Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the Chemical Society of Japan

Novel Electron Correlation in the Scattering Continuum for a Stability Analysis of the Electron Pair in the “Atomic” Level

Akitomo Tachibana

Published Nov 1, 1993• 4 citations
Publisher

Abstract

Abstract Wannier phenomenon is examined for a stability analysis of a time-reversal electron pair scattering. Imagine a pair of electrons interacting one another. It is found that the nature of the interelectron interaction is to stabilize the time-reversal scattering state. This nature survives even under the influence of a scattering center. To conclude, we shall prove the following results: 1) inside the reaction zone of the scattering center, one of the electrons is trapped, pressing the other electron to the barrier of the reaction zone, or letting the other electron go away over the barrier of the reaction zone, namely, a time-reversal scattering state of the electron pair is unstable, while 2) outside the reaction zone, if the critical radius rc is reached, then the time-reversal scattering state of the electron pair is stabilized. The critical radius rc has an intrinsic importance as a measure of the coherence length ξ of the Cooper pair that exhibits the time-reversal symmetry.

DOI
10.1246/bcsj.66.3319

Related papers

Theory of Electronic Transitions

H. Klar

We investigate scattering of electrons from atoms in the nonrelativistic energy range. In contrast to the pioneer work by Born, we take correlation properly into account and describe electrons by waves rather than by mass points. To this end, we start from a novel parabolic partial differential equation, which resembles the inhomogeneous heat equation. Calculation of the kernels for incoming and outgoing waves allows us to formulate initial value problems. A converging Fresnel distribution is shown to control the incident electron and pulls the target electron onto an equilibrium location. The electron-electron interaction is here attractive. Finally, the two electrons are attracted by the nucleus and arrive at a triple condensation point, where they form a compound state comparable to a Cooper pair. This three-body configuration is highly unstable, described by an unstable Fresnel distribution, and leads finally to excited target states plus an escaping electron. There is no way for a one-step transition. The excitation process always goes through a ladder consisting of Fresnel states. The Wannier mode has been identified as an unstable Fresnel distribution, which is not an energy eigenstate, but it is an eigenstate of the action curvature. This unusual mode cannot be expected as a discrete line in a Rydberg spectrum, but seems to manifest itself as noise. We show that this noise is heavily suppressed near the threshold.

Journal of Applied Mathematics and Physics•Jan 1, 2025•0 citations

Reciprocity in electron diffraction

J. Gunning, Penelope J. Goodman

The symmetry of reciprocity is reviewed in the context of relativistic quantum mechanics with the specific aim of relating to C, P and T invariances. From this investigation global time reversal is found to be a sufficient condition for reciprocity to hold in scattering from a vector potential. The present proof is free from assumptions of small-angle scattering and from restrictions on z-dependent terms in the scattering equation, and by avoiding S-matrix theory is thought to be accessible to undergraduate teaching.

Acta Crystallographica Section A Foundations of Crystallography•Jul 1, 1992•2 citations

Near-threshold excitation of Rydberg series by strong laser fields

G. Alber, P. Zoller

We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.

Physical Review A•Jan 1, 1988•73 citations

Resonant electron scattering and dielectronic recombination in two-center atomic systems

A. Eckey, A. Jacob, Alexander B Voitkiv +1 more

Electron scattering and dielectronic recombination with an ion in the presence of a neighboring atom is studied. The incident electron is assumed to be captured by the ion, leading to resonant excitation of the atom which afterwards may stabilize either by electron reemission or radiative decay. We show that the participation of the atom can strongly affect, both quantitatively and qualitatively, the corresponding processes of electron scattering and recombination. Various ion-atom systems and electronic transitions are considered. In particular we show that electron scattering under backward angles may be strongly enhanced, provided the incident energy lies very close to the resonance. Besides, we derive the scaling behavior of two-center dielectronic recombination with the principal quantum numbers of the participating atomic states. The resonant enhancement in this process is shown to be so strong that it can compete with ordinary single-center recombination even after integrating over a rather broad distribution of incident electron energies.

arXiv:1805.03458•Physical Review A•Jul 23, 2018•12 citations

Time-Reversal Symmetry-Protected Coherent Control of Ultracold Molecular Collisions

Adrien Devolder, Timur V. Tscherbul, Paul W. Brumer

Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process. However, the incoherent addition of different partial wave contributions to the integral cross-sections, commonly encountered in systems with complex collisional dynamics, poses a significant challenge, often limiting the control. This work demonstrates that time-reversal symmetry can be used to overcome these limitations by constraining the relation between the S-matrix elements. For example, the preparation of a superposition of two states related by the time-reversal superposition can provide extensive control for transitions to a time-reversal invariant final state, such as the J = 0, M = 0. Using the example of ultracold O 2 –O 2 scattering, we show that for such states coherent control is robust against short-range dynamical complexity. Furthermore, the time-reversal symmetry also protects the control against a distribution of collisional energies. Beyond the ultracold regime, we observe significant differences in the controllability of crossed-molecular beam vs trap experiments with complete control achievable in the former case at any temperature, emphasizing the cooperative role of time-reversal and permutation symmetries in maintaining control at any temperature. These results open new avenues for the coherent control of complex inelastic collisions and chemical reactions both in and outside of the ultracold regime.

