We discuss the complicated resonance structure of the endohedral atom photoionization cross section. Very strong enhancement and interference patterns in the photoionization cross-section of the valent and subvalent subshells of noble gas endohedral atoms A@C60 are demonstrated. It is shown also that the atomic Giant resonance can be either completely destroyed or remains almost untouched depending on the velocity of photoelectrons that are emitted in the resonance's decay process. These effects are results of dynamic modification of the incoming beam of radiation due to polarization of the fullerenes electron shell and reflection of photoelectrons be the fullerenes shell static potential. We have considered the outer np- and subvalent ns-subshells for Ne, Ar, Kr and Xe noble gas atoms. The modification of the Giant resonances is considered for a whole sequence of endohedrals with atoms and ions Xe, Ba, La, Ce+, Ce+4, Eu. The polarization of the fullerene shell is expressed via the total photoabsorption cross section. The photoelectron reflection from the static potential is taken into account in the frame of the so-called bubble potential that is a spherical -type potential.
We demonstrate that the structure of confinement resonances in the photoionization cross section of an endohedral atom is very sensitive to the mean displacement <a> of the atom from the cage center. The resonances are strongly suppressed if 2<a> exceeds the photoelectron half-wavelength. We explain the results of recent experiments which contradict the earlier theoretical predictions on the existence of confinement resonances in particular endohedral systems.
Considering the photoionization of Ar@C60, we predict resonant femtosecond decays of both Ar and C60 vacancies through the continua of atom-fullerene hybrid final states. The resulting resonances emerge from the interference between simultaneous autoionizing and intercoulombic decay (ICD) processes. For Ar 3s-->np excitations, these resonances are far stronger than the Ar-to-C60 resonant ICDs, while for C60 excitations they are strikingly larger than the corresponding Auger features. The results indicate the power of hybridization to enhance decay rates, and modify lifetimes and line profiles.
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.
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 photo…
We demonstrate serious misrepresentation of existing experimental data and important omissions in the List of references in the paper [1]. We demonstrate that what is called in [1] total photoionization cross-section is in fact a partial photoionization cross-section. We demonstrate that long before [1] and presented there experimental data for photoionization of Xe@C60+ were obtained, a theoretical prediction for Xe@C60 have been published that was in a reasonable agreement with experiment. These data are even not mentioned in [1].
We present the main features of the electronic structure of the heavy atoms that is best of all seen in photoionization. We acknowledge how important was and still is investigation of the interaction between low- and high frequency lasers with big intensity. We discuss the fullerenes and endohedrals as big atoms concentrating upon their most prominent features revealed in photoionization. Namely, we discuss reflection of photoelectron wave by the static potential that mimics the fullerenes electron shell and modification of the incoming photon beam under the action of the polarizable fullerene…
We demonstrate strong interference patterns in the photoionization cross-section of the subvalent subshells of noble gas (NG) endohedral atoms NG@F. This interference is a result of common action of three factors: the effect of neighboring atomic subshells, reflection of photoelectron waves by the fullerene F shell and resonance modification of the incoming photon beam by the complex effect under the action of the F electrons. We have considered the outer ns-subshells for Ne, Ar, Kr and Xe noble gas atoms. The polarization of the fullerene shell is expressed via the F total photoabsorption cro…
We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe, Cs and Ba endohedral atoms. It is shown that for all of the considered atoms the reflection by the fullerene shell of photoelectrons produced by the 3d subshell photoionization affects greatly partial photoionization cross-sections of 3d5/2 and 3d3/2 levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The results obtained demonstrate distinctive differences betw…
We study the double electronic emission by photon impact from He in the center of a spherical fullerene, which is modeled by a square-well shell. This system exhibits a manifold of avoided crossings as a function of the well depth, and present mirror colapses. However, this symmetry is broken in the triple differential cross section due to the delocalization of the He electrons in the initial state. Moreover, the fullerene potential involves higher angular momenta partial waves to be included in the process, which modifies the well-known two-lobe cross section from isolated He.
