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 Lifetimes for the Hydrogen Atom

John R. Hiskes, C. Bruce Tarter, D. A. Moody

Published Jan 20, 1964• 49 citations
Publisher

Abstract

The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through $n=25$. In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers ${n}_{1}$, ${n}_{2}$, and $m$. For $m>0$ and to within an error of the order of one percent the radiative lifetimes are functions only of $n$, $m$. The radiative lifetimes are presented graphically for all states from $n=2$ through $n=25$.

DOI
10.1103/physrev.133.a424

Related papers

Radiative widths of Stark components of fine-structure levels of a hydrogen atom. [transition probabilities, electric field strength]

B. A. Zon, Boris G. Katsnelson, Yu. N. Mitin +1 more

The probabilities of electromagnetic decay of fine-structure states of a hydrogen atom are calculated as a function of the strength of an external constant electric field. (AIP)

•Apr 1, 1976•0 citations

Sum rules and expansion formula for Stark radiative transitions in the hydrogen atom

David R. Herrick

An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large-$n$ regime.

Physical Review A•Nov 1, 1975•24 citations

Model-potential calculation of lifetimes of Rydberg states of alkali atoms

Xinghong He, Baiwen Li, Aiqiu Chen +1 more

A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 28, 1990•61 citations

Radiative Cascade Theory

Pyare Lal, P. T. Landsberg

A steady-state cascade theory has been set up for radiative electron transitions. These are assumed to occur between a continuum and various excited states, as well as between any two excited states, of hydrogen-like atoms. The work contains two features which have not previously been fully taken into account: (1) Both spontaneous and induced transition probabilities have been included exactly. (2) In addition to the radiative transitions, the reverse transitions due to absorption of background radiation have also been included. The following graphical results are given: (a) The steady-state occupation probabilities of the excited states as a function of excess electron density. (b) A "sticking probability" ${P}_{n}$ (for an electron from a level $n$ to reach the ground state without leaving the atom) as a function of the principal quantum number $n$. (c) The effect of the cascade on the transition rate into the ground state. The calculation is valid for semiconductors and for the analogous astrophysical problem. Temperature dependences have also been studied. The graphs shown bear out quantitatively the expectation that ${P}_{n}$ decreases as either the temperature or the principal quantum number increases.

Physical Review•Oct 4, 1965•12 citations

Transition probabilities, lifetimes, and branching ratios in hydrogen-like atoms in the linear stark effect

Kazem Omidvar

Atomic Data and Nuclear Data Tables•Mar 1, 1983•15 citations

Classical calculation of the lifetimes and branching ratios for radiative decays of hydrogenic atoms

Marko Horbatsch, Eric A. Hessels, Marko Horbatsch

The correspondence principle for atomic radiation is extended to all hydrogenic states $n$ and $l>0$. Lifetimes and branching ratios are obtained using analytic calculations of the classical radiated spectrum for the elliptical orbit corresponding to a particular quantum state. The polarization of the radiation is used to separate out the angular momentum decreasing and increasing transitions. The lifetimes show excellent agreement with quantum mechanics for all principal quantum numbers $n$ and $l\ensuremath{\geqslant}1$ (e.g., $<100\phantom{\rule{0.3em}{0ex}}\text{parts}\phantom{\rule{0.3em}{0ex}}\text{per}\phantom{\rule{0.3em}{0ex}}\text{million}$ for $l\ensuremath{\geqslant}30$, $<0.1%$ for $l\ensuremath{\geqslant}9$, $<1%$ for $l\ensuremath{\geqslant}3$). The calculated branching ratios are in reasonable agreement with quantum results for all ${n}^{\ensuremath{'}}$, ${l}^{\ensuremath{'}}$, $n$, and $l\ensuremath{\geqslant}1$.

Physical Review A•Feb 10, 2005•10 citations
The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through n=25n=25n=25. In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers n1{n}_{1}n1​, n2{n}_{2}n2​, and mmm. For m>0m>0m>0 and to within an error of the order of one percent the radiative lifetimes are functions only of nnn, mmm. The radiative lifetimes are presented graphically for all states from n=2n=2n=2 through n=25n=25n=25.
An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large-nnn regime.
A comprehensive set of transition probabilities and radiative lifetimes of Rydberg states of alkali atoms (for Na, K, Cs, n<or=30; and for Rb, n<or=50) is obtained by using a simple, exactly solvable potential model for atoms. The results agree well with the available experimental values and other theoretical ones. Scaling relations for evaluating transition probabilities and lifetimes of high Rydberg states are also discussed. The well known (n*) -5 scaling law of the transition probabilities A n(inf) not=n(inf) / with n' approximately=n>>1 is generally valid; however, the authors also find deviations from this law for some d to p and f to d transitions for Rb. A third-power polynomial is found to be better than the currently used exponential scaling law in predicting the lifetimes of even higher excited states.
A steady-state cascade theory has been set up for radiative electron transitions. These are assumed to occur between a continuum and various excited states, as well as between any two excited states, of hydrogen-like atoms. The work contains two features which have not previously been fully taken into account: (1) Both spontaneous and induced transition probabilities have been included exactly. (2) In addition to the radiative transitions, the reverse transitions due to absorption of background radiation have also been included. The following graphical results are given: (a) The steady-state occupation probabilities of the excited states as a function of excess electron density. (b) A "sticking probability" Pn{P}_{n}Pn​ (for an electron from a level nnn to reach the ground state without leaving the atom) as a function of the principal quantum number nnn. (c) The effect of the cascade on the transition rate into the ground state. The calculation is valid for semiconductors and for the analogous astrophysical problem. Temperature dependences have also been studied. The graphs shown bear out quantitatively the expectation that Pn{P}_{n}Pn​ decreases as either the temperature or the principal quantum number increases.
The correspondence principle for atomic radiation is extended to all hydrogenic states nnn and l>0l>0l>0. Lifetimes and branching ratios are obtained using analytic calculations of the classical radiated spectrum for the elliptical orbit corresponding to a particular quantum state. The polarization of the radiation is used to separate out the angular momentum decreasing and increasing transitions. The lifetimes show excellent agreement with quantum mechanics for all principal quantum numbers nnn and $l\ensuremath{\geqslant}1$ (e.g., <100partspermillion<100\phantom{\rule{0.3em}{0ex}}\text{parts}\phantom{\rule{0.3em}{0ex}}\text{per}\phantom{\rule{0.3em}{0ex}}\text{million}<100partspermillion for $l\ensuremath{\geqslant}30$, <0.1<0.1%<0.1 for $l\ensuremath{\geqslant}9$, <1<1%<1 for $l\ensuremath{\geqslant}3$). The calculated branching ratios are in reasonable agreement with quantum results for all ${n}^{\ensuremath{'}}$, ${l}^{\ensuremath{'}}$, nnn, and $l\ensuremath{\geqslant}1$.