We present a scattering theory for charged particles suitable for electron atom collisions. Starting from the Hamilton-Jacobi equation for N electrons in the field of a nucleus or an ion core, we derive a parabolic di...We present a scattering theory for charged particles suitable for electron atom collisions. Starting from the Hamilton-Jacobi equation for N electrons in the field of a nucleus or an ion core, we derive a parabolic differential equation that resembles the heat equation. We identify a Fresnel distribution as the main ingredient of its kernel. In particular, we show that high multiply excited states are strongly suppressed increasingly so for approaching the ionization threshold. That effect compares favorably with experimental data. Also, the Wannier channel is controlled by a Fresnel distribution. Moreover, that channel represents a novel continuum to our knowledge that has never been considered so far. The classical action has been employed to derive quatum wave functions in the semiclassical limit. The curvature of the N-elctron potential surface is shown to be the essential ingredient of an initial value problem for elastic and/or inelastic processes. The spectral region near the ionization threshold needs a special action to describe the Wannier phenomenon. This Wannier channel manifests itself by a novel continuum never considered before.展开更多
Two-electron atoms have been investigated near threshold of double escape within the framework of hyperspherical coordinates. A particularly useful set of hyperspherical angles has been used. It is well known for many...Two-electron atoms have been investigated near threshold of double escape within the framework of hyperspherical coordinates. A particularly useful set of hyperspherical angles has been used. It is well known for many years that the hyperradial motion is nearly separable from the hyperspherical angular motion. Therefore, the Born-Oppenheimer separation method should be useful. However, the success of that method in molecular physics is based on the small mass ratio, electron mass to nuclear mass. In the atomic application such a small parameter does not exist. Nevertheless the method works surprisingly well in the lower part of the spectrum. For increasing excitation energy the method becomes shaky. Near ionization threshold, it breaks even down. The author will present elsewhere an improved Born-Oppenheimer method. First pilot developments and comparison with the experimental situation are presented already here. Inclusion of a momentum-momentum radial coupling delivers an improved basis. We show that our extended Born-Oppenheimer approach leads to a deformation of the whole potential energy surface during the collision. In consequence of this deformation we outline a quantum derivation of the Wannier threshold cross section law, and we show that (e, 2e) angular distribution data are strongly influenced by that surface deformation. Finally, we present a mechanism for electron pair formation and decay leading to a supercurrent independent of the temperature. Our framework can be extended to more than two electrons, say 3 or 4. We conclude that our improved Born-Oppenheimer method <a href="#ref.1">[1]</a> is expected not only to deliver better numerical data, but it is expected to describe also the Wannier phenomenon. The idea of the new theory together with first qualitative results is presented in this paper.展开更多
We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. O...We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.展开更多
We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation <a href="#1">[1]</a> to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e<...We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation <a href="#1">[1]</a> to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e<sup>-</sup> + He(1<em>s</em> <em>n</em><em>s</em>)→He<sup>-** </sup>for <em>n</em> <span style="white-space:nowrap;">≫</span> 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by <img src="Edit_b22c3b40-4eb3-4060-aa36-c333530638c6.bmp" alt="" />. The coupling constant <em>g</em> has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.展开更多
We present, for the first time, a unified description of adiabatic collision channels and the Wannier channel in electron-atom scattering. We identify the Wannier channel as the solution of a recently presented partia...We present, for the first time, a unified description of adiabatic collision channels and the Wannier channel in electron-atom scattering. We identify the Wannier channel as the solution of a recently presented partial differential equation of parabolic type. The kernel of that equation has been constructed near the ionization threshold. Its eigenstates are shown to be members of a Banach space. For the purpose of demonstration, this paper embeds one adiabatic channel into a Bannach space. The full set of an adiabatic spectrum will be embedded into the Wannier continuum of a Banach space in a forthcoming paper. This technique delivers amended non-adiabatic collision channnels with ebergy-dependent potentials. That dependence manifests itself as energy-dependent discontinuity at the threshold. The branch above threshold describes the double escape of electrons, whereas the branch below threshold replaces an infinity of strongly coupled adiabatic channels by one new channel. The present paper is restricted to two-electron atoms consisting only of <em>s</em><sup>2</sup> <sup>1</sup><em>S</em> configurations. Our model shows new unexpected effects including an electron-electron attraction similar to a Cooper pair except that our electron pair couples only to one nucleus at rest rather than to a vibrating lattice. Our electron-electron attraction stems from a dynamic deformation of the potential surface.展开更多
For nonrelativistic two-electron atoms, we employ a phase-amplitude method to derive an energy-dependent three-body force which controls the dynamics of the atom near the threshold for double escape. Its potential ene...For nonrelativistic two-electron atoms, we employ a phase-amplitude method to derive an energy-dependent three-body force which controls the dynamics of the atom near the threshold for double escape. Its potential energy has been taken into account to derive beyond a static adiabatic basis a novel partial differential equation that replaces an adiabatic basis. That equation whose solutions span a Banach space has been solved exactly in the energy window near threshold. In that energy range, we find the formation of unstable electron pairs, comparable to Cooper pairs. In contrast to Cooper pairs, our pairs are bound by dominant correlation rather than by the coupling to a phonon field. These ingredients are suspected to allow for a super current independent of the temperature.展开更多
文摘We present a scattering theory for charged particles suitable for electron atom collisions. Starting from the Hamilton-Jacobi equation for N electrons in the field of a nucleus or an ion core, we derive a parabolic differential equation that resembles the heat equation. We identify a Fresnel distribution as the main ingredient of its kernel. In particular, we show that high multiply excited states are strongly suppressed increasingly so for approaching the ionization threshold. That effect compares favorably with experimental data. Also, the Wannier channel is controlled by a Fresnel distribution. Moreover, that channel represents a novel continuum to our knowledge that has never been considered so far. The classical action has been employed to derive quatum wave functions in the semiclassical limit. The curvature of the N-elctron potential surface is shown to be the essential ingredient of an initial value problem for elastic and/or inelastic processes. The spectral region near the ionization threshold needs a special action to describe the Wannier phenomenon. This Wannier channel manifests itself by a novel continuum never considered before.
