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We study the interconnection between the results of two qualitatively different approximate calculations of photoionization cross sections, $\sigma_{n\ell}$, for neutral atoms ($A$) or their cations ($A^+$), centrally confined inside a fullerene-anion shell, $C_{N}^{q}$ , where $q$ represents the negative excess charge on the shell. One of the approximations, frequently employed in previous studies, assumes a uniform excess negative charge distribution over the entire fullerene shell, by analogy with a charged metallic sphere. The other approximation, not previously discussed in the literature, considers the quantum states of the excess electrons on the shell, determined by specific $n$ and $\ell$ values of their quantum numbers. Remarkably, both methods yield photoionization cross sections for the encapsulated species that are close to each other. Consequently, we find that the photoionization of the encapsulated atoms or cations inside a $C_{N}^{q}$ anion is minimally influenced by the quantum states of the excess electrons on the fullerene shell. Furthermore, we demonstrate that the aforementioned influence decreases even further with an increasing size of the confining fullerene shell. All this holds true at least under the assumption that the confined atom or cation is compact, i.e., its electron density remains primarily within itself rather than being drawn into the fullerene shell. This remarkable finding results from Hartree-Fock calculations combined with a popular modeling of the fullerene shell, where it is modeled by an attractive spherical annular potential., Comment: 8 pages, 5 figures

We theoretically study the positron elastic scattering by an atom with a multielectron semifilled subshell in its structure. The positron scattering by the Mn($...3d^{5}4s^{2}$,$^{6}S)$ atom with a $3d^{5}$ semifilled subshell ($e^{+}+Mn$ scattering) is chosen as a case study. We account for both the electron correlation and the formation of a $e^{+}+e^{-}$ virtual positronium (Ps) in the intermediate states of the $e^{+}+Mn$ system. Electron correlation is taken into account in the framework of the self-energy part of the scattering positron Green function generalized for the application to semifilled-shell atoms. The influence of the virtual Ps formation on $e^{+}+Mn$ scattering is taken into account by the reduction of the energy of the virtual \textit{positron plus atomic-excited-configuration} states by the Ps-binding energy, to a reasonable approximation. We unravel the importance and specificity of the influence of both the virtual Ps and electron correlation on $e^{+}+Mn$ elastic scattering. We demonstrate spectacular differences between the electron and positron scattering processes., Comment: 9 pages, 8 figures

We prove in the present paper that a simple modeling of a complicated highly polarizable C$_{60}$ target by a rectangular (in a radial coordinate) square well potential in combination with the static polarization potential provides a viable approximation for a low-energy elastic electron scattering off this target. The proof is based on the results of the comparison of the calculated angle-differential elastic electron scattering cross section off C$_{60}$ versus corresponding experimental data., Comment: 4 pages, 3 figures

We provide the initial insight into the angle-differential photodetachment spectra of fullerene anions beyond the dipole approximation by utilizing a broadly used modelling of C$_{n}$. In the model, the C$_{n}$ cage is approximated by a spherical attractive potential of a certain inner radius, thickness and depth which binds an external electron, thereby turning into a C$_{n}^{-}$ anion. It is demonstrated in the framework of the utilized model, which a single-electron model in its essence, that the dipole and dipole-quadrupole approximations might get broken down in the angle-differential photodetachment spectra of fullerene anions, C$_{n}^{-}$, at a great number of photon energies of only a few tens of eV. Moreover, the breakdown occurrences are shown to start developing at lower photon energies, and the frequency of the occurrences grows with increasing size of C$_{n}^{-}$. The findings are demonstrated by direct calculations of angle-differential photodetachment cross sections of the C$_{60}^{-}$, C$_{240}^{-}$, C$_{540}^{-}$ and C$_{1500}^{-}$ anions. It is not clear beforehand how electron correlation might affect the predicted anomalies in the C$_{n}^{-}$ angle-differential photodetachment spectra, so that the verification(s) of the predicted breakdowns by means of more sophisticated theories is urged., Comment: 7 pages, 4 figures, 33 references, regular paper

