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 A

Photon-Scattering Theory of the Quenching of Hydrogenic Metastables

G. W. F. Drake, R. B. Grimley

Published Jul 1, 1973• 26 citations
Publisher

Abstract

The quenching of hydrogenic metastables is formulated as a near-resonant photon-scattering problem, and a complete analysis of the polarization and angular distribution of the emitted radiation is presented. The contribution from $\mathrm{np}$ states with $n>2$ is calculated, and an alternative method of measuring the Lamb shift is suggested.

DOI
10.1103/physreva.8.157

Related papers

Test of the anisotropy method for Lamb-shift measurements—theory and experiment

G. W. F. Drake, Péter Faragó, Adriaan J. van Wijngaarden

We show that a measurement of the anisotropy in the angular distribution of the quenching radiation emitted by metastable hydrogen and deuterium atoms in an electric field can be used to determine the Lamb shift to an accuracy of at least \ifmmode\pm\else\textpm\fi{}0.1%. The method can be extended to the hydrogenic ions, where it offers several advantages over the quench-rate technique used in earlier measurements. The experiment is interpreted by means of a nonperturbative theory of the quenching process, which includes hyperfine structure and time-dependent effects. In the limit of zero field strength, the anisotropies of H and D are measured to be 0.139 01 \ifmmode\pm\else\textpm\fi{} 0.000 12 and 0.141 21 \ifmmode\pm\else\textpm\fi{} 0.000 14, while the theoretical values are 0.139 078 and 0.141 30, respectively. The corresponding Lamb shifts are 1057.3 \ifmmode\pm\else\textpm\fi{} 0.9 MHz and 1058.7 \ifmmode\pm\else\textpm\fi{} 1.1 MHz.

Physical Review A•May 1, 1975•30 citations

Interaction of Optical and Infrared Radiation with Metastable Hydrogen Atoms

Wolfgang Zernik

This paper is an extension of a previous one and discusses the theory of the quenching of the metastable $2S$ state of atomic hydrogen by means of optical radiation, for example by the light from a ruby laser. The case discussed is that for which the incident intensity is sufficiently weak for the usual quantum-electrodynamical perturbation theory to be valid. A procedure developed by Schwartz and others is used to carry out the sum over intermediate states without explicit enumeration. The results are given for a range of incident wavelengths from 5000 \AA{} to 5\ensuremath{\mu}. For unpolarized light from a ruby laser (6934 \AA{}), the total cross section for quenching is found to be ${\ensuremath{\sigma}}_{Q}=1.27\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ ${\mathrm{cm}}^{2}$. The cross section for coherent scattering has also been calculated for the same range of wavelengths; for ruby laser light, the total cross section for scattering is found to be ${\ensuremath{\sigma}}_{S}=1.03\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ ${\mathrm{cm}}^{2}$.

Physical Review•Jan 6, 1964•41 citations

Two-photon decay of hydrogenic atoms

J. H. Tung, X. M. Salamo, F. T. Chan

The two-photon decay mode of hydrogenic atoms from an arbitrary state (${n}_{1}$, ${l}_{1}$, ${m}_{1}$) to an arbitrary state (${n}_{2}$, ${l}_{2}$, ${m}_{2}$) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the $2s$ metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.

Physical Review A•Sep 1, 1984•72 citations

Comments on the polarization of the quenched radiation from the 2s state of hydrogen

Edward J. Kelsey, J. H. Macek

This paper examines two theoretical aspects of the measurement of polarization of the quenched radiation which comes from the application of a weak electric field to the $2s$ state of hydrogen. Specifically, it outlines the justification of the Bethe-Lamb phenomenological analysis of this problem from the external field approximation of quantum electrodynamics. Further, it includes the lowest-order effects of the $J$-breaking part of the hyperfine structure in Rayleigh-Schr\"odinger perturbation theory. While it was expected that these terms would contribute to the polarization fraction a correction to the lowest order of the relative size of the ratio of the hyperfine splittings to the fine-structure splitting of the $n=2$ state or about one part in ${10}^{3}$, cancellations occur and these $J$-breaking terms give a correction in the fourth place of the polarization fraction.

