Physical Review A

Stark effect of nonhydrogenic Rydberg spectra

U. Fano

Published Jul 1, 1981• 97 citations

Abstract

Rydberg states of an atom in an electric field are represented in terms of hydrogen eigenfunctions for the same field but scattered by the ionic core of the actual atom. The effect of the Stark field on photoabsorption is expressed in terms of scattering and frame-transformation parameters.

DOI: 10.1103/physreva.24.619

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Stark effect of nonhydrogenic Rydberg spectra

U. Fano

Rydberg states of an atom in an electric field are represented in terms of hydrogen eigenfunc-tions for the same field but scattered by the ionic core of the actual atom. The effect of the Stark field on photoabsorption is expressed in terms of scattering and frame-transformation parameters.

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Field-ionization Stark spectra of Ba Rydberg atoms at high density of states

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Argon atoms in Stark states at n approximately 25 have been decelerated and accelerated in inhomogeneous electric fields. The acceleration and deceleration behavior can be understood only by considering the adiabatic Landau-Zener dynamics that take place at the avoided crossings between the Stark states and the limited fluorescence lifetimes of approximately 10 micros.

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On the Theory of the Stark Effect in Hydrogenic Atoms

Vladimir Rojansky

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Physical Review A

Stark effect of nonhydrogenic Rydberg spectra

U. Fano

Published Jul 1, 1981• 97 citations

Publisher

Abstract

DOI: 10.1103/physreva.24.619

Related papers

Stark effect of nonhydrogenic Rydberg spectra

U. Fano

Routledge eBooksJan 22, 20190 citations

Field-ionization Stark spectra of Ba Rydberg atoms at high density of states

Andreas Sebastian Konig, Jörg Neukammer, H. Hieronymus +1 more

Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.

Physical Review AMar 1, 19918 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)].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 ANov 1, 198470 citations

Stark–Zeeman and Blokhintsev Spectra of Rydberg Atoms

Andrei Letunov, Valerii S. Lisitsa

The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.

Journal of Experimental and Theoretical PhysicsNov 1, 20202 citations

Nonhydrogenic Effects in the Deceleration of Rydberg Atoms in Inhomogeneous Electric Fields

E. Vliegen, Hans Jakob Wörner, T. P. Softley +1 more

Physical Review LettersJan 23, 2004104 citations

On the Theory of the Stark Effect in Hydrogenic Atoms

Vladimir Rojansky

The Stark effect of the fine structure of hydrogenic atoms is discussed in the light of the quantum mechanics. Explicit formulas are given for the energy levels in either a weak or a strong electric field, including in each case both the relativity corrections and the Stark effect. (The conventional treatment neglects either one or the other.) The results are, except in form, similar to those recently given by Schlapp. In the new mechanics, in contradistinction to the old Bohr theory, there is a linear Stark effect even in weak fields, because of the identity of energy for the $\mathrm{ns}$ and $n{p}_{1}$ levels in the absence of external fields. This degeneracy is shown to account for the results of the recent experiments of Ornstein, Zernike, and Snoek, who found that the $2s$ level in $H$ is not metastable.The coefficients are found for the development of the "parabolic" eigenfunctions in terms of the "polar" ones, and a set of numerical values of these coefficients is tabulated.Methods are given for the calculation of the relative intensities in the Stark effect in terms of the already available theoretical fine structure intensities in the absence of fields.The Stark effect of the fine structure of hydrogenic atoms is discussed in the light of the quantum mechanics. Explicit formulas are given for the energy levels in either a weak or a strong electric field, including in each case both the relativity corrections and the Stark effect. (The conventional treatment neglects either one or the other.) The results are, except in form, similar to those recently given by Schlapp. In the new mechanics, in contradistinction to the old Bohr theory, there is a linear Stark effect even in weak fields, because of the identity of energy for the $\mathrm{ns}$ and $n{p}_{1}$ levels in the absence of external fields. This degeneracy is shown to account for the results of the recent experiments of Ornstein, Zernike, and Snoek, who found that the $2s$ level in $H$ is not metastable.The coefficients are found for the development of the "parabolic" eigenfunctions in terms of the "polar" ones, and a set of numerical values of these coefficients is tabulated.Methods are given for the calculation of the relative intensities in the Stark effect in terms of the already available theoretical fine structure intensities in the absence of fields.

Physical ReviewJan 1, 192943 citations

{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)].

\mathrm{ns}

and

n{p}_{1}

levels in the absence of external fields. This degeneracy is shown to account for the results of the recent experiments of Ornstein, Zernike, and Snoek, who found that the

2s

level in

H

is not metastable.The coefficients are found for the development of the "parabolic" eigenfunctions in terms of the "polar" ones, and a set of numerical values of these coefficients is tabulated.Methods are given for the calculation of the relative intensities in the Stark effect in terms of the already available theoretical fine structure intensities in the absence of fields.