文摘Two-electron atoms have been investigated near threshold of double escape within the framework of hyperspherical coordinates. A particularly useful set of hyperspherical angles has been used. It is well known for many years that the hyperradial motion is nearly separable from the hyperspherical angular motion. Therefore, the Born-Oppenheimer separation method should be useful. However, the success of that method in molecular physics is based on the small mass ratio, electron mass to nuclear mass. In the atomic application such a small parameter does not exist. Nevertheless the method works surprisingly well in the lower part of the spectrum. For increasing excitation energy the method becomes shaky. Near ionization threshold, it breaks even down. The author will present elsewhere an improved Born-Oppenheimer method. First pilot developments and comparison with the experimental situation are presented already here. Inclusion of a momentum-momentum radial coupling delivers an improved basis. We show that our extended Born-Oppenheimer approach leads to a deformation of the whole potential energy surface during the collision. In consequence of this deformation we outline a quantum derivation of the Wannier threshold cross section law, and we show that (e, 2e) angular distribution data are strongly influenced by that surface deformation. Finally, we present a mechanism for electron pair formation and decay leading to a supercurrent independent of the temperature. Our framework can be extended to more than two electrons, say 3 or 4. We conclude that our improved Born-Oppenheimer method <a href="#ref.1">[1]</a> is expected not only to deliver better numerical data, but it is expected to describe also the Wannier phenomenon. The idea of the new theory together with first qualitative results is presented in this paper.
文摘We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.
文摘We employ a recently amended Born-Oppenheimer (hereafter shortly BO) approximation <a href="#1">[1]</a> to treat inelastic scattering of slow electrons from highly excited Rydberg atoms like e<sup>-</sup> + He(1<em>s</em> <em>n</em><em>s</em>)→He<sup>-** </sup>for <em>n</em> <span style="white-space:nowrap;">≫</span> 1. Along these lines we replace the standard BO set of potentials by an evolution operator. In this way we take a momentum-momentum coupling inadvertently disregarded by BO into account. The BO eigenvalue problem is now replaced by an evolution equation. One eigen-evolution has been identified as Wanner channel. That channel describes the diffraction of electron pairs from a potential ridge. That diffraction causes a phase jump of π/2 in the channel evolution. Moreover we present a new conservative attractive force controlling the motion of the electron pair as a whole in the nuclear field whose potential is given by <img src="Edit_b22c3b40-4eb3-4060-aa36-c333530638c6.bmp" alt="" />. The coupling constant <em>g</em> has been calculated. That potential foreign to the standard BO approximation manifests itself by an entirely new series of isolated resonances located slightly below the double ionization threshold. This resonance ensemble compares favorably with experimental data. Further we present an evolution which forces the electron pair to the electrostatically unstable top of the potential ridge. That evolution may be regarded as quantum version of Wannier’s converging trajectory, and manifests itself here as Fresnel distribution.
文摘We present, for the first time, a unified description of adiabatic collision channels and the Wannier channel in electron-atom scattering. We identify the Wannier channel as the solution of a recently presented partial differential equation of parabolic type. The kernel of that equation has been constructed near the ionization threshold. Its eigenstates are shown to be members of a Banach space. For the purpose of demonstration, this paper embeds one adiabatic channel into a Bannach space. The full set of an adiabatic spectrum will be embedded into the Wannier continuum of a Banach space in a forthcoming paper. This technique delivers amended non-adiabatic collision channnels with ebergy-dependent potentials. That dependence manifests itself as energy-dependent discontinuity at the threshold. The branch above threshold describes the double escape of electrons, whereas the branch below threshold replaces an infinity of strongly coupled adiabatic channels by one new channel. The present paper is restricted to two-electron atoms consisting only of <em>s</em><sup>2</sup> <sup>1</sup><em>S</em> configurations. Our model shows new unexpected effects including an electron-electron attraction similar to a Cooper pair except that our electron pair couples only to one nucleus at rest rather than to a vibrating lattice. Our electron-electron attraction stems from a dynamic deformation of the potential surface.
文摘For nonrelativistic two-electron atoms, we employ a phase-amplitude method to derive an energy-dependent three-body force which controls the dynamics of the atom near the threshold for double escape. Its potential energy has been taken into account to derive beyond a static adiabatic basis a novel partial differential equation that replaces an adiabatic basis. That equation whose solutions span a Banach space has been solved exactly in the energy window near threshold. In that energy range, we find the formation of unstable electron pairs, comparable to Cooper pairs. In contrast to Cooper pairs, our pairs are bound by dominant correlation rather than by the coupling to a phonon field. These ingredients are suspected to allow for a super current independent of the temperature.
