No abstract

Three different types of resonances arise in the photoionization spectra of atoms endohedrally confined within a fullerene cage: atomic resonances, confinement resonances and molecular resonances. In each case, a different mechanism is involved, and different theoretical models are necessary for their study. In this work, we exploit the flexibility of the spherical modelpotential method to explore the properties of confinement resonances. Both repulsive and attractive shells are considered. It is demonstrated that the nature of confinement resonances (CRs) emerging in each case is not the same. For attractive shells it is found that CRs result from interference between three waves: the incident wave, and the waves reflected at each of the inner and outer cavity boundaries. We find significant sensitivity of near-threshold confinement resonances to the size and thickness of the shell, we demonstrate modulations and 'beats' in the intensities of the resonances and we study them, both as a function of the parameters of the confining shell, and as a function of photoelectron energy. In the case of repulsive shells, the resonances can result from three-wave interference, as above, or can be due to quasi-discrete states appearing as a result of confinement.

Double photoionization accompanied by loss of n C atoms (n = 0, 2, 4, 6) was investigated by merging beams of Xe@C + 60 ions and synchrotron radiation and measuring the yields of product ions. The giant 4d dipole resonance of the caged Xe atom has a prominent signature in the cross section for these product channels, which together account for 6.2 ± 1.4 of the total Xe 4d oscillator strength of 10. Compared to that for a free Xe atom, the oscillator strength is redistributed in photon energy due to multipath interference of outgoing Xe 4d photoelectron waves that may be transmitted or reflected by the spherical C + 60 molecular cage, yielding so-called confinement resonances. The data are compared with an earlier measurement and with theoretical predictions for this single-molecule photoelectron interferometer system. Relativistic R-matrix calculations for the Xe atom in a spherical potential shell representing the fullerene cage show the sensitivity of the interference pattern to the molecular geometry.

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C60 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@C60 and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C60 [PRL 111, 203003 (2013)]. PACS numbers: 32.80.Rm 32.80.Fb 42.50.Hz Unprecedented advances in experimental techniques in measuring time intervals at the attosecond level [1] have engendered the ability to scrutinize the time delay in photoionization of atomic systems in the laboratory [2][3][4], thereby allowing us to probe the fundamental process of photoionization in the time domain. Specifically, using attosecond pulses of electromagnetic radiation, the time difference between the emergence of photoelectrons from two neighboring atomic subshells has been measured both in Ne [3] and Ar [4, 5]. These experimental results have stimulated a host of theoretical calculations to explain and to further explore this phenomenon [6][7][8][9]. This is of great interest, not only as a new way to study a fundamental process of nature, but also as an outstanding, unique opportunity towards a deeper understanding of the most informative parameter of the process, the photoionization amplitude. This is because the time delay is related to the energy derivative of the phase of the amplitude driving the process [10]. Indeed, to date, the only method for getting the maximum experimental information on photoionization lies through a set of measurements of total and differential photoionization cross sections, but allows only the absolute values and relative phases of matrix elements to be deduced; this is known as a complete photoionization experiment [11]. Time delay investigations, however, go beyond the complete experiment strategy and yield the derivative of the phase with respect to the photoelectron energy. Time delay investigations, thus, provide a new avenue to discern the characteristics of the basic physical quantity -the photoionization amplitude -and, thus, of the photoionization phenomenon itself. It is the ultimate aim of this paper to promote the expansion of time delay studies towards situations where they have not yet been exploited and where novel effects might occur -to atoms under confinement.The theory of time delay in physics was developed some time ago [12] and was originally envisioned as a way to study resonances -the temporary trapping of one (or more) electrons in a quasi-bound state or a potential well. Indeed, the Breit-Wigner formula of resonant scattering τ = 2/Γ equates the time delay τ with the resonant width Γ at half maximum of the cross-section [13]. Resonances are ubiquitous in photoionization of atoms, and these resonances can be of different natures: inner-shell excitations, tw...

No abstract