Physical Review

Double Scattering of Electrons with a Dipole Moment

M. H. Zaidi

Published Oct 15, 1959• 1 citation

Abstract

The double scattering of electrons with a small intrinsic electric dipole moment is investigated theoretically for the case where magnetic and electric fields are present in the space between the two targets. It is shown by using density matrix techniques that the plane of polarization of the electron beam, after the first scattering, would be rotated by the magnetic and electric fields just as predicted by regarding the electrons as classical spinning tops with magnetic moments and classical electric dipoles precessing about the directions of the magnetic and electric fields, respectively.

DOI: 10.1103/physrev.116.241

Related papers

Spin-Exchange Scattering in Uniform Magnetic Fields

A. E. Glassgold, James F. Walker

Physical ReviewAug 5, 19674 citations

Electric and magnetic target polarization in quantum radar

Matthew J. Brandsema, Ram M. Narayanan, Marco O. Lanzagorta

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 1, 201725 citations

Dipole in a magnetic field, work, and quantum spin

Robert J. Deissler

Physical Review EMar 21, 200810 citations

Dual Magnetic and Electric Dipole Symmetry: Pseudo Angular Momentum in Parity Space and the Electric Landé $g$-Factor

Michael E. Tobar

physics.atom-phCross-listedarXiv:2511.07692Nov 12, 2025

Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments

Georg A. Raithel, M. Fauth, HERBERT WALTHER

Physical Review AJan 1, 199366 citations

Polarization effects in penetration of a barrier with a magnetic field applied

J. Schmit, Robert H. Good

Physical review. B, Solid stateAug 1, 19774 citations

Physical Review

Double Scattering of Electrons with a Dipole Moment

M. H. Zaidi

Published Oct 15, 1959• 1 citation

Publisher

Abstract

DOI: 10.1103/physrev.116.241

Related papers

Spin-Exchange Scattering in Uniform Magnetic Fields

A. E. Glassgold, James F. Walker

The role of a uniform magnetic field in the collision of two one-electron atoms is analyzed using previously developed density-matrix techniques. During the collision, all magnetic-moment interactions are small compared to the usual singlet and triplet potentials, and the only effect of the magnetic field is to alter the asymptotic states. This effect may be described in terms of the unitary transformation which diagonalizes the Breit-Rabi Hamiltonian. The properties of this transformation are given in detail for electronic spin \textonehalf{} and arbitrary nuclear spin. In addition to presenting a general formulation for this scattering problem, explicit formulas are given for spin exchange in the scattering of polarized beams from unpolarized targets.The role of a uniform magnetic field in the collision of two one-electron atoms is analyzed using previously developed density-matrix techniques. During the collision, all magnetic-moment interactions are small compared to the usual singlet and triplet potentials, and the only effect of the magnetic field is to alter the asymptotic states. This effect may be described in terms of the unitary transformation which diagonalizes the Breit-Rabi Hamiltonian. The properties of this transformation are given in detail for electronic spin \textonehalf{} and arbitrary nuclear spin. In addition to presenting a general formulation for this scattering problem, explicit formulas are given for spin exchange in the scattering of polarized beams from unpolarized targets.

Physical ReviewAug 5, 19674 citations

Electric and magnetic target polarization in quantum radar

Matthew J. Brandsema, Ram M. Narayanan, Marco O. Lanzagorta

In this paper, we discuss the effect that photon polarization has on the quantum radar cross section (QRCS) during the special case scenario of when the target is enveloped in either a uniform electric field or magnetic field and all of its atomic electric/magnetic dipole moments become aligned (target polarization). This target polarization causes the coupling between the photon and the matter to change and alter the scattering characteristics of the target. Most notably, it causes scattering to be very near zero at a specified angle. We also investigate the relationship between electric and magnetic types of coupling and find that the electric contribution dominates the QRCS response.In this paper, we discuss the effect that photon polarization has on the quantum radar cross section (QRCS) during the special case scenario of when the target is enveloped in either a uniform electric field or magnetic field and all of its atomic electric/magnetic dipole moments become aligned (target polarization). This target polarization causes the coupling between the photon and the matter to change and alter the scattering characteristics of the target. Most notably, it causes scattering to be very near zero at a specified angle. We also investigate the relationship between electric and magnetic types of coupling and find that the electric contribution dominates the QRCS response.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 1, 201725 citations

Dipole in a magnetic field, work, and quantum spin

Robert J. Deissler

The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether or not it does work on the electron-spin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a Stern-Gerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy -- translational plus rotational -- being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant.The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether or not it does work on the electron-spin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a Stern-Gerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy -- translational plus rotational -- being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant.

