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

Optics and Spectroscopy

Radiative properties of Zeeman components of atomic multiplets: Dependence of line intensities on the magnetic field

V. D. Ovsyannikov, Evgenii V Chaplygin

Published Dec 1, 2000• 2 citations
Publisher

Abstract

Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m . Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.

DOI
10.1134/1.1335027

Related papers

Effect of the diamagnetic interaction on the intensity of the radiation lines of an atom in a magnetic field

Vitalii D Ovsiannikov, V V Chernushkin

Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δ l | ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.

Journal of Experimental and Theoretical Physics•Sep 1, 2000•1 citation

Radiative properties of Zeeman components of atomic multiplets: Magnetically induced decay of metastable 3 P 2 and 3 P 0 states of inert gases

V. D. Ovsyannikov, Evgenii V Chaplygin

It is shown that the magnetic field induces the radiative decay of metastable states of inert gases by mixing them with resonant sublevels of the lowest multiplet. The polarization and frequency structures of the “forbidden” lines induced by the magnetic field are determined, and the dependence of the intensity of π and σ components of these lines on the magnetic field is calculated. The effect is totally governed by the paramagnetic atom-field interaction, and the influence of the diamagnetic interaction is insignificant.

Optics and Spectroscopy•Feb 1, 2001•2 citations

Radiative properties of diamagnetic levels in atoms: Dependence of transition probability on magnetic field strength

V. D. Ovsyannikov, V. V. Chernushin

We study the effect of diamagnetic interaction on the probability of radiative transitions of an atom from states split by a field. We write the analytic expressions for the diamagnetic corrections to the matrix elements of transitions belonging to the Lyman and Balmer series and of transitions between arbitrary nondegenerate states in hydrogen. We also discuss the perturbation theory for transitions from degenerate diamagnetic states. The theory is based on expanding in powers of the field strength the eigenfunctions and eigenvalues of the matrix of diamagnetic interaction in the subspace of states with given principal and magnetic quantum numbers. The field changes the coefficients in both the superposition and the degenerate basis. To derive the analytic expressions for the higher-order matrix elements, we use the Sturm expansion of the reduced Coulomb Green’s function. We also elaborate on the features of the frequency dependence of the corrections to the radiative matrix elements, which correlate with the structure of the diamagnetic spectrum of excited levels. Finally, we establish that the magnetic field acts selectively on the diamagnetic components of emission lines: as the field strength increases, an increase in the intensity of certain lines is accompanied by a decrease in the intensity of the other lines.

Journal of Experimental and Theoretical Physics•Oct 1, 1999•2 citations

Stark effect on probabilities of radiation transitions

Alexander A. Kamenski, Vitalii D Ovsiannikov

Analytical dependences on a static electric field F 0 are derived for the wave functions, matrix elements and probabilities of radiation transitions between multiplet substates interacting in field in pairs, ranging from ordinary doublet states with spin S =1/2, pair-wise interacting sublevels of triplet and quintet states with the magnetic quantum number M =0, to the most general case of states with arbitrary angular L and spin S momenta and maximal magnitude of the magnetic quantum number | M |= L + S -1. Equalization of doublet line intensities in the anticrossing field region and vanishing of one of the two doublet lines in the high-field regime are demonstrated. A general relation is determined between the anticrossing field F A , multiplet splitting and tensor polarizability.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 15, 2007•0 citations

Crystal-field Paschen-Back effect on ruby in ultrahigh magnetic fields

Masaki Gen, Tomoki Kanda, Takashi Shitaokoshi +2 more

This paper reports the anomalous Zeeman effect of the R lines of ruby in megagauss region. This observation owes to the Paschen-Back effect, where the Zeeman energy overcomes the crystal-field energy splitting, resulting in the renormalization of the good quantum number.

arXiv:2006.06199•Physical Review Research•Aug 17, 2020•4 citations

Electric-field-induced redistribution of radiation transition probabilities in atomic multiplet lines