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 …
It is demonstrated that outer and inner electron shells, including that formed by collectivized electrons of the fullerene C60, affects dramatically the cross section of the subvalent ns-subshells of the noble gas endohedral atoms A@C60. The calculations are performed within the framework of a very simple, so-called "orange skin", model that makes it possible, in spite of its simplicity, to take into account the modification of the ns-subshell due to its interaction with inner and outer atomic shells, as well as with the collectivized electrons of the C60. As a concrete example, we consider th…
The localization of the valence electron of $H$, $Li$ and $Na$ atoms enclosed by three different fullerene molecules is studied. The structure of the fullerene molecules is used to calculate the equilibrium position of the endohedrally atom as the minimum of the classical $(N+1)$-body Lennard-Jones potential. Once the position of the guest atom is determined, the fullerene cavity is modeled by a short range attractive shell according to molecule symmetry, and the enclosed atom is modeled by an effective one-electron potential. In order to examine whether the endohedral compound is formed by a …
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 identif…
We investigate positron scattering upon endohedrals and compare it with electron-endohedral scattering. We show that the polarization of the fullerene shell considerably alters the polarization potential of an atom, stuffed inside a fullerene. This essentially affects both the positron and electron elastic scattering phases as well as corresponding cross-sections. Of great importance is also the interaction between the incoming positron and the target electrons that leads to formation the virtual positronium. We illustrate the general trend by concrete examples of positron and electron scatter…
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 …
We suggest an explanation of the recently observed discrepancy between the experimental and theoretical results on ionization of atoms, encapsulated into the fullerenes by photons with the energies of about 80-190eV. On the ground of previous theoretical considerations we conclude that the photoionization of the caged atom without excitation of the fullerene shell has low probability.
Photoionization cross section of the fullerene ion C60+ has been calculated within a single-electron approximation and also by using a consistent many-body theory accounting for many-electron correlations.
It is demonstrated that the fullerene shell affects dramatically the radiative and Auger vacancy decay of an endohedral atom A@C60. The collectivized electrons of the C60 shell add new possibilities for radiative and non-radiative decays similar to that in ordinary atoms where initial and final state vacancies almost always belong to different subshells. It is shown that the smallness of the atomic shell radii as compared to that of the fullerenes shell provides an opportunity to derive the simple formulas for the probabilities of the electron transitions. It is shown that the radiative and Au…
We demonstrate that the Auger decay rate in an endohedral atom is very sensitive to the atom's location in the fullerene cage. Two additional decay channels appear in an endohedral system: (a) the channel due to the change in the electric field at the atom caused by dynamic polarization of the fullerene electron shell by the Coulomb field of the vacancy, (b) the channel within which the released energy is transferred to the fullerene electron via the Coulomb interaction. % The relative magnitudes of the correction terms are dependent not only on the position of the doped atom but also on the t…
It is demonstrated that in photoabsorption by endohedral atoms some atomic Giant resonances are almost completely destroyed while the others are totally preserved due to different action on it of the fullerenes shell. As the first example we discuss the 4d10 Giant resonance in Xe@C60 whereas as the second serves the Giant autoionization resonance in Eu@C60. The qualitative difference comes from the fact that photoelectrons from the 4d Giant resonance has small energies (tens of eV) and are strongly reflected by the C60 fullerenes shell. As to the Eu@C60, Giant autoionization leads to fast phot…
It is demonstrated by the example of the Xe atom stuffed inside the C60 fullerene, that the so-called confinement resonances in 4d subshell strongly affect the photoionization cross-section of outer 5p and subvalent 5s electrons near 4d ionization threshold. It is a surprise that these narrow inner 4d shell resonances are not smeared out in the outer shell photoionization cross-section. On the contrary; the inner shell resonances affect the outer cross-section by enhancing them enormously. Close to its own photoionization thresholds, 5p and 5s photoionization cross-sections of Xe endohedral ar…
We analyze the role of shake-off and of the final state interactions in inelastic processes in the fullerene shell which follow ionization of the caged atom. We demonstrate that in the broad interval of the photon energies the process is dominated by the final state interactions. Its contribution is calculated in a model-independent way. In the large energy intervals the cross section of the process is close to that of photoionization of isolated atom.
The photoionization of a two-shell endohedral A@CN1@CN2 is considered. Formulas are presented for cross-sections and angular anisotropy parameters, both dipole and non-dipole. The effect of the fullerenes shell upon photoelectron from atom A is taken into account substituting the action of the fullerene by two zero-thickness "bubble potential". The fullerenes shells polarization is included assuming that the radius of the outer shell R2 is much bigger than the inner R1 and both much exceeds the atomic radius r. This permits to express the effect via CN1,N2 polarizabilities, which are connected…
We investigate here the fast electron scattering upon endohedral atoms that present a fullerene CN staffed by an atom A, A@CN. We calculate the inelastic scattering cross-section expressing it via generalized oscillator strengths (GOS) density. We take into account two major effects of CN upon ionization of the atom A. Namely, the scattering of the electron by the static potential of the fullerenes shell and modification of the interaction between the fast incoming and atomic electrons due to polarization of the fullerenes shell by the incoming electron beam. To obtain the main features of the…
The probability that photoionization of the caged atom in an endohedral system is accompanied by excitation of the fullerene shell is shown to be close to unity in broad intervals of the photoelectron energies. The result is obtained by summation of the perturbative series for the interaction between the photoelectron and the fullerene shell. This result means that the interaction between the photoelectron ejected from the cage atom and the fullerene shell cannot be described by a static potential, since inelastic processes become decisively important.
