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

Physical Review

Stark Effects in Line Broadening

Henry Margenau, M LEWIS

Published Apr 15, 1957• 2 citations
Publisher

Abstract

Earlier calculations, based on customary radiation theory, fail to yield a meaningful finite answer for the second-order Stark effect upon line broadening. The reason for this occurrence is found in the assumption that, at some definite time, the radiating atom as well as the perturbing electron is in a precise energy state. When the electron is represented in a suitable way by a wave packet a finite line width results, and this answer agrees within reasonable limits with that of the classical impact theory provided certain enumerated conditions are satisfied.

DOI
10.1103/physrev.106.244

Related papers

Stark-Effect Broadening of Hydrogen Lines

Lyman Spitzer

The profile of a hydrogen emission line is investigated on the assumption that the hydrogen atom is perturbed by passing ions. Provided that the ions do not approach to within ten times the average atomic radius the electric field of the ion may be assumed homogeneous and the matrix elements calculated for the usual Stark effect may be used. For a collision at low velocity or with close approach, the adiabatic approximation is valid, and the profile depends solely on the total phase shift produced by the collision. The Fourier analysis of the wave train may be carried through exactly for certain values of this phase shift. Nonadiabatic transitions are examined for the lowest lines, and an exact solution given for this case also. For higher lines a modified Born approximation is used. The Weisskopf collision broadening formula is shown to hold only in certain cases, and the dispersion curve smearing function for impact broadening is shown to lead in some instances to incorrect results.

Physical Review•Apr 15, 1939•20 citations

Quantum Theory of Spectral Line Broadening

Stanley Bloom, Henry Margenau

Simple radiation theory is used to derive a formula proposed earlier by P. W. Anderson, for calculating the intensity within a collision-broadened spectral line. The problem is considered, first from the point of view of molecular transitions, and then by computing the work done by the light wave. The general result for absorption is stated in Eq. (18), wherein the first double integral represents true absorption, the second induced emission.

Physical Review•Jun 1, 1953•60 citations

Quantum theory of Stark broadening by electrons

N. Tran-Minh, Henri Van Regemorter

The one electron approximation is used to determine the exact form of the wings of a line broadened by electron-atom collisions. The validity of this model is examined. The profile being proportional to the square of the scalar product of scattered waves, the impact approximation is obtained by replacing the exact form of the scattered waves by their asymptotic form. In this case of hydrogen the quasistatic approximation is obtained by using the JWKB method together with the usual assumptions.

Journal of Physics B Atomic and Molecular Physics•May 1, 1972•22 citations

Resonance Broadening of Absorption Lines

Bandel Bezzerides

A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.

Physical Review•Jul 5, 1967•37 citations

Classical-Path Calculation of the Impact-Broadening Operator for the Stark Broadening of Hα

Michael E. Bacon

The impact-broadening operator $\ensuremath{\Phi}$ for the hydrogen line ${\mathrm{H}}_{\ensuremath{\alpha}}$ is calculated by solving numerically for the $S$ matrices using the straight-line classical-path approximation. All contributing multipoles in the perturber- (free-electron-) atom interaction [$V(t)$] are included; time ordering of the operators in the $S$ matrices is retained. The matrix elements are compared with previous approximations based on the same model; the effects on the ${\mathrm{H}}_{\ensuremath{\alpha}}$ line profile are considered.

Physical Review A•Feb 1, 1971•42 citations

A quantum unified theory of Stark broadening in the wings of spectral lines

N T Mihn, N. Feautrier, Henri Van Regemorter

A simple and tractable quantum expression of the line wings is given when the upper and lower levels of the spectral lines are both perturbed. This quantum profile converges towards the impact regime at small distances from the line centre and towards the quasistatic limit when the usual semiclassical approximations are made. The correspondence between quantum and semiclassical expressions is examined, and the passage from the former to the latter clarifies the implicit assumptions which are always made in any unified semiclassical approach.

Journal of Physics B Atomic and Molecular Physics•Aug 1, 1975•18 citations
Earlier calculations, based on customary radiation theory, fail to yield a meaningful finite answer for the second-order Stark effect upon line broadening. The reason for this occurrence is found in the assumption that, at some definite time, the radiating atom as well as the perturbing electron is in a precise energy state. When the electron is represented in a suitable way by a wave packet a finite line width results, and this answer agrees within reasonable limits with that of the classical impact theory provided certain enumerated conditions are satisfied.
The profile of a hydrogen emission line is investigated on the assumption that the hydrogen atom is perturbed by passing ions. Provided that the ions do not approach to within ten times the average atomic radius the electric field of the ion may be assumed homogeneous and the matrix elements calculated for the usual Stark effect may be used. For a collision at low velocity or with close approach, the adiabatic approximation is valid, and the profile depends solely on the total phase shift produced by the collision. The Fourier analysis of the wave train may be carried through exactly for certain values of this phase shift. Nonadiabatic transitions are examined for the lowest lines, and an exact solution given for this case also. For higher lines a modified Born approximation is used. The Weisskopf collision broadening formula is shown to hold only in certain cases, and the dispersion curve smearing function for impact broadening is shown to lead in some instances to incorrect results.
A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.
The impact-broadening operator $\ensuremath{\Phi}$ for the hydrogen line ${\mathrm{H}}_{\ensuremath{\alpha}}$ is calculated by solving numerically for the SSS matrices using the straight-line classical-path approximation. All contributing multipoles in the perturber- (free-electron-) atom interaction [V(t)V(t)V(t)] are included; time ordering of the operators in the SSS matrices is retained. The matrix elements are compared with previous approximations based on the same model; the effects on the ${\mathrm{H}}_{\ensuremath{\alpha}}$ line profile are considered.
A simple and tractable quantum expression of the line wings is given when the upper and lower levels of the spectral lines are both perturbed. This quantum profile converges towards the impact regime at small distances from the line centre and towards the quasistatic limit when the usual semiclassical approximations are made. The correspondence between quantum and semiclassical expressions is examined, and the passage from the former to the latter clarifies the implicit assumptions which are always made in any unified semiclassical approach.