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

Journal of Physics B Atomic and Molecular Physics

Systematic theoretical study of the Stark spectrum of atomic hydrogen. II. Density of oscillator strengths. Comparison with experimental absorption spectra in solid-state and atomic physics

Eliane Luc-Koenig, Annik Bachelier

Published May 14, 1980• 77 citations
Publisher

Abstract

For pt.I see ibid., vol.13, no.9, p.1743 (1980). Absolute values for the density of oscillator strengths in the photoabsorbtion spectrum of hydrogen-like atoms in the presence of a uniform electric field are calculated using the wavefunctions obtained from the method described in the previous paper. The symmetry properties of the wavefunctions with respect to the plane z=0 are analysed-z is the direction of the electric field. Cancellation effects can appear in the calculation of oscillator strengths due to the symmetry properties of the wavefunctions and of the polarisation of the light. The hydrogenic model is used to interpret the structures observed in the absorption spectra of alkali atoms and of semiconductors in the presence of an external electric field.

DOI
10.1088/0022-3700/13/9/010

Related papers

Hydrogen atoms in arbitrary magnetic fields. II. Bound-bound transitions

H Forster, W. Strupat, Wolfgang Rösner +3 more

For pt.I see ibid., vol.17, p.29-52 (1984). Wavelengths, dipole strengths, oscillator strengths and transition probabilities for electromagnetic transitions between low-lying states of the hydrogen atom embedded in a magnetic field of arbitrary strength (0<B<or=4.70*10 8 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B values using the wavefunctions and energy values determined in paper I by expanding the wavefunctions in terms of spherical harmonics (weak and moderate fields), or in terms of Landau states (strong and very strong fields). Effects caused by the finiteness of the proton mass are taken into account, and the scaling laws are quoted by the aid of which the results presented can be utilised to cover quantitatively the whole hydrogenic sequence in intense magnetic fields; finally, the quality of the results of previous calculations is checked.

Journal of Physics B Atomic and Molecular Physics•Apr 14, 1984•84 citations

WANNIER-MOTT EXCITONS AND ATOMS IN A DC ELECTRIC FIELD: PHOTOIONIZATION, STARK EFFECT, RESONANCES IN THE IONIZATION CONTINUUM

Alexander V. Glushkov, Ya. I. Lepikh, О. Yu. Khetselius +3 more

A numerical calculation of the DC Stark effect for hydrogen and sodium atoms and Wannier-Mott excitons in an external uniform DC electric field is carried out within the operator perturbation theory method. New adequate model for description of the unique especialitites in the photoionization spectra of the hydrogenic atoms is proposed. It is found that the Stark shift for the n=2 state of excitons in the Cu2 O semiconductor (yellow series) at the electric field strength 600 V/cm results in — 3,1 10 -4 eV which agrees well with experimental data of Gross et al. It is indicated also that the analogous unique especialitites may possibly take a place in the Wannier-Mott excitons spectra near the threshold boundary

Sensor Electronics and Microsystem Technologies•Oct 28, 2008•0 citations

Analytical study of quasidiscrete Stark levels in Rydberg atoms

David A. Harmin

A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths ${f}_{r}^{F}$ are derived in terms of matrices ${\mathit{H}}^{F}$ and ${\mathit{h}}^{F}$, which represent the hydrogenic density of states in a Stark field $F$. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements ${d}_{l}^{0}$. Normalized oscillator strengths ${\overline{f}}_{r}^{F}$ are defined which are independent of all ${d}_{l}^{0}$ for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with $m=0 \mathrm{and} 1$ are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields $F<\frac{1}{3{n}^{5}}$ level positions are given analytically with respect to H levels of fixed $n$; $m=0$ intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At $F>\frac{1}{3{n}^{5}}$, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at $m=1$ anticrossings in Li, as observed in ZLKK. For $m=0$ the lower levels usually vanish instead. A full Stark map of calculated intensities ${\overline{f}}_{r}^{F}$ is presented for Li ($m=0$) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include $\mathrm{ls}$ coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].

Physical Review A•Nov 1, 1984•70 citations

Oscillator strengths in the spectra of highly excited atomic hydrogen in crossed electric and magnetic fields

Petr A. Braun

A study is made of the spectra of a highly excited hydrogen atom in crossed external l-mixing electric and magnetic fields. A semiclassical model is suggested for the radiative transitions between the perturbed Rydberg levels and the low-lying levels of the atom. The emitted light is shown to be a superposition of radiation of two effective linear vibrators symmetrically placed with respect to the external fields' plane. The interference between the vibrators is the source of rapid oscillations of the observed line intensities and polarization accompanying even small variation of the external fields. The averaged spectral intensity is shown to be unchanged by the presence of the magnetic field, being the same as in Stark splitting.

Journal of Physics B Atomic Molecular and Optical Physics•May 14, 1991•2 citations

H(3s) beam production by laser excitation of metastable hydrogen atoms in an electric field. II. Theoretical approach

D. Fussen, W. Claeys, A Cornet +1 more

For pt.I see ibid., vol.18, no.18, p.3557-37 (1985). A quantitative description of H(3s) atoms produced by laser excitation of a metastable hydrogen beam in an electric field is performed and compared with the recent experimental results of Claeys et al. (1985). The Stark effect for n=3 is calculated to obtain the relative intensities of the five Stark transitions as a function of the field strength. Good agreement with the experimental values is found. The dynamical behaviour of the 3s and 3p Stark states when the atoms leave the field is then analysed. Due to the adiabatic evolution we found that only one Stark state can produce H(3s) atoms.

