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 cross section. The photoelectron reflection from the static F potential is taken into account in the frame of the so-called bubble potential that is a spherical zero--thickness type potential. It is assumed in the derivations that NG is centrally located in the fullerene. It is assumed also, in accordance with the available experimental data, that the fullerene radius is much bigger than the atomic radius and the thickness of the fullerene shell. These assumptions permit, as demonstrated recently, the NG@F photoionization cross section to be presented as a product of the NG subvalent cross section and two calculated factors that account for polarization of the F electron shell and reflection of photoelectrons by the fullerene static potential.
Deep Dive into On photoionization of the subvalent subshells of noble gas endohedral atoms.
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 cross section. The photoelectron reflection from the static F potential is taken into account in the frame of the so-called bubble potential that is a spherical zero–thickness type potential. It is assumed in the derivations that NG is centrally located in the fullerene. It is assumed also, in accordance with the available experimental data, that the fullerene radius is much bigger than the atom
In this paper we will consider the photoionization of subvalent ns-subshells of noble gas (NG) endohedral atoms, formed by a fullerene F, inside which a noble gas atom is embedded, NG@F. We will present data on all the noble gases except He. In concrete calculations, as a fullerene F we will consider C 60 .
The pronounced action of the multi-electron neighboring shell upon a few-electron one was considered for the first time thirty-five years ago. As the first example, the influence of 3p 6 electrons upon the 3s 2 in Ar has been presented [1]. A more complicated case with three interacting subshells was considered in [2]. It was demonstrated that the 5p 6 and 4d 10 subshells act upon 5s 2 in Xe very strong, completely modifying the 5s 2 photoionization cross section. All corresponding calculations were performed in the frame of the so-called Random Phase Approximation with Exchange (RPAE). The first experimental confirmations of these predictions were obtained soon [3]. Since then the investigations of the effects of intershell interaction in atoms have become a permanent subject of research (see, e.g. [4,5]).
The physical nature of these intershell effects in photoionization is as follows. A manyelectron atomic subshell is polarized by an electromagnetic wave and a dipole moment is induced in it. Under the action of this dipole moment a neighboring atomic subshell is ionized. RPAE is extremely convenient to describe this effect. So, the ionization of a given electron can proceed via several pathways: directly, after photon absorption by the ionizing electron, and indirectly, in two or even several steps, via virtual excitation of other subshells. Since the electronic subshells in an atom are not separated spatially well enough, the amplitude of these two-or multi-step photo-processes cannot be expressed accurately enough via the dipole polarizability of the many-electron subshells.
In this sense the situation for the endohedral atoms NG@F is quite different. The radius of the fullerene shell significantly exceeds that of an encapsulated atom. This makes it possible for photoionization of the NG atom, in the first approximation, to consider the electronic sub-systems of the fullerene shell and atom as practically independent of each other. For this reason, the amplitude of atom photoionization going through virtual excitation of F shell electrons can be expressed directly via the dynamic polarizability of the fullerene shell ) (
. In those cases when the frequency of electromagnetic radiation is close to frequencies of plasma oscillations of the collectivized electrons of the fullerene, the role of this two-step process becomes decisively important, as the role of 4d 10 upon 5s 2 in isolated Xe.
Along with F shell polarization, one has to take into account also the reflection and refraction of the photoelectron wave, which goes from ns 2 subvalent shell, by the static potential of the fullerene. This reflection leads to formation of oscillating pattern of the cross section (see e.g. [6,7]).
As we will see below, the ns subshell photoionization in the endohedral system NG@F is a remarkable concrete example illustrating the role of the intershell interactions in the fullerene-like molecules, qualitatively similar but even much stronger than in the isolated atoms.
It has been demonstrated recently that the photoionization cross section of the Xe 5s subshell is strongly modified due to reflection of the photoelectron wave by the fullerene shell [8]. A simple method was developed to take into account this process. The potential of the C 60 shell was presented by of a zero-thickness δ -type bubble potential. In this approach the inner degrees of freedom of the C 60 shell, namely its ability to be polarized, was neglected.
Some time ago we investigated also the role of C 60 electron shell polarization upon the cross section of 5s 2 electrons in Xe@C 60 [9]. We expressed there the effect of the C 60 shell via the fullerene dipole polarizability and the latter was calculated using considerably simplified expression for the experimental photoabsorption cross section of the C 60 . It appeared, however, that its shape essentially affects the polarizability [10]. That is why here we will not relay on the numerical results in [9] and recalculate them.
Recently, a great deal of attention has been and still is concentrated on photoionization of endohedral atoms. It was demonstrated in a number of papers [11][12][13][14][15][16][17][18][19] that the C 60 shell adds prominent resonance structure in the photoionization cross section of endohedral atoms. Although the experimental investigation of A@C 60 photoionization seems to be very difficult at this moment, these objects will be inevitably intensively studied in the future 1 . This justifies the current efforts of the theorists in predicting rather non-trivial effects waiting for verification.
We will show in this paper that the dynamic polarization of C 60 drast
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