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

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

Distortion and preservation of Giant resonances in Endohedral Atoms A@C60

It is demonstrated in this Letter that the effect of the fullerene shell upon atomic Giant resonance decisively depends upon energy of photoelectrons, by which the resonance decay. According to the prediction in [1], the Giant resonance in Xe is strongly modified in the endohedral Xe@C60 being transformed from a single broad and powerful maximum in Xe into four quite narrow but with almost the same total oscillator strength. On the contrary, the 4d Giant resonances in ions Ce3+ (the electronic structure that Ce has, when stuffed into fullerene), in Ce4+, and Eu are considered. In none of them the 4d Giant resonance in endohedrals is affected essentially. This is because the decay of the Giant resonances in these endohedrals proceeds by emission of fast photoelectrons that are almost unaffected by the C60 shell. The results obtained give at least qualitative explanation to the fact that recent observation of 4d Giant resonance in Ce@C82+, where the Giant resonance was observed as a maximum without noticeable structure.Comment: 10 pages, 5 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

Qualitative difference between the angular anisotropy parameters in fast electron scattering and photoionization

It is demonstrated for the first time that in spite of well known big similarities between atomic ionization by photons and fast electrons, a qualitative difference exists in angular anisotropy parameters of electrons knocked out in these processes. The difference is disclosed here and attributed to distinction between normal (transverse) and virtual (longitudinal) photons. Formulas are derived for dipole and non-dipole angular anisotropy parameters in fast electronatom scattering. The ratio of quadrupole-to-dipole matrix elements is determined by the parameter \omega R/v << 1 where \omega is the transferred in collision energy, R is the ionized shell radius and v is the speed of projectile. This factor can be much bigger than in the case of photoionization, where one has the speed of light c that is much bigger than v . We illustrate general formulas by concrete results for outer s-subshells of noble gas atoms Ar and Xe. Even for very small transferred momentum q, in the so-called optical limit, the deviation from photoionization case is prominent and instructive.Comment: 8 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1012.546