Fast-electron impact ionization of molecular hydrogen: energy and angular distribution of double and single differential cross sections and Young-type interference

Chatterjee, Shyamal; Kasthurirangan, S; Kelkar, Aditya H.; Stia, C. R.; Fojón, O A; Rivarola, R D; Tribedi, Lokesh C.

doi:10.1088/0953-4075/42/6/065201

Cited by 28 publications

(28 citation statements)

References 48 publications

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“…Over the last few years, a substantial experimental effort has been devoted to investigate these two-center interferences in the simplest diatomic molecules, mainly in the context of photoionization [see, e.g., (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)], but also in ionizing collisions with fast ions (18)(19)(20)(21) and electrons (22)(23)(24). 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).…”

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confidence: 99%

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

Canton

Plésiat

Bozek

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

111

120

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Vibrationally resolved valence-shell photoionization spectra of H 2 , N 2 and CO have been measured in the photon energy range 20-300 eV using third-generation synchrotron radiation. Young's double-slit interferences lead to oscillations in the corresponding vibrational ratios, showing that the molecules behave as two-center electron-wave emitters and that the associated interferences leave their trace in the angle-integrated photoionization cross section. In contrast to previous work, the oscillations are directly observable in the experiment, thereby removing any possible ambiguity related to the introduction of external parameters or fitting functions. A straightforward extension of an original idea proposed by Cohen and Fano [Cohen HD, Fano U (1966) photoelectron spectroscopy | molecular spectroscopy | molecular ionization | density functional theory | quantum chemistry T he recognition of wave-particle duality, resolving centuries of scientific debate, is nowadays considered as a milestone in the development of Quantum Mechanics. This revolutionary concept has been repeatedly demonstrated in variations of Young's double-slit experiment, where a beam of massive particles, from electrons (1) to fullerenes (2), with momentum p e , passing through two slits separated by a distance comparable to their associated de Broglie wavelength (λ e ¼ h∕p e ) displays temporal and spatial coherence evidenced through interferogram fringes (3). In the 1960's, Cohen and Fano (4) conjectured the possibility to realize the double-slit experiment on the microscopic length scale by photoionizing a diatomic molecule, where the source of free electrons is delocalized over two atomic centers. A sketch of the interference expected from the coherent emission of the two centers is shown in Fig. 1.Coherence is observable when the electron-wave length λ e is of the order of R e , or equivalently, when the photon energy hν is of the order of I p þ h 2 ∕ð2m e R 2 e Þ, where R e is the internuclear distance at equilibrium, m e is the electron mass, and I p is the vertical ionization potential. These energies correspond to incoming photons of a few hundred eV, i.e., to vacuum or extreme ultraviolet radiation. Fingerprints of this coherent emission can be found in the total photoionization cross section, which in the case of a homonuclear diatomic molecule is approximately given by the formulawhere σ 0 is an atomic photoionization cross section (for an effective charge Z eff ) and k e ¼ 2π∕λ e is the electron-wave vector. The oscillatory term within brackets quantifies the interference effect (hereafter called Cohen-Fano, CF, interference). The beauty of such a simple expression is that it is proportional to the very general intensity pattern produced by two dipole antennas separated by a distance R e that radiate coherently (5). Eq. 1 is obtained by assuming that the ionized molecular orbital ψ can be expressed by a linear combination of atomic orbitals (LCAO):where 1s A and 1s B are identical 1s atomic orbitals centered on atoms A and B of...

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mentioning

confidence: 99%

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

Canton

Plésiat

Bozek

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

111

120

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“…The coherent emission was then traced by analyzing oscillations in the mentioned ratios. In the same way, interferences effects were observed subsequently in the case of electronic impact [4,5]. Moreover, the case of photoionization of hydrogen molecules was revisited in order to provide a realistic description of the photoionization spectra including the influence of the nuclear motion.…”

Section: Introductionmentioning

confidence: 94%

Interference and non-Franck-Condon effects in ionization of H₂molecules by photon impact

Fojón

Fernández

Palacios

et al. 2011

J. Phys.: Conf. Ser.

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Abstract. We analyze theoretically interference effects in the spectra of electrons emitted in the H2 photoionization by high energy linearly polarized photons. Molecular bound and continuum states are accurately described by means of B-spline basis allowing the inclusion of the nuclear degrees of freedom. One interesting feature is observed: the usual FranckCondon behavior is not followed when the H2 internuclear axis is parallel to the polarization direction. Moreover, this is related to the fact that for this molecular orientation and under certain conditions, the electron cannot be emitted in the direction of the radiation field. On the contrary, for H2 molecules perpendicular to the polarization direction, the angular distribution of electrons is analogous to the one observed in the two slits Young's experiment. IntroductionNowadays, the study of interference effects in the electronic emission from diatomic molecules is a very active subject of research (see for instance [1]). In the sixties, Cohen and Fano explained anomalies in the photoelectron spectra of diatomic molecules [2]. They argued that the coherent emission from both molecular centers produced interferences when the de Broglie wavelength of the ejected electrons is of the order of the internuclear distance of the molecule in analogy with the Young's two slit experiment. They elaborated a simple model based on the following assumptions: i) ionization is basically a one-electron process, ii) the lowest molecular orbital ψ g is well described in the Linear combination of atomic orbitals (LCAO) approximation (ψ g ∼ 1s A +1s B , where 1s A and 1s B are atomic orbitals centred in nucleus A and B, respectively) and iii) the ionized electron is well described by a single-centre plane wave. In this way, Cohen and Fano showed that the total photoionization cross section is given by the analytical form

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“…Electrons are emitted coherently from the two centers of the molecule giving rise to interference oscillations. Several works towards the interference effect have been carried out in case of the simplest diatomic molecule, H 2 in collisions with fast electrons, heavy ions or photons [3][4][5][6]. Extending the work further from H 2 to more complex diatomic molecules, such as N 2 and O 2 , oscillation has been observed in individual orbitals when impacted with photons [7].…”

Section: Introductionmentioning

confidence: 99%

Coherent electron emission from O2 in collisions with fast electrons

et al. 2017

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Absolute double differential cross sections (DDCS) of secondary electrons emitted in ionization of O2 by fast electrons have been measured for different emission angles. Theoretical calculations of atomic DDCS were obtained using the first Born approximation with an asymptotic charge of ZT = 1. The measured molecular DDCS were divided by twice the theoretical atomic DDCS to detect the presence of interference effects which was the aim of the experiment. The experimental to theoretical DDCS ratios showed clear signature of first order interference oscillation for all emission angles. The ratios were fitted by a first order Cohen-Fano type model. The variation of the oscillation amplitudes as a function of the electron emission angle showed a parabolic behaviour which goes through a minimum at 90 • . The single differential and total ionization cross sections have also been deduced, besides the KLL Auger cross sections. In order to make a comparative study, we have discussed these results along with our recent experimental data obtained for N2 molecule.

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Fast-electron impact ionization of molecular hydrogen: energy and angular distribution of double and single differential cross sections and Young-type interference

Cited by 28 publications

References 48 publications

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

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

Interference and non-Franck-Condon effects in ionization of H₂molecules by photon impact

Coherent electron emission from O2 in collisions with fast electrons

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Fast-electron impact ionization of molecular hydrogen: energy and angular distribution of double and single differential cross sections and Young-type interference

Cited by 28 publications

References 48 publications

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

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

Interference and non-Franck-Condon effects in ionization of H2molecules by photon impact

Coherent electron emission from O2 in collisions with fast electrons

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Interference and non-Franck-Condon effects in ionization of H₂molecules by photon impact