Photoionization cross sections, photoelectron angular-asymmetry parameters and photoionization time delays for $A$@C$_{60}$ endohedral atoms are studied with account for both the individual and combined effects of dipole static polarization (DSP) of C$_{60}$ by the outgoing photoelectron, interior static polarization (ISP) of C$_{60}$ by the ion-remainder, $A^{+}$, and atomic-core relaxation of the encapsulated atom upon its ionization. It is unraveled that the DSP effect is weak; it changes the phase of confinement-resonant oscillations in $\sigma_{n\ell}$, $\beta_{n\ell}$ and $\tau_{n\ell}$ without generally noticeable changes in their magnitudes, unless $\sigma_{n\ell}$ concentrates a relatively large part of oscillator strength of the continuum spectrum near threshold. This is counter-intuitive in view of a large dipole static polarizability of C$_{60}$, $\alpha > 800$ $a.u.$. Furthermore, it is demonstrated that the DSP effect results in the transmission of a part of oscillator strength of the continuum spectrum of $A$@C$_{60}$ into its discrete spectrum. It is shown that the DSP effect is counteracted by ISP. Possible reasons behind the made findings are provided. Photoionization of Xe@C$_{60}$, Ne@C$_{60}$, H@C$_{60}$ and some hypothetical C$^{-}_{60}$ fullerene anions is chosen as a case study. For Xe@C$_{60}$, the role of atomic-core relaxation of the ionized encapsuled Xe$^{+}$-ion-remainder on the $\rm 4d$ photoionization of Xe@C$_{60}$ is revealed to be of utter significance, as in free Xe. The random phase approximation with exchange (RPAE) and generalized RPAE were used in the study. The C$_{60}$ 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., Comment: 16 pages, 19 figures, regular paper

A deeper insight into electron elastic scattering off endohedral fullerenes $A$@C$_{60}$ is provided. The study accounts for polarization of both the encapsulated atom $A$ and C$_{60}$ cage by an incident electron. It is carried out in the framework of the combination of both a model and the first-principle approximations. A core principle of the model is that the C$_{60}$ cage itself is presented by an attractive spherical potential of a certain inner radius, thickness, and depth. The main idea of the first-principle approximation is that the polarization of $A$@C$_{60}$ by an incident electron is accounted with the help of the Dyson equation for the self-energy part of the Green's function of an incident electron. Calculations are performed for, and comparison is made between the individual cases: (a) when $A$@C$_{60}$ is regarded as a static system, (b) when C$_{60}$ is a static cage, but the encapsulated atom is polarizable, (c) when both C$_{60}$ and $A$ are polarized simultaneously but independently of each other, and (d), as the most general scenario, when polarizabilities of C$_{60}$ and $A$ are coupled. Spectacular similarities and discrepancies between results of each of the exploited approximations are demonstrated. Revealed features of the overall significant impact of $A$@C$_{60}$ polarization by an incident electron on its elastic scattering off $A$@C$_{60}$ are demonstrated. Choosing Ne, Xe, and Ba as "probing" atoms, the dependence of $e + A@{\rm C_{60}}$ scattering on the size and polarizability of the encapsulated atom is unraveled., Comment: 9 pages, 6 figures, submitted to Physical Review A

Angular dependence of photoemission time delay for the valence $np_{3/2}$ and $np_{1/2}$ subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.

This work describes the first observations of the ionisation of neon in a metastable atomic state utilising a strong-field, few-cycle light pulse. We compare the observations to theoretical predictions based on the Ammosov-Delone-Krainov (ADK) theory and a solution to the time-dependent Schrodinger equation (TDSE). The TDSE provides better agreement with the experimental data than the ADK theory. We optically pump the target atomic species and demonstrate that the ionisation rate depends on the spin state of the target atoms and provide physically transparent interpretation of such a spin dependence in the frameworks of the spin-polarised Hartree-Fock and random-phase approximations., Comment: 12 pages, 6 figures

The present paper explores possible features of electron elastic scattering off endohedral fullerenes $A$@C$_{60}$. It focuses on how dynamical polarization of the encapsulated atom $A$ by an incident electron might alter scattering off $A$@C$_{60}$ compared to the static-atom-$A$ case, as well as how the C$_{60}$ confinement modifies the impact of atomic polarization on electron scattering compared to the free-atom case. The aim is to provide researchers with a "relative frame of reference" for understanding which part of the scattering processes could be due to electron scattering off the encapsulated atom and which due to scattering off the C$_{60}$ cage. To meet the goal, the C$_{60}$ cage is modeled by an attractive spherical potential of a certain inner radius, thickness, and depth which is a model used frequently in a great variety of fullerene studies to date. Then, the Dyson equation for the self-energy part of the Green's function of an incident electron moving in the combined field of an encapsulated atom $A$ and C$_{60}$ is solved in order to account for the impact of dynamical polarization of the encaged atom upon $e + A@{\rm C_{60}}$ scattering. The Ba@C$_{60}$ endohedral is chosen as the case study. The impact is found to be significant, and its utterly different role compared to that in $e + Ba$ scattering is unraveled., Comment: 7 pages, 5 figures, published in Phys. Rev. A, the attached file is the original authors' file, i.e., not a PRA copyedited file

