Young's double-slit experiment using core-level photoemission from N₂: revisiting Cohen–Fano's two-centre interference phenomenon

Abstract

The core-level photoelectron spectra of N2 molecules are observed at high energy resolution, resolving the 1σg and 1σu components as well as the vibrational components in the extended energy region from the threshold up to 1 keV. The σg/σu cross section ratios display modulation as a function of photoelectron momentum due to the two-centre interference, analogous to the classical Young's double-slit experiment, as predicted by Cohen and Fano a long time ago. The Cohen–Fano interference modulations display different phases depending on the vibrational excitations in the core-ionized state. Extensive ab initio calculations have been performed within the Hartree–Fock and random phase approximations in prolate spheroidal coordinates. The dependence of photoionization amplitudes on the vibrational states was taken into account using the Born–Oppenheimer approximation. The ab initio results are in reasonable agreement with the experimental data. The theoretical analysis allows the modulation to be connected with the onset of transitions to the states of increasing orbital angular momentum which occurs at increasing photon energies. Deviation from the Cohen–Fano formula is found for both the experimental and the ab initio results and is attributed to electron scattering by the neighbouring atom. A new formula for the interference modulation is derived within the framework of the multiple scattering technique. It differs from the classical Cohen–Fano formula by the addition of twice the scattering phase of the photoelectron by the neighbouring atom. We demonstrate that one can measure directly the scattering phase by fitting our formula to the experimental results.

Partial photoionization cross sections of C60 and C70: A gas versus adsorbed phase comparison

“…These oscillations which were predicted more than forty years ago by Cohen and Fano [9] have been experimentally corroborated since the last ten years only [10,11]. Regarding photoionization this was even more recently [12]. The showcase example exhib- …”

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.…”

“…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.…”

Molecular ionization and dissociation using synchrotron radiation and ultrashort laser pulses

“…The signature of interferences is, as usual, the oscillatory term within the brackets. However, due to the rapid decrease of σ A with photon energy, i.e., with k e , oscillations are usually observed in a rather indirect way, e.g., by dividing the total cross section by a "reasonable" independent estimate of σ A [64,65] or by studying the ratio of two rapidly decreasing partial cross sections [66].…”