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 continuous boundary conditions at $r_i$ and $r_0$. The photoionization cross sections for the Xe 4d, $5s$ and $5p$ ele ctrons in the Xe@C$_{60}$ endohedral molecule have been evaluated and compared with those of the photoionization for the free Xe atom and other previo us calculations for the Xe@C$_{60}$ fullerene. Our method surmounted the weaknesses of the previous model potential calculation s and demonstrated significantly stronger correlated confinement resonances for the Xe@C$_{60}$ photoionization.
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.
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 $V(r)$.
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.
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.
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…
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.
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 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 fu…
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…
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 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 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…
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…
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.
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…
Photoionization of the Ce$^{3+}$ - Ce$^{4+}$ process has been studied using the random phase approximation with exchange method in the energy region 100-150 eV. Comparison of our results with the recent measurement [Müller {\it et al}, Phys. Rev. Lett. {\bf 101}, 133001 (2008)] confirms the suppression effect of the carbon cage in the endohedral fullerene Ce@C$_{82}^+$ photoionization. The reasons for the cause of the confinement resonance and the suppression effect are discussed.
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.
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 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.
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…
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…
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 …
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…
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.
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…
By considering photoionization of the C$_{60}$ fullerene, we elucidate the contributions of various classical and quantum physics phenomena appearing in this process. By comparing the results, based on the {\it ab initio} and model approaches, we map the well-resolved features of the photoabsoprtion spectrum to single-particle and collective excitations which have the different physical nature. It is demonstrated that the peculiarities arising in the photoionization spectrum of C$_{60}$ atop the dominating plasmon excitations have the quantum origin. In particular, we demonstrate that a series…
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 demonstrate an effective method for calculating bound-to-continuum cross-sections by examining transitions to bound states above the ionization energy that result from placing the system of interest within an infinite spherical well. Using photoionization of the hydrogen atom as an example, we demonstrate convergence between this approach for a large volume of confinement and an exact analytical alternate approach that uses energy-normalized continuum wavefunctions, which helps to elucidate the implementation of Fermi's Golden Rule. As the radius of confinement varies, the resulting changes…
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…
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 …
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…
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…
We produce large numbers of low-energy ions by photoionization of laser-cooled atoms inside a surface-electrode-based Paul trap. The isotope-selective trap loading rate of $4\times10^{5}$ Yb$^{+}$ ions/s exceeds that attained by photoionization (electron impact ionization) of an atomic beam by four (six) orders of magnitude. Traps as shallow as 0.13 eV are easily loaded with this technique. The ions are confined in the same spatial region as the laser-cooled atoms, which will allow the experimental investigation of interactions between cold ions and cold atoms or Bose-Einstein condensates.
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…
Considering the photoionization of Ar@C60 and Kr@C60 endofullerenes, the decay of C60 innershell excitations through the outershell continuum of the confined atom via the inter-Coulombic decay (ICD) pathway is detailed. Excitations to atom-C60 hybrid states demonstrate coherence between ICD and electron-transfer mediated decay (ETMD). This should be the dominant above-threshold decay process for a variety of confined systems, and the strength of these resonances is such that they should be amenable for study by photoelectron spectroscopy.
We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on Rydberg-atom lifetime ranges from noticeable to highly dominant when compared with natural decay. The PI behavior is governed by the generally rapid decrease of the PI cross sections as a function of angular-momentum ($\ell$), and by lattice-induced $\ell$-mixing across the optical-lattice PECs. In GHz-deep lattices, $\ell$-mixing leads to a rich P…
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…
In this work, we consider the hydrogen atom confined inside a penetrable spherical potential. The confining potential is described by an inverted-Gaussian function of depth $ω_0$, width $σ$ and centered at $r_c$. In particular, this model has been used to study atoms inside a $C_{60}$ fullerene. For the lowest values of angular momentum $l=0,1,2$, the spectra of the system as a function of the parameters ($ω_0,σ,r_c$) is calculated using three distinct numerical methods: (i) Lagrange-mesh method, (ii) fourth order finite differences and (iii) the finite element method. Concrete results with no…