Electron elastic-scattering phase shifts and cross sections along with the differential and total cross sections and polarization of low-frequency bremsstrahlung upon low-energy electron collision with endohedral fullerenes $A$@C$_{60}$ are theoretically scrutinized versus the nature, size and spin of the encapsulated atom $A$. The case-study-atoms $A$ are N, Ar, Cr, Mn, Mo, Tc, Xe, Ba, and Eu. They are thoughtfully picked out of different rows of the periodic table. The study is performed in the framework of a model static approximation. There, both the encapsulated atom $A$ and C$_{60}$ cage are regarded as non-polarizable targets. The C$_{60}$ cage is modeled by an attractive spherical annular potential well. The study provides the most complete initial understanding of how the processes of interest might evolve upon electron collision with various $A$@C$_{60}$. Calculated results identify the most interesting and/or useful future measurements or more rigorous calculations to perform., Comment: 44 pages, 22 figures, 28 references. Unfortunate typos in the original submission - version 1 - are corrected

The initial insight into time delay in Mn photoionization in the region of the $3p \to 3d$ giant autoionization resonance is gained in the framework of the "spin-polarized" random phase approximation with exchange. The dramatic effect of the giant autoionization resonance on time delay of photoemission from the $3d$ and $4s$ valence subshells of the Mn atom is unraveled. Strong sensitivity of the time delay of the $4s$ photoemission to the final-state term of the ion-remainder [${\rm Mn^{+}}(4s^{1},$$^{5}S)$ vs.~${\rm Mn^{+}}(4s^{1},$$^{7}S)$] is discovered. It is shown that photoionization time delay in the autoionizing resonance region is explicitly associated with the resonance lifetime, which can, thus, be directly measured in attosecond time delay experiments. Similar features are expected to emerge in photoionization time delays of other transition-metal and rare-earth atoms with half-filed subshells that possess giant autoionization resonances as well., Comment: 8 pages, 4 figures, 49 references

A question whether there exists an interaction between the spins of the endohedral atom $A$@C$_{60}$ and the properties of the confining shell which might affect the alignment of, or manipulation by, the spins for building a register for a quantum computer is discussed. It is argued that an effect, termed the `C$_{60}$ spin-charging' effect, can occur in endohedral atoms and would affect the operation of a quantum register. The effect is exemplified by choosing the $\rm 3d$ (Cr and Mn) and $\rm 4d$ (Mo and Tc) transition metal atoms as well as a rare-earth Eu atom as the case study. A class of high-spin atoms which are less suitable for building a quantum register is, thus, identified., Comment: 5 pages, 1 figure, submitted to J. Phys. B: At. Mol. Opt. Phys

Electron elastic scattering off a spin-polarized Cr(...$3d^{5}4s^{1}$, $^{7}S$) atom is theoretically studied in the region of electron energies up to $15$ eV using both a one-electron "spin-polarized" Hartree-Fock and multielectron "spin-polarized" random phase approximation with exchange. It is found that scattering phase shifts of oppositely spin-polarized incoming electrons and corresponding cross sections of the scattering reactions significantly differ from each other, in general, even without accounting for spin-orbit interaction. This is shown to be associated with the presence of two semifilled $3d^{5}$ and $4s^{1}$ subshells in the Cr's configuration which induce considerably different exchange in the interaction of oppositely spin-polarized incoming electrons with the atom-target. The importance of electron correlation in $e^{-}+\rm Cr$ elastic scattering process is revealed. Moreover, correlation is shown to induce strong differences between scattering of oppositely spin-polarized electrons off Cr. A physically transparent interpretation for the latter is provided., Comment: 6 pages, 7 figures, submitted to Phys. Rev. A

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C$_{60}$ cage have been studied theoretically using both relativistic and non-relativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the $4d$ shell of Xe@C$_{60}$ and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C$_{60}$ [PRL 111, 203003 (2013)]

The initial insight into electron elastic scattering off endohedral fullerenes A@C60 is gained in the framework of a theoretical approach where the C60 cage is modelled by a rectangular (in the radial coordinate) potential well, as in many other A@C60 studies. The effect of a noticeably weaker electron elastic scattering off A@C60 compared to that off empty C60 or even the isolated atom A itself, as well as a strong sensitivity of e + A@C60 scattering to the spin of the captured atom A are unraveled, for certain kinds of atoms. Obtained results lay out the initial qualitative basis for identifying interesting measurements and/or more rigorous calculations of e + A@C60 elastic scattering to perform., Comment: 12 pages, 5 figures, submitted to J. Phys. B