Physical Review EMar 21, 200810 citations

Dual Magnetic and Electric Dipole Symmetry: Pseudo Angular Momentum in Parity Space and the Electric Landé $g$ -FactorDual Magnetic and Electric Dipole Symmetry: Pseudo Angular Momentum in Parity Space and the Electric Landé $g$-Factor

Michael E. Tobar

Electric dipole moments (EDMs) are sensitive probes of fundamental symmetries and central to searches for physics beyond the Standard Model. We present a symmetry-based, Zeeman-analogue operator framework that places magnetic and electric dipole physics on parallel footing under electromagnetic duality, and introduce a polar-sector pseudo-angular-momentum degree of freedom in parity space together with an associated electric Landé factor that organizes induced orbital dipoles. Following Ohanian's effective-current formulation of the Zeeman effect, we construct its electric dual: the wavefunction's microscopic polarization admits an equivalent effective magnetic probability-current representation, providing a field-equivalence description of parity-mixed charge displacement. In this notation the total EDM expectation takes the unified form $\langle \hat{\vec d}_{\rm tot}\rangle= d_B(g_E\,\frac{\langle \hat{\vec J}_p\rangle}{\hbar}+ g_E^{e}\,\frac{\langle \hat{\vec S}\rangle}{\hbar})$ , with $g_E^{e}=\frac{2d_{\rm int}}{d_B}$ , where $\hat{\vec J}_p$ captures Stark-induced pseudo-angular momentum and $\hat{\vec S}$ encodes any intrinsic (spin-aligned) EDM $d_{\rm int}$ from symmetry-violating interactions. We define a natural electric dipole unit (the ``Bohr EDM'') as $d_B \equiv e a_0=\frac{2μ_B}{cα}$ ( $a_0$ the Bohr radius and $μ_B$ the Bohr magneton). As a canonical analytic benchmark, we show in the hydrogenic problem that a static electric field couples within a fixed $n$ manifold through the scaled Runge--Lenz structure, yielding a compact Landé-like description and reproducing the Stark doublet (e.g.\ $|\langle d_{\rm orb}\rangle|=3d_B$ for the $2s$ -- $2p_{m=0}$ mixing).Electric dipole moments (EDMs) are sensitive probes of fundamental symmetries and central to searches for physics beyond the Standard Model. We present a symmetry-based, Zeeman-analogue operator framework that places magnetic and electric dipole physics on parallel footing under electromagnetic duality, and introduce a polar-sector pseudo-angular-momentum degree of freedom in parity space together with an associated electric Landé factor that organizes induced orbital dipoles. Following Ohanian's effective-current formulation of the Zeeman effect, we construct its electric dual: the wavefunction's microscopic polarization admits an equivalent effective magnetic probability-current representation, providing a field-equivalence description of parity-mixed charge displacement. In this notation the total EDM expectation takes the unified form $\langle \hat{\vec d}_{\rm tot}\rangle= d_B(g_E\,\frac{\langle \hat{\vec J}_p\rangle}{\hbar}+ g_E^{e}\,\frac{\langle \hat{\vec S}\rangle}{\hbar})$, with $g_E^{e}=\frac{2d_{\rm int}}{d_B}$, where $\hat{\vec J}_p$ captures Stark-induced pseudo-angular momentum and $\hat{\vec S}$ encodes any intrinsic (spin-aligned) EDM $d_{\rm int}$ from symmetry-violating interactions. We define a natural electric dipole unit (the ``Bohr EDM'') as $d_B \equiv e a_0=\frac{2μ_B}{cα}$ ($a_0$ the Bohr radius and $μ_B$ the Bohr magneton). As a canonical analytic benchmark, we show in the hydrogenic problem that a static electric field couples within a fixed $n$ manifold through the scaled Runge--Lenz structure, yielding a compact Landé-like description and reproducing the Stark doublet (e.g.\ $|\langle d_{\rm orb}\rangle|=3d_B$ for the $2s$--$2p_{m=0}$ mixing).