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)]
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 $dσ^{++}(ω)/dε$. 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 $ε$ values, of about 2$÷$3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(ω,ε)\equiv dσ^{++}(ω,ε)/dσ^{a++}(ω,ε)$, where $dσ^{a++}(ω,ε)/dε$ is the two-electron diff…
Powerful hybridization of the Cd 4$d$ state with the $d$-angular momentum state of C$_{60}$ $π$ symmetry is found in the local density approximation (LDA) structure of Cd@C$_{60}$ ground state. The photoionization of the resulting symmetric and antisymmetric levels are computed using the time dependent LDA method to include electron correlations. Cross sections exhibit effects of the C$_{60}$ plasmonic motion coherently coupled to the diffraction-type cavity oscillations induced by local emissions from C$_{60}$. The Cd@C$_{60}$ results exhibit a substantial difference from our previous results…
We discuss the influence of a single or double fullerenes shell upon photoionization and vacancy decay of an atom, stuffed inside the fullerenes construction. The main manifestations of this influence are additional structures in the photoionization cross-section and variation of the vacancy decay probability. The main mechanisms, with which fullerenes shells affect the processes in caged atoms is the scattering of the outgoing electrons by the fullerenes shell and modification of the photon beam due to fullerenes shell polarization. General consideration will be illustrated by numeric calcula…
Photoionization of two buckyonions, C$_{60}$@C$_{240}$ and C$_{20}$@C$_{60}$, is investigated by means of time-dependent density-functional theory (TDDFT). The TDDFT-based photoabsorption spectrum of C$_{60}$@C$_{240}$, calculated in a broad photon energy range, resembles the sum of spectra of the two isolated fullerenes, thus illustrating the absence of strong plasmonic coupling between the fullerenes which was proposed earlier. The calculated spectrum of the smaller buckyonion, C$_{20}$@C$_{60}$, differs significantly from the sum of the cross sections of the individual fullerenes because of…
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 pos…
We show that the theoretical predictions on high energy behavior of the photoionization cross section of fullerenes depends crucially on the form of the function $V(r)$ which approximates the fullerene field. The shape of the high energy cross section is obtained without solving of the wave equation. The cross section energy dependence is determined by the analytical properties of the function $V(r)$.
We have studied the energy dependence of several first scattering phases with multi-atomic object. As concrete examples representing the general trends endohedrals Neon inside C60 and Argon inside C60 are considered. It appeared that the presence of an inner atom, either Ne or Ar, qualitatively affects the scattering phases, in spite of the fact that the fullerene consists of 60 carbon atoms, while the atom staffed inside is only one. Calculations are performed in the one-electron Hartree-Fock (HF) and random phase approximation with exchange (RPAE) for the inner atom while the fullerenes shel…
Photoionization of a Xe atom confined inside C$_{60}$ has been studied using the random phase approximation with exchange (RPAE) method. The C$_{60}$ fullerene has been descr ibed by an attractive short range spherical well with potential $V(r)$, given by $V(r)=-V_ 0$ for $r_i<r<r_0$, otherwise $V(r)=0$ where $r_i$ and $r_0$ are respectively, the inner and outer radii of the spherical shell. The radial parts of the wave funct ion in the three regions $r<r_i$, $r_i<r<r_0$ and $r>r_0$ have been obtained by solving the Schrödinger equation using both regular and irregular solutions and the contin…
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.
