Interference modulation in the vibrationally resolved photoionization of the 1σ_gand 1σ_ucore levels of the N₂molecule

Abstract

The ratios of photoionization cross sections of the 1σg and 1σu shells of the N2 molecule for the vibrational transitions to the v′ = 0 and v′ = 1 core-ionized states in the photon energy region between 440 and 550 eV have been measured. The calculations in the random phase approximation well reproduce the experimental data. The variation of the ratio with photon energy is attributed to the interference modulation that is caused by coherent photoemission from the two atoms, as an analogue of the Young's double-slit experiment. The calculations extended up to 1.8 keV allow connecting the modulation with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies and demonstrate that the main contribution to these modulations comes from the σ continuum states.

Vibrational branching ratios in the photoelectron spectra of N2 and CO: interference and diffraction effects

“…In the N 2 figures, we compare our results obtained by using the DFT method (including the nuclear motion) with recent theoretical calculations reported by Semenov et al 61,64 in the fixed nuclei approximation. The authors employed RPA within the relaxed-core Hartree Fock (RCHF) approximation at low photon energy in order to describe the strong electronic correlation in this region.…”

“…RCHF is used for higher energies (> 3 a.u.). Since the authors claim that the standard RCHF method generally overestimates the influence of the relaxation effects for K-shells and give rise to a shift of the cross section toward higher energies, they make use of an adjustable parameter, the fractional charge z e , which corresponds to some intermediate value of the charge of the hole state 61 . The value z e = 0.7 has been empirically chosen to give the best agreement with the experimental data.…”

“…In particular, a wealth of experimental and theoretical data has been published for total cross sections corresponding to core as well as valence-shell photoionization of the prototype N 2 1-35 and CO 1,2,5,6,12,13,34,[36][37][38][39][40][41][42][43][44][45][46][47][48][49] molecules, from the ionization threshold up to a few tens of eV above it. More recently, the advent of high-brilliance 3rd-generation synchrotron radiation sources in combination with high energy-resolution detection techniques has opened the way for the determination of vibrationally resolved photoionization spectra of these molecules, both at low and high photon energies 30,35,38,39,[50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] . These experimental achievements have fostered the development of new theoretical methods that, in addition to accounting for electronic degrees of freedom, are also able to describe the molecule's vibrations 13,30,35,…”

“…More recent theoretical investigations have addressed the features appearing in the photoelectron spectra at high energy, mostly in core photoionization. In particular, results for N 2 and CO obtained from these methods have led to the observation of interesting interference phenomena that are often difficult to identify in total photoelectron spectra, especially at high photon energies 4,11,61,64,69,[74][75][76][77][78] . Two of these phenomena, which lie at the heart of quantum mechanics, have been recently observed in vibrationally resolved photoelectron spectra from valence-shell orbitals 78 : (i) two-center coherent electron emission leading to Young's type double-slit interferences 79 and (ii) electron diffraction by the molecule's atomic centers.…”

Direct observation of Young’s double-slit interferences in vibrationally resolved photoionization of diatomic molecules

“…However, due to the rapid decrease of σ 0 with photoelectron energy, i.e., with k e , the oscillations are usually hidden and must be uncovered through dividing the total cross section by an independent but arbitrary estimate of σ 0 , leading to equivocal interpretations (18,19). This difficulty has been so far circumvented by considering the ratio of two rapidly decreasing cross sections associated with different molecular ionization channels [e.g., the g/u ratio resulting from K-shell photoionization of N 2 (11,25)]. …”