Physical Review A•Sep 1, 1977•9 citations

Two-photon polarization Fourier spectroscopy of metastable atomic hydrogen

Alan J. Duncan, Z. A. Sheikh, H. J. Beyer +1 more

A novel Fourier-transform spectroscopic method using two-photon polarization to determine the spectral distribution of the two photons emitted in the spontaneous decay of metastable atomic hydrogen is described. The method uses birefringent retardation plates and takes advantage of the subtle interplay between the spectral properties and the entangled polarization properties of the radiation emitted in the decay. Assuming the validity of the theoretical spectral distribution, it is shown that the experimental results agree well with theory. On the other hand, success in solving the inverse problem of determining the spectral distribution from the experimental results is limited by the small number of experimental points. However, making reasonable assumptions it is deduced that the observed spectrum is characterized by a broadband signal of width and centre angular frequency in good agreement with the predictions of and , respectively, obtained from the theoretical spectral distribution modified to take account of the absorption of the two-photon radiation in air. The values of 1.5 fs for the coherence time and 440 nm for the coherence length for single photons of the two-photon pair which are obtained from the measured bandwidth imply that, in the ideal case, these values are determined by the essentially zero lifetime of the virtual intermediate state of the decay process rather than the long lifetime of the metastable state which, it is suggested, determines the coherence time and coherence length appropriate to certain types of fourth-order interference experiments.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 14, 1997•6 citations

Polarization of Quench-Induced Lyman- α Radiation

John W. Wooten, J. H. Macek

The polarization of quench-induced ${\mathrm{L}}_{\ensuremath{\alpha}}$ radiation is calculated for a metastable hydrogen atom entering an electric field with entry conditions intermediate between adiabatic and impulsive. We find that for most common experimental geometries the adiabatic value for the polarization may be used with less than 10% error.