The impacts of both exchange interaction and electron correlation, as well as their combined impact, on electron elastic scattering off a semifilled shell Mn(...$3d^{5}$$4s^{2}$, $^{6}S$) atom are theoretically studied in the electron energy range of $\epsilon= 0-25$ eV. Corresponding elastic scattering phase shifts $\delta_{\ell}(\epsilon)$ as well as partial $\sigma_{\ell}(\epsilon)$ and total $\sigma(\epsilon)$ cross sections are found to be subject to a strong correlation impact. The latter is shown to be drastically different for oppositely spin-polarized scattered electrons, in some cases, thereby bringing significant differences in corresponding $\delta_{\ell}(\epsilon)$s, $\sigma_{\ell}(\epsilon)$s, and $\sigma(\epsilon)$s between said electrons. This is proven to be an inherent features of electron scattering off a semifilled shell atom in general. Electron correlation is accounted for in the framework of the self-energy part $\Sigma$ of the Green function of a scattered electron concept. The latter is calculated both in the second-order perturbation theory in the Coulomb interelectron interaction as well as beyond it by solving the Dyson equation for $\Sigma$. The significance of the "Dyson" correlation corrections in e$^{-}+$Mn scattering is unraveled. They are shown to aggravate noticeably the inherent differences between elastic scattering phase shifts and cross sections of spin-up ($\uparrow$) and spin-down ($\downarrow$) polarized electrons scattered off a spin-polarized Mn atom, in some cases. In particular, the existence of a narrow resonant maximum in $\sigma^{\downarrow}(\epsilon)$ near $\epsilon \approx 8$ eV but the absence of such in $\sigma^{\uparrow}(\epsilon)$ in e$^{-}+$Mn scattering is predicted., Comment: 8 pages, 6 figures, submitted to Phys. Rev. A

Alternate contraction and drastic expansion, i.e., `breathing' of electronic subshells, the effects of fusion of two subshells into one subshell and its subsequent fission (splitting) into the original subshells, as well as multiple alteration of the order of subshells in confined semifilled shell atoms with a progressively narrowing confinement are theoretically discovered. The confinement is represented by a repulsive penetrable spherical potential of an inner radius $r_{0}$. The effects are exemplified by calculated data for confined semifilled shell atoms from the second, third and fourth rows of Mendeleev's table - Li, N, P and Cr atoms with semifilled ${2\rm s}^{1}$, ${2\rm p}^{3}$, ${3\rm p}^{3}$ and ${3\rm d}^{5}$ subshells, respectively - for the completeness of the study. The underlying physics behind the discovered effects is explained., Comment: 15 pages, 7 figures; to be submitted to J. Phys. B: At. Mol. Opt. Phys

The hydrogen atom under the pressure of a spherical penetrable confinement potential of a decreasing radius $r_{0}$ is explored, as a case study. A novel counter-intuitive effect of atomic swelling rather than shrinking with decreasing $r_{0}$ is unraveled, when $r_{0}$ reaches, and remains smaller than, a certain critical value. Upon swelling, the size of the atom is shown to increase by an order of magnitude, or more, compared to the size of the free atom. Examples of changes of photoabsorption properties of confined hydrogen atom upon its swelling are uncovered and demonstrated., Comment: 5 pages, 4 figures

Attention: this version-$2$ of the manuscript differs from its previously uploaded version-$1$ (arXiv:1112.6158v1) and subsequently published in 2012 J. Phys. B \textbf{45} 105102 only by a removed typo in Eq.(2) of version-$1$; there was the erroneous factor "2" in both terms in the right-hand-side of the Eq.(2) of version-$1$. Now that the typo is removed, Eq.(2) is correct. A perceived advantage for the replacement of a discontinuous square-well pseudo-potential, which is often used by various researchers as an approximation to the actual C$_{60}$ cage potential in calculations of endohedral atoms $A$@C$_{60}$, by a more realistic diffuse potential is explored. The photoionization of endohedral H@C$_{60}$ and Xe@C$_{60}$ is chosen as the case study. The diffuse potential is modelled by a combination of two Woods-Saxon potentials. It is demonstrated that photoionization spectra of $A$@C$_{60}$ atoms are largely insensitive to the degree $\eta$ of diffuseness of the potential borders, in a reasonably broad range of $\eta$'s. Alternatively, these spectra are found to be insensitive to discontinuity of the square-well potential either. Both potentials result in practically identical calculated spectra. New numerical values for the set of square-well parameters, which lead to a better agreement between experimental and theoretical data for $A$@C$_{60}$ spectra, are recommended for future studies., Comment: 11 pages, 4 figures