Aleksandr A. Kamenski, Vitalii D Ovsiannikov

Analytical dependences on a static electric field F 0 are derived for the wavefunctions, matrix elements and probabilities of radiation transitions between multiplet substates interacting in field in pairs, ranging from ordinary doublet states with spin S = 1/2, pairwise interacting sublevels of triplet and quintet states with the magnetic quantum number M = 0, to the most general case of states with arbitrary angular L and spin S momenta and maximal magnitude of the magnetic quantum number | M | = L + S − 1. Equalization of doublet line intensities in the anticrossing field region and vanishing of one of the two doublet lines in the high-field regime are demonstrated. A general relation is determined between the anticrossing field F A , multiplet splitting and tensor polarizability. The data of numerical computations with the Fues' model potential for polarizabilities of triplet states in helium and doublet states in alkali atoms are extrapolated with a three-term polynomial including 5th, 6th and 7th powers of effective principal quantum number and providing accuracy better than 0.5% in a wide range of the principal quantum number n , up to n = 1000.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 24, 2006•20 citations
Analytical expressions for the dependence of the intensity of Zeeman components of doublet lines on the magnetic field are obtained. Sharp changes of these function on passing from the anomalous Zeeman effect to the Paschen-Back effect lead to the disappearance of marginal lines and the equalization of intensities of remaining lines. In the region of the complete Paschen-Back effect, a strong influence on these dependences is produced by the dynamic atom-field interaction, which weakens the paramagnetic effect in the states with a positive magnetic quantum number m and enhances the effect in the states with a negative m . Simple analytical expressions are obtained that take into account the effect of the diamagnetic interaction on line intensities. The role of the diamagnetic interaction increases in Rydberg atomic states with a large spin-orbit splitting. For the states with m > 0, it can lead to the “diamagnetic reversal” of the Paschen-Back effect, i.e., the recovery of the anomalous Zeeman effect.
Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δ l | ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.
It is shown that the magnetic field induces the radiative decay of metastable states of inert gases by mixing them with resonant sublevels of the lowest multiplet. The polarization and frequency structures of the “forbidden” lines induced by the magnetic field are determined, and the dependence of the intensity of π and σ components of these lines on the magnetic field is calculated. The effect is totally governed by the paramagnetic atom-field interaction, and the influence of the diamagnetic interaction is insignificant.
We study the effect of diamagnetic interaction on the probability of radiative transitions of an atom from states split by a field. We write the analytic expressions for the diamagnetic corrections to the matrix elements of transitions belonging to the Lyman and Balmer series and of transitions between arbitrary nondegenerate states in hydrogen. We also discuss the perturbation theory for transitions from degenerate diamagnetic states. The theory is based on expanding in powers of the field strength the eigenfunctions and eigenvalues of the matrix of diamagnetic interaction in the subspace of states with given principal and magnetic quantum numbers. The field changes the coefficients in both the superposition and the degenerate basis. To derive the analytic expressions for the higher-order matrix elements, we use the Sturm expansion of the reduced Coulomb Green’s function. We also elaborate on the features of the frequency dependence of the corrections to the radiative matrix elements, which correlate with the structure of the diamagnetic spectrum of excited levels. Finally, we establish that the magnetic field acts selectively on the diamagnetic components of emission lines: as the field strength increases, an increase in the intensity of certain lines is accompanied by a decrease in the intensity of the other lines.
Analytical dependences on a static electric field F 0 are derived for the wave functions, matrix elements and probabilities of radiation transitions between multiplet substates interacting in field in pairs, ranging from ordinary doublet states with spin S =1/2, pair-wise interacting sublevels of triplet and quintet states with the magnetic quantum number M =0, to the most general case of states with arbitrary angular L and spin S momenta and maximal magnitude of the magnetic quantum number | M |= L + S -1. Equalization of doublet line intensities in the anticrossing field region and vanishing of one of the two doublet lines in the high-field regime are demonstrated. A general relation is determined between the anticrossing field F A , multiplet splitting and tensor polarizability.
Analytical dependences on a static electric field F 0 are derived for the wavefunctions, matrix elements and probabilities of radiation transitions between multiplet substates interacting in field in pairs, ranging from ordinary doublet states with spin S = 1/2, pairwise interacting sublevels of triplet and quintet states with the magnetic quantum number M = 0, to the most general case of states with arbitrary angular L and spin S momenta and maximal magnitude of the magnetic quantum number | M | = L + S − 1. Equalization of doublet line intensities in the anticrossing field region and vanishing of one of the two doublet lines in the high-field regime are demonstrated. A general relation is determined between the anticrossing field F A , multiplet splitting and tensor polarizability. The data of numerical computations with the Fues' model potential for polarizabilities of triplet states in helium and doublet states in alkali atoms are extrapolated with a three-term polynomial including 5th, 6th and 7th powers of effective principal quantum number and providing accuracy better than 0.5% in a wide range of the principal quantum number n , up to n = 1000.