physics.atom-phCross-listedarXiv:2511.07692Nov 12, 2025

Atoms in strong crossed electric and magnetic fields: Evidence for states with large electric-dipole moments

Georg A. Raithel, M. Fauth, HERBERT WALTHER

This paper reports on the evidence for large permanent electric-dipole moments of Rydberg atoms in crossed electric and magnetic fields. It was found that the dipole moments have a large value if the scaled electric-field strength \ensuremath{\epsilon}=${\mathit{EB}}^{\mathrm{\ensuremath{-}}4/3}$ has the value \ensuremath{\epsilon}\ensuremath{\approxeq}0.75 (with electric- and magnetic-field strengths E and B in atomic units). The experimental technique employed to determine the atomic dipole moment was to add a slight inhomogeneity to the electric field and to measure the deflection of the atoms, this deflection being proportional to the field inhomogeneity and the atomic dipole moment. In order to discuss the experimental results, different theoretical approaches to the E\ifmmode\times\else\texttimes\fi{}B problem are reviewed. The occurrence of Rydberg atoms with large dipole moments can be explained as being caused by a distinct type of classical orbit.This paper reports on the evidence for large permanent electric-dipole moments of Rydberg atoms in crossed electric and magnetic fields. It was found that the dipole moments have a large value if the scaled electric-field strength \ensuremath{\epsilon}=${\mathit{EB}}^{\mathrm{\ensuremath{-}}4/3}$ has the value \ensuremath{\epsilon}\ensuremath{\approxeq}0.75 (with electric- and magnetic-field strengths E and B in atomic units). The experimental technique employed to determine the atomic dipole moment was to add a slight inhomogeneity to the electric field and to measure the deflection of the atoms, this deflection being proportional to the field inhomogeneity and the atomic dipole moment. In order to discuss the experimental results, different theoretical approaches to the E\ifmmode\times\else\texttimes\fi{}B problem are reviewed. The occurrence of Rydberg atoms with large dipole moments can be explained as being caused by a distinct type of classical orbit.

Physical Review AJan 1, 199366 citations

Polarization effects in penetration of a barrier with a magnetic field applied

J. Schmit, Robert H. Good

The spin polarization of an electron moving nonrelativistically through a potential barrier $V(z)$ , with also a constant uniform magnetic field ( $0,0,B$ ) applied, is calculated using the WKB approximation for the $z$ dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.The spin polarization of an electron moving nonrelativistically through a potential barrier $V(z)$, with also a constant uniform magnetic field ($0,0,B$) applied, is calculated using the WKB approximation for the $z$ dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.

Physical review. B, Solid stateAug 1, 19774 citations

Dual Magnetic and Electric Dipole Symmetry: Pseudo Angular Momentum in Parity Space and the Electric Landé

g

-Factor

\langle \hat{\vec d}_{\rm tot}\rangle= d_B(g_E\,\frac{\langle \hat{\vec J}_p\rangle}{\hbar}+ g_E^{e}\,\frac{\langle \hat{\vec S}\rangle}{\hbar})

, with

g_E^{e}=\frac{2d_{\rm int}}{d_B}

, where

\hat{\vec J}_p

captures Stark-induced pseudo-angular momentum and

\hat{\vec S}

encodes any intrinsic (spin-aligned) EDM

d_{\rm int}

from symmetry-violating interactions. We define a natural electric dipole unit (the ``Bohr EDM'') as

d_B \equiv e a_0=\frac{2μ_B}{cα}

(

a_0

the Bohr radius and

μ_B

the Bohr magneton). As a canonical analytic benchmark, we show in the hydrogenic problem that a static electric field couples within a fixed

n

manifold through the scaled Runge--Lenz structure, yielding a compact Landé-like description and reproducing the Stark doublet (e.g.\

|\langle d_{\rm orb}\rangle|=3d_B

for the

2s

2p_{m=0}

mixing).

The spin polarization of an electron moving nonrelativistically through a potential barrier

V(z)

, with also a constant uniform magnetic field (

0,0,B

) applied, is calculated using the WKB approximation for the

z

dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.