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arXiv:2601.17797

A comparison of Fraunhofer-type diffraction from an atomic single-slit and a molecular double-slit

Jibak Mukherjee, Kamal Kumar, Harpreet Singh, Manojit Das, Guo-Peng Zhao, Ling Liu, Károly Tőkési, Lokesh C. Tribedi, Deepankar Misra

Published Jan 25, 2026• 0 citations
arXivHTMLPDF

Abstract

We measured the Q-value and the scattering angle distributions for non-dissociative state selective single electron capture in collisions of 7.5 keV H$^+$ and 15 keV H$_2^+$ with He. The experimental data are compared with semiclassical close-coupling calculations and predictions from the classical trajectory Monte Carlo simulations. By analogy with Fraunhofer diffraction, we also developed a toy model to reconstruct an imaginary screen that reflects the reaction impact-parameter dependence, in channels where the magnetic quantum number remains unchanged. It is well established that H$_2^+$ acts as a molecular double-slit in scattering processes. By demodulating the Young's double-slit-type interference pattern, we extracted the individual slit diffraction pattern of H$_2^+$ and compared it with that of the H$^+$ atomic single-slit. For ground state electron capture, we found that the single and the double slit diffraction patterns have equal fringe width, whereas for excited state electron capture, diffraction patterns are quite different.

DOI
10.48550/arxiv.2601.17797

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We measured the Q-value and the scattering angle distributions for non-dissociative state selective single electron capture in collisions of 7.5 keV H+^++ and 15 keV H2+_2^+2+​ with He. The experimental data are compared with semiclassical close-coupling calculations and predictions from the classical trajectory Monte Carlo simulations. By analogy with Fraunhofer diffraction, we also developed a toy model to reconstruct an imaginary screen that reflects the reaction impact-parameter dependence, in channels where the magnetic quantum number remains unchanged. It is well established that H2+_2^+2+​ acts as a molecular double-slit in scattering processes. By demodulating the Young's double-slit-type interference pattern, we extracted the individual slit diffraction pattern of H2+_2^+2+​ and compared it with that of the H+^++ atomic single-slit. For ground state electron capture, we found that the single and the double slit diffraction patterns have equal fringe width, whereas for excited state electron capture, diffraction patterns are quite different.
Evidence is given for Young-type interferences caused by a single electron acting on a given double-center scatterer analogous to an atomic-size double-slit system. The electron is provided by autoionization of a doubly excited He atom following the capture of the electrons of H2 by a He2+ incoming ion. The autoionizing projectile is a single-electron source, independent of the interferometer provided by the two H+ centers of the fully ionized H2 molecule. This experiment resembles the famous thought experiment imagined by Feynman in 1963, in which the quantum nature of the electron is illustrated from a Young-like double-slit experiment. Well-defined oscillations are visible in the angular distribution of the scattered electrons, showing that each electron interferes with itself.
For the last 50 years, there has been considerable interest in the possibility of observing the equivalence of a Young's double-slit wave interference at the quantum level for diatomic molecules. For electron-impact ionization of diatomic molecules, indirect evidence for this type of interference has been found by changing the energy (wavelength) of the ejected electron while keeping the incident projectile scattering angle fixed. The present work represents an experimental and theoretical collaboration to better understand the physics of this type of interference. In addition to examining the effect of changing the ejected electron energy for a fixed scattered projectile angle, we have also examined the effect of keeping the ejected electron energy fixed while varying the projectile scattering angle. Model calculations are performed for three different types of possible two-center interference effects, and it is found that the most important one is diffraction of the projectile off two scattering centers.
The dissociative electron transfer from He into 10 keV H2+ was measured in a kinematically complete experiment by using the cold target recoil ion momentum spectroscopy imaging technique in combination with a highly resolving molecular fragment imaging technique. The electron transfer into the dissociative b(3)Sigma+_(u) state of H2 could be selected by kinematic conditions. We find a striking double slit interference pattern in the transverse momentum transfer which we can modify by selecting different internuclear distances. Compared to an optical double slit, interference minima and maxima are interchanged. The latter is the result of a phase shift in the electronic part of the wave function.
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.
Abstract The paper presents the results of a quantum interference study using an asymmetrical double-slit experiment with a low-intensity laser beam, conducted in the single-photon approximation and the Fresnel near-field transition pre-Fraunhofer condition. In addition to the temporal separation achieved by recording each particle individually, the hybrid-asymmetrical double-slit design (in both width and height) also allows spatial separation of the first satellite diffraction bands created by each slit, thereby minimising the mixing background effects from the opposite slit. Isolating the satellite bands of a diffraction pattern from one of the two slits enables which-way identification of the quantum particle, contributing maximally to the path-distinguishability parameter D=1. Within these satellite bands, we observed interference fringes with reliability at their diffraction peaks for the wide slit and the narrow slit. After subtracting multiphoton-mixing interference noises V(mix), we obtain significant single-photon wave visibility values = 0.051±.009(stat.+sys.) and = 0.065±.009(stat.+sys.), respectively, at the wide-slit I1 and narrow-slit I2 diffraction bands. The results suggest the possibility of establishing an unusual correlation, D + V > 1, in which a significant number of photons exhibit both wave and particle properties simultaneously within the same experimental spectrum. This differs from the Copenhagen interpretation and therefore requires further explanation. PACS numbers: 03.65.-w, 03.65.Ta, 42.50.Xa
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.