Journal of Physics B Atomic and Molecular Physics•Sep 28, 1985•7 citations

Model Potential Calculations of Oscillator Strength Spectra of Rydberg Li Atoms in External Fields

Meng Hui-Yan, Ting-Yun Shi

By combining the B-spline basis set with model potential (B-spline + MP), we present oscillator strength spectra of Rydberg Li atoms in external fields. The photoabsorption spectra are analyzed. Over the narrow energy ranges considered in this paper, the structure of the spectra can be independent of the initial state chosen for a given atom. Our results are in good agreement with previous high-precision experimental data and theoretical calculations, where the R-matrix approach together with multichannel quantum defect theory (R-matrix+MQDT) was used. It is suggested that the present methods can be applied to deal with the oscillator strength spectra of Rydberg atoms in crossed electric and magnetic fields.

Communications in Theoretical Physics•Aug 1, 2009•4 citations
For pt.I see ibid., vol.13, no.9, p.1743 (1980). Absolute values for the density of oscillator strengths in the photoabsorbtion spectrum of hydrogen-like atoms in the presence of a uniform electric field are calculated using the wavefunctions obtained from the method described in the previous paper. The symmetry properties of the wavefunctions with respect to the plane z=0 are analysed-z is the direction of the electric field. Cancellation effects can appear in the calculation of oscillator strengths due to the symmetry properties of the wavefunctions and of the polarisation of the light. The hydrogenic model is used to interpret the structures observed in the absorption spectra of alkali atoms and of semiconductors in the presence of an external electric field.
For pt.I see ibid., vol.17, p.29-52 (1984). Wavelengths, dipole strengths, oscillator strengths and transition probabilities for electromagnetic transitions between low-lying states of the hydrogen atom embedded in a magnetic field of arbitrary strength (0<B<or=4.70*10 8 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B values using the wavefunctions and energy values determined in paper I by expanding the wavefunctions in terms of spherical harmonics (weak and moderate fields), or in terms of Landau states (strong and very strong fields). Effects caused by the finiteness of the proton mass are taken into account, and the scaling laws are quoted by the aid of which the results presented can be utilised to cover quantitatively the whole hydrogenic sequence in intense magnetic fields; finally, the quality of the results of previous calculations is checked.
A numerical calculation of the DC Stark effect for hydrogen and sodium atoms and Wannier-Mott excitons in an external uniform DC electric field is carried out within the operator perturbation theory method. New adequate model for description of the unique especialitites in the photoionization spectra of the hydrogenic atoms is proposed. It is found that the Stark shift for the n=2 state of excitons in the Cu2 O semiconductor (yellow series) at the electric field strength 600 V/cm results in — 3,1 10 -4 eV which agrees well with experimental data of Gross et al. It is indicated also that the analogous unique especialitites may possibly take a place in the Wannier-Mott excitons spectra near the threshold boundary
A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths frF{f}_{r}^{F}frF​ are derived in terms of matrices HF{\mathit{H}}^{F}HF and hF{\mathit{h}}^{F}hF, which represent the hydrogenic density of states in a Stark field FFF. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements dl0{d}_{l}^{0}dl0​. Normalized oscillator strengths f‾rF{\overline{f}}_{r}^{F}f​rF​ are defined which are independent of all dl0{d}_{l}^{0}dl0​ for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with m=0and1m=0 \mathrm{and} 1m=0and1 are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields F<13n5F<\frac{1}{3{n}^{5}}F<3n51​ level positions are given analytically with respect to H levels of fixed nnn; m=0m=0m=0 intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At F>13n5F>\frac{1}{3{n}^{5}}F>3n51​, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at m=1m=1m=1 anticrossings in Li, as observed in ZLKK. For m=0m=0m=0 the lower levels usually vanish instead. A full Stark map of calculated intensities f‾rF{\overline{f}}_{r}^{F}f​rF​ is presented for Li (m=0m=0m=0) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include ls\mathrm{ls}ls coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].
A study is made of the spectra of a highly excited hydrogen atom in crossed external l-mixing electric and magnetic fields. A semiclassical model is suggested for the radiative transitions between the perturbed Rydberg levels and the low-lying levels of the atom. The emitted light is shown to be a superposition of radiation of two effective linear vibrators symmetrically placed with respect to the external fields' plane. The interference between the vibrators is the source of rapid oscillations of the observed line intensities and polarization accompanying even small variation of the external fields. The averaged spectral intensity is shown to be unchanged by the presence of the magnetic field, being the same as in Stark splitting.
For pt.I see ibid., vol.18, no.18, p.3557-37 (1985). A quantitative description of H(3s) atoms produced by laser excitation of a metastable hydrogen beam in an electric field is performed and compared with the recent experimental results of Claeys et al. (1985). The Stark effect for n=3 is calculated to obtain the relative intensities of the five Stark transitions as a function of the field strength. Good agreement with the experimental values is found. The dynamical behaviour of the 3s and 3p Stark states when the atoms leave the field is then analysed. Due to the adiabatic evolution we found that only one Stark state can produce H(3s) atoms.
By combining the B-spline basis set with model potential (B-spline + MP), we present oscillator strength spectra of Rydberg Li atoms in external fields. The photoabsorption spectra are analyzed. Over the narrow energy ranges considered in this paper, the structure of the spectra can be independent of the initial state chosen for a given atom. Our results are in good agreement with previous high-precision experimental data and theoretical calculations, where the R-matrix approach together with multichannel quantum defect theory (R-matrix+MQDT) was used. It is suggested that the present methods can be applied to deal with the oscillator strength spectra of Rydberg atoms in crossed electric and magnetic fields.