated factors.Comment: 19 pages, 9 figure

Photoionization of Xe 3d electrons in molecule Xe@C60: interplay of intra-doublet and confinement resonances

We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe@C60. It is shown that the reflection of photoelectrons produced by the 3d Xe photoionization affects greatly partial photoionization cross-sections of and levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The calculations are performed treating the 3/2 and 5/2 electrons as electrons of different kinds with their spins "up" and "down". The effect of C60 shell is accounted for in the frame of the "orange" skin potential model.Comment: 13 pages, 12 figure

Density Functional Theory versus the Hartree Fock Method: Comparative Assessment

We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure

Two-electron photoionization of endohedral atoms

Using $He@C_{60}$ as an example, we demonstrate that static potential of the fullerene core essentially alters the cross section of the two-electron ionization differential in one-electron energy $d\sigma ^{++}(\omega )/d\epsilon$. We found that at high photon energy prominent oscillations appear in it due to reflection of the second, slow electron wave on the $C_{60}$ shell, which "dies out" at relatively high $\epsilon$ values, of about 2$\div$3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(\omega ,\epsilon)\equiv d\sigma ^{++}(\omega ,\epsilon)/d\sigma ^{a++}(\omega,\epsilon)$, where $d\sigma ^{a++}(\omega,\epsilon)/d\epsilon$ is the two-electron differential photoionization cross section. We have calculated the ratio $R_{i,ful}= \sigma_{i} ^{++}(\omega)/\sigma_{i}^{a++}(\omega)$, that accounts for reflection of both photoelectrons by the $C_{60}$ shell. We have calculated also the value of two-electron photoionization cross section $\sigma ^{++}(\omega)$ and found that this value is close to that of an isolated $He$ atom.Comment: 13 pages, 4 figure