arXiv:2412.14425•The Journal of Physical Chemistry Letters•Mar 10, 2025•2 citations

Understanding entangled spins in QED

Haijun Wang, W. T. Geng

We have studied the stability of two entangled spins dressed by electrons by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form e −α r . Our results show that if the (Einstein–Podolsky–Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wavefunction will be constrained to be parity dependent. The spin-singlet state s = 0 and the polarized state along the z -axis give rise to two different kinds of phase shifts . Interestingly, the interaction between electrons in the spin-singlet pair is found to be attractive. Using this attraction we propose a mechanism to produce entangled pairs of massive spin-1/2 particles.

arXiv:quant-ph/0510016•Journal of Physics A Mathematical and Theoretical•Sep 4, 2007•7 citations
Abstract Wannier phenomenon is examined for a stability analysis of a time-reversal electron pair scattering. Imagine a pair of electrons interacting one another. It is found that the nature of the interelectron interaction is to stabilize the time-reversal scattering state. This nature survives even under the influence of a scattering center. To conclude, we shall prove the following results: 1) inside the reaction zone of the scattering center, one of the electrons is trapped, pressing the other electron to the barrier of the reaction zone, or letting the other electron go away over the barrier of the reaction zone, namely, a time-reversal scattering state of the electron pair is unstable, while 2) outside the reaction zone, if the critical radius rc is reached, then the time-reversal scattering state of the electron pair is stabilized. The critical radius rc has an intrinsic importance as a measure of the coherence length ξ of the Cooper pair that exhibits the time-reversal symmetry.
We investigate scattering of electrons from atoms in the nonrelativistic energy range. In contrast to the pioneer work by Born, we take correlation properly into account and describe electrons by waves rather than by mass points. To this end, we start from a novel parabolic partial differential equation, which resembles the inhomogeneous heat equation. Calculation of the kernels for incoming and outgoing waves allows us to formulate initial value problems. A converging Fresnel distribution is shown to control the incident electron and pulls the target electron onto an equilibrium location. The electron-electron interaction is here attractive. Finally, the two electrons are attracted by the nucleus and arrive at a triple condensation point, where they form a compound state comparable to a Cooper pair. This three-body configuration is highly unstable, described by an unstable Fresnel distribution, and leads finally to excited target states plus an escaping electron. There is no way for a one-step transition. The excitation process always goes through a ladder consisting of Fresnel states. The Wannier mode has been identified as an unstable Fresnel distribution, which is not an energy eigenstate, but it is an eigenstate of the action curvature. This unusual mode cannot be expected as a discrete line in a Rydberg spectrum, but seems to manifest itself as noise. We show that this noise is heavily suppressed near the threshold.
The symmetry of reciprocity is reviewed in the context of relativistic quantum mechanics with the specific aim of relating to C, P and T invariances. From this investigation global time reversal is found to be a sufficient condition for reciprocity to hold in scattering from a vector potential. The present proof is free from assumptions of small-angle scattering and from restrictions on z-dependent terms in the scattering equation, and by avoiding S-matrix theory is thought to be accessible to undergraduate teaching.
We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.
Electron scattering and dielectronic recombination with an ion in the presence of a neighboring atom is studied. The incident electron is assumed to be captured by the ion, leading to resonant excitation of the atom which afterwards may stabilize either by electron reemission or radiative decay. We show that the participation of the atom can strongly affect, both quantitatively and qualitatively, the corresponding processes of electron scattering and recombination. Various ion-atom systems and electronic transitions are considered. In particular we show that electron scattering under backward angles may be strongly enhanced, provided the incident energy lies very close to the resonance. Besides, we derive the scaling behavior of two-center dielectronic recombination with the principal quantum numbers of the participating atomic states. The resonant enhancement in this process is shown to be so strong that it can compete with ordinary single-center recombination even after integrating over a rather broad distribution of incident electron energies.
Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process. However, the incoherent addition of different partial wave contributions to the integral cross-sections, commonly encountered in systems with complex collisional dynamics, poses a significant challenge, often limiting the control. This work demonstrates that time-reversal symmetry can be used to overcome these limitations by constraining the relation between the S-matrix elements. For example, the preparation of a superposition of two states related by the time-reversal superposition can provide extensive control for transitions to a time-reversal invariant final state, such as the J = 0, M = 0. Using the example of ultracold O 2 –O 2 scattering, we show that for such states coherent control is robust against short-range dynamical complexity. Furthermore, the time-reversal symmetry also protects the control against a distribution of collisional energies. Beyond the ultracold regime, we observe significant differences in the controllability of crossed-molecular beam vs trap experiments with complete control achievable in the former case at any temperature, emphasizing the cooperative role of time-reversal and permutation symmetries in maintaining control at any temperature. These results open new avenues for the coherent control of complex inelastic collisions and chemical reactions both in and outside of the ultracold regime.
We have studied the stability of two entangled spins dressed by electrons by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form e −α r . Our results show that if the (Einstein–Podolsky–Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wavefunction will be constrained to be parity dependent. The spin-singlet state s = 0 and the polarized state along the z -axis give rise to two different kinds of phase shifts . Interestingly, the interaction between electrons in the spin-singlet pair is found to be attractive. Using this attraction we propose a mechanism to produce entangled pairs of massive spin-1/2 particles.