The impact of both confinement and electron correlation on generalized oscillator strengths (GOS's) of endohedral atoms, A@C60, is theoretically studied choosing the Xe@C60 4d, 5s, and 5p fast electron impact ionization as the case study. Calculations are performed in the transferred to the atom energy region beyond the 4d threshold, omega = 75--175 eV. The calculation methodology combines the plane wave Born approximation, Hartree-Fock approximation, and random phase approximation with exchange in the presence of the C60 confinement. The confinement is modeled by a spherical delta-function-like potential as well as by a square well potential to evaluate the effect of the finite thickness of the C60 cage on the Xe@C60 GOS's. Dramatic distortion of the 4d, 5p, and 5s GOS's by the confinement is demonstrated, compared to the free atom. Considerable contributions of multipolar transitions beyond dipole transitions in the calculated GOS's is revealed, in some instances. The vitality of accounting for electron correlation in calculation of the Xe@C60 5s and 5p GOS's is shown., Comment: 7 pages, 3 figures, submitted to Physical Review A

Re-evaluated parameters for the square-well potential model for photoionization of endo-fullerenes are proposed and employed to reveal the spectacular modifications in the Xe 4d photoionization giant resonance along the path from Xe@C60 to Xe@C240 to multi-walled Xe@C60@C240., Comment: 1 page, 1 figure. 2011 International Conference on Photonic, Electronic, and Atomic Collisions (Belfast, UK, 2011), abstract Tue131

Spectacular trends in the modification of the Xe 5s photoionization via interchannel coupling with confinement resonances emerging in the Xe 4d giant resonance upon photoionization of the Xe@C60, Xe@C240 and Xe@C60@C240 endo-fullerenes are theoretically unraveled and interpreted., Comment: 1 page, 1 figure. 2011 International Conference on Photonic, Electronic, and Atomic Collisions (Belfast, UK, 2011). Paper number We158

Possible reasons that confinement resonances are not observed in a recent photoionization experiment on the endohedral fullerene Ce@C82+ are explored. The effect of the polarization of the fullerene shell in response to the ionization of the endohedrally encaged atom A@Cn, termed the "shielding" effect, has been investigated and found to be relatively small; no more than a 20% effect near threshold, and much less at higher energies. It is argued that most likely, the absence of confinement resonances in Ce@C82+ is due primarily to the finite thickness of the carbon cage; the off-the-center position and thermal vibration of the encaged atom, discussed elsewhere, further weaken the resonances rendering them beyond the sensitivity of the experiment to detect, in this case. For other situations/endohedrals, the confinement resonances should well be observable, and Ne@C60 is suggested as an excellent candidate., Comment: 4 pages, 3 figures, Revtex4, to be submitted to Phys. Rev. A.

Trends in resonances, termed confinement resonances, in photoionization of atoms A in endohedral fullerene anions A@C60^{z-} are theoretically studied and exemplified by the photoionization of Ne in Ne@C{60}^{z-}. Remarkably, above a particular nl ionization threshold of Ne in neutral Ne@C60 (I_{nl}^{z=0}), confinement resonances in corresponding partial photoionization cross sections sigma_{nl} of Ne in any charged Ne@C60^{z-} remain almost intact by a charge z on the carbon cage, as a general phenomenon. At lower photon energies, omega < I_{nl}^{z=0}, the corresponding photoionization cross sections develop additional, strong, z-dependent resonances, termed Coulomb confinement resonances, as a general occurrence. Furthermore, near the innermost 1s ionization threshold, the 2p photoionization cross section sigma_{2p} of the outermost 2p subshell of thus confined Ne is found to inherit the confinement resonance structure of the 1s photoionization spectrum, via interchannel coupling. As a result, new confinement resonances emerge in the 2p photoionization cross section of the confined Ne atom at photoelectron energies which exceed the 2p threshold by about a thousand eV, i.e., far above where conventional wisdom said they would exist. Thus, the general possibility for confinement resonances to resurrect in photoionization spectra of encapsulated atoms far above thresholds is revealed, as an interesting novel general phenomenon., Comment: 6 pages, 4 figures, Latex2e, jpconf.cls style

It is discovered theoretically that significant confinement resonances in an $nl$ photoionization of a \textit{multielectron} atom $A$ encaged in carbon fullerenes, A@C$_{60}$, may re-appear and be strong at photon energies far exceeding the $nl$ ionization threshold, as a general phenomenon. The reasons for this phenomenon are unraveled. The Ne $2p$ photoionization of the endohedral anion Ne@C$_{60}^{5-}$ in the photon energy region of about a thousand eV above the $2p$ threshold is chosen as case study., Comment: 3 pages, 1 figure, Revtex4