In this Letter, we investigate the non-dipole effects in time delay of photoelectrons emitted by multi-electron atoms, negative ions, and respective endohedrals. We present the necessary general formulas in the frame of the random phase approximation with exchange (RPAE) applied to atoms, negative ions, and properly adjusted to endohedrals. We concentrate on low photon energy region, where non-dipole effects are very small in the cross-sections but become observable in angular distributions. We not only derive the formulas for non-dipole effects in time delay, but perform corresponding numeric…
The spatial distributions of electric charges forming the C60 shell have been analyzed with the Poisson equation. It has been shown that the modification of formulas for the rectangular-potential-well as a model potential of the C60 shell by means of addition to them the Coulomb-potential-like terms does not describe the monopole polarization of the shell by the electric charge Z in the center of the shell. The phenomenological potentials simulating the C60 shell potential should belong to a family of potentials with a non-flat bottom. In the paper some model potentials have been proposed and …
A theoretical proposal for reducing an entire atomic clock to micron dimensions. A phosphorus or nitrogen atom is introduced into a fullerene cage. This endohedral fullerene is then coated with an insulating shell and a number of them are deposited as a thin layer on a silicon chip. Next to this layer a GMR sensor is fabricated which is close to the endohedral fullerenes. This GMR sensor measures oscillating magnetic fields on the order of micro-gauss from the nuclear spins varying at the frequency of the hyperfine transition (413 MHz frequency). Given the micron scale and simplicity of this s…
Our previous studies [J. Phys. B 53, 125101 (2020); Euro. Phys. J. D 74, 191 (2020)] have predicted that the atom-fullerene hybrid photoionization properties for X = Cl, Br and I endohedrally confined in C60 are different before and after an electron transfers from C60 to the halogen. It was further found as a rule that the ionization dynamics is insensitive to the C60 level the electron originates from to produce X-@C60+. In the current study, we report an exception to this rule in F@C60. It is found that when the electron vacancy is situated in the C60 level that participates in the hybridiz…
The photon-ion merged-beams technique for the photoionization of mass/charge selected ionized atoms, molecules and clusters by x-rays from synchrotron radiation sources is introduced. Examples for photoionization of atomic ions are discussed by going from outer-shell ionization of simple few-electron systems to inner-shell ionization of complex many-electron ions. Fundamental ionization mechanisms are elucidated and the importance of the results for applications in astrophysics and plasma physics is pointed out. Finally, the unique capabilities of the photon-ion merged-beams technique for the …
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 en…
We have carried out theoretical investigations of electron correlation effects on the atomic properties of the Ca atom trapped inside an attractive spherically symmetric potential well of an endohedral fullerene C$_{60}$ cluster. Relativistic coupled-cluster (RCC) theory has been employed to obtain electron correlation energy, ionization potential and dipole polarizability of this atom. We have also performed calculations using the Dirac-Hartree-Fock (DF), relativistic second-order many-body perturbation theory (RMBPT(2) method) and relativistic random phase approximation (RRPA) to demonstrate…
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.
We consider photoionization of a system bound by the central potential $V(r)$. We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann--Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the an…
Inter-Coulombic decay (ICD) resonances in the photoionization of Cl@C60 endofullerene molecule are calculated using a perturbative density functional theory (DFT) method. This is the first ICD study of an open shell atom in a fullerene cage. Three classes of resonances are probed: (i) Cl inner vacancies decaying through C60 outer continua, (ii) C60 inner vacancies decaying through Cl outer continua, and (iii) inner vacancies of either system decaying through the continua of Cl-C60 hybrid levels, the hybrid Auger-ICD resonances. Comparisons with Ar@C60 results reveal that the properties of hybr…
We concentrate on several relatively new aspects of the study of fast electron scattering by atoms and atom-like objects, namely endohedral atoms and fullerenes. We show that the corresponding cross sections, being expressed via so-called Generalized Oscillator Strengths (GOS), give information on the electronic structure of the target and on the role of electron correlations in it. We consider what sort of information became available when analyzing the dependence of GOS upon their multipolarity, transferred momentum and energy. We demonstrate the role of nondipole corrections in the small-an…
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 endohedra…
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 $σ_{n\ell}$, $β_{n\ell}$ and $τ_{n\ell}$ without gene…
We continue our studies of the high energy nonrelativistic asymptotics for the photoionization cross section of the systems bound by a central field $V(r)$. We consider the bound states with the orbital momentum $\ell=1$. We show, that as well as for the $s$ states the asymptotics can be obtained without solving of the wave equations for the bound and outgoing electrons. The asymptotics of the cross sections is expressed in terms of the asymptotics of the Fourier transform $V(p)$ of the field and its derivative $V'(p)$ by employing the Lippmann--Schwinger equation. The shape of the energy depe…
Photoionization calculations of the endofullerene molecule Cl@$C_{60}$ with an open-shell chlorine atom are performed in the time-dependent local density approximation (TDLDA) based on a spherical jellium model. Cross sections for atom-fullerene hybrid photoemission studied show the effects of the hybridization symmetry, the giant plasmon and the molecular cavity. Comparisons with the results of Ar@$C_{60}$ provide insights in the role of a shell-closing electron and its influence on the dynamics. The results for Cl@$C_{60}$ are further compared with those of a more stable, lower energy config…
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…