Physical Review A•Jan 1, 1972•17 citations
The quenching of hydrogenic metastables is formulated as a near-resonant photon-scattering problem, and a complete analysis of the polarization and angular distribution of the emitted radiation is presented. The contribution from np\mathrm{np}np states with n>2n>2n>2 is calculated, and an alternative method of measuring the Lamb shift is suggested.
We show that a measurement of the anisotropy in the angular distribution of the quenching radiation emitted by metastable hydrogen and deuterium atoms in an electric field can be used to determine the Lamb shift to an accuracy of at least \ifmmode\pm\else\textpm\fi{}0.1%. The method can be extended to the hydrogenic ions, where it offers several advantages over the quench-rate technique used in earlier measurements. The experiment is interpreted by means of a nonperturbative theory of the quenching process, which includes hyperfine structure and time-dependent effects. In the limit of zero field strength, the anisotropies of H and D are measured to be 0.139 01 \ifmmode\pm\else\textpm\fi{} 0.000 12 and 0.141 21 \ifmmode\pm\else\textpm\fi{} 0.000 14, while the theoretical values are 0.139 078 and 0.141 30, respectively. The corresponding Lamb shifts are 1057.3 \ifmmode\pm\else\textpm\fi{} 0.9 MHz and 1058.7 \ifmmode\pm\else\textpm\fi{} 1.1 MHz.
This paper is an extension of a previous one and discusses the theory of the quenching of the metastable 2S2S2S state of atomic hydrogen by means of optical radiation, for example by the light from a ruby laser. The case discussed is that for which the incident intensity is sufficiently weak for the usual quantum-electrodynamical perturbation theory to be valid. A procedure developed by Schwartz and others is used to carry out the sum over intermediate states without explicit enumeration. The results are given for a range of incident wavelengths from 5000 \AA{} to 5\ensuremath{\mu}. For unpolarized light from a ruby laser (6934 \AA{}), the total cross section for quenching is found to be ${\ensuremath{\sigma}}_{Q}=1.27\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ cm2{\mathrm{cm}}^{2}cm2. The cross section for coherent scattering has also been calculated for the same range of wavelengths; for ruby laser light, the total cross section for scattering is found to be ${\ensuremath{\sigma}}_{S}=1.03\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ cm2{\mathrm{cm}}^{2}cm2.
The two-photon decay mode of hydrogenic atoms from an arbitrary state (n1{n}_{1}n1​, l1{l}_{1}l1​, m1{m}_{1}m1​) to an arbitrary state (n2{n}_{2}n2​, l2{l}_{2}l2​, m2{m}_{2}m2​) is studied within the framework of nonrelativistic quantum mechanics. In the dipole approximation, these decay rates, which involve infinite summation over intermediate states, are derived exactly via a general second-order matrix element obtained by Kelsey and Macek and an implicit technique introduced by Dalgarno and Lewis. The results are expressed in terms of hypergeometric functions. For transitions ${n}_{1}s\ensuremath{\rightarrow}{n}_{2}s$, our results reduce to those of Klarsfeld whose starting point is the Coulomb Green's function. For transitions to the ground state, an alternative expression involving a simple one-dimensional integral is presented. The decay rate of the 2s2s2s metastable state of atomic hydrogen is calculated as an illustration of the method. The result, $\frac{1}{\ensuremath{\tau}}=8.2284$ ${\mathrm{sec}}^{\ensuremath{-}1}$, agrees with Klarsfeld. For transitions of ${n}_{1}s\ensuremath{\rightarrow}1s$ and ${n}_{1}d\ensuremath{\rightarrow}1s ({n}_{1}\ensuremath{\ge}3)$, the transition rates exhibit interesting and unexpected structures. In particular, "zeros" are found in the two-photon emission spectrum indicating that two-photon emission is not possible at certain frequencies. Physically, these "zeros" are the result of destructive interference between the radiating dipole terms associated with the sum over intermediate states. In addition to the emission spectrum the expected coincidence signal between two detectors monitoring the two photons simultaneously emitted during a two-photon transition is calculated as a function of the angle between the detectors. The angular distribution for the ${n}_{1}d\ensuremath{\rightarrow}1s$ transitions is shown to be significantly different from the ${n}_{1}s\ensuremath{\rightarrow}1s$ transitions. Finally, a possible experiment is suggested to test the results presented in this paper.
This paper examines two theoretical aspects of the measurement of polarization of the quenched radiation which comes from the application of a weak electric field to the 2s2s2s state of hydrogen. Specifically, it outlines the justification of the Bethe-Lamb phenomenological analysis of this problem from the external field approximation of quantum electrodynamics. Further, it includes the lowest-order effects of the JJJ-breaking part of the hyperfine structure in Rayleigh-Schr\"odinger perturbation theory. While it was expected that these terms would contribute to the polarization fraction a correction to the lowest order of the relative size of the ratio of the hyperfine splittings to the fine-structure splitting of the n=2n=2n=2 state or about one part in 103{10}^{3}103, cancellations occur and these JJJ-breaking terms give a correction in the fourth place of the polarization fraction.
A novel Fourier-transform spectroscopic method using two-photon polarization to determine the spectral distribution of the two photons emitted in the spontaneous decay of metastable atomic hydrogen is described. The method uses birefringent retardation plates and takes advantage of the subtle interplay between the spectral properties and the entangled polarization properties of the radiation emitted in the decay. Assuming the validity of the theoretical spectral distribution, it is shown that the experimental results agree well with theory. On the other hand, success in solving the inverse problem of determining the spectral distribution from the experimental results is limited by the small number of experimental points. However, making reasonable assumptions it is deduced that the observed spectrum is characterized by a broadband signal of width and centre angular frequency in good agreement with the predictions of and , respectively, obtained from the theoretical spectral distribution modified to take account of the absorption of the two-photon radiation in air. The values of 1.5 fs for the coherence time and 440 nm for the coherence length for single photons of the two-photon pair which are obtained from the measured bandwidth imply that, in the ideal case, these values are determined by the essentially zero lifetime of the virtual intermediate state of the decay process rather than the long lifetime of the metastable state which, it is suggested, determines the coherence time and coherence length appropriate to certain types of fourth-order interference experiments.