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Physical Review A

Decay of H atoms excited in small electric fields

B. Van Zyl, B. K. Van Zyl, W. B. Westerveld

Published Jun 1, 1988• 3 citations
Publisher

Abstract

The branching ratios for radiative decay of H atoms excited in small electric fields (0--5 V/cm) have been calculated for the nl states up to n=6. A simple computational procedure was employed, allowing only for Stark-effect mixing of levels with the same values of the quantum numbers (n,j,${m}_{j}$). The results are compared with more detailed calculations available for 3l-state decay made using the density-matrix formalism, and new calculations of this type reported here for 4l-state decay. In conjunction with theory, this allowed the domain of validity of the simple computational procedure to be established as a function of n. The results show that the branching ratios depend quite strongly on electric-field magnitude, pointing to the need to exercise caution in measurements of H emissions, and in application of the available data to other problems.

DOI
10.1103/physreva.37.4201

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The branching ratios for radiative decay of H atoms excited in small electric fields (0--5 V/cm) have been calculated for the nl states up to n=6. A simple computational procedure was employed, allowing only for Stark-effect mixing of levels with the same values of the quantum numbers (n,j,mj{m}_{j}mj​). The results are compared with more detailed calculations available for 3l-state decay made using the density-matrix formalism, and new calculations of this type reported here for 4l-state decay. In conjunction with theory, this allowed the domain of validity of the simple computational procedure to be established as a function of n. The results show that the branching ratios depend quite strongly on electric-field magnitude, pointing to the need to exercise caution in measurements of H emissions, and in application of the available data to other problems.
The branching ratios for the n=3 to n=2 Balmer-\ensuremath{\alpha} decay of hydrogen atoms in axial and transverse electric fields in the range 0--1000 V/cm have been calculated with use of a density-matrix formalism to take into account the time evolution of the atomic states in the presence of an electric field. The branching ratios are useful when the production of 2s hydrogen atoms is measured with the use of an electric field and when it is desired to correct for cascade contributions from the n=3 level. The total n=3 to n=2 branching ratio is found to depend on each of the 14 independent quantities which determine the axially symmetric n=3 density matrix, thus emphasizing the need to determine the complete density matrix including the off-diagonal coherence terms. If the off-diagonal density-matrix elements are not known, it is preferable to use transverse electric fields since, in this configuration, the contributions to the branching ratios from the off-diagonal terms are less than with axial electric fields. For transverse fields of approximately 200 V/cm, the contribution from the off-diagonal terms are nearly zero.
We have measured certain ratios of transition intensities between excited hydrogen Stark sublevels over a range of electric-field values. CO2{\mathrm{CO}}_{2}CO2​ lasers were used to excite a fast beam of hydrogen atoms. The \ensuremath{\pi}-polarized transitions studied were from extremal Stark sublevels of principal quantum number n=10 to extremal and next extremal sublevels of n=30 and 44, at fields from 2 to 700 V/cm. The observed ratios are compared with those obtained using a non-relativistic zero-field formula attributed to Gordon [Ann. Phys. (Leipzig 2, 1031 (1929)] and with calculations employing matrix diagonalization including fine structure. Even for those relatively high n values, we find at low field significant deviations from results from Gordon's formula due to fine structure in the lower state as well as deviations at high field due to n mixing in the upper state induced by the static electric field. The experimental results and the matrix diagonalization calculations agree to within a few percent, which is the order of magnitude of possible saturation effects.
We have measured the lifetimes of 1Pe^{1}P^{e}1Pe (n=9−−12)(n=9--12)(n=9−−12) doubly excited states in static electric fields (1−−6kV∕cm)(1--6\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm})(1−−6kV∕cm) by observing the decay of the fluorescence signal as a function of time. The effects of the field on these helium states below the second ionization threshold are twofold: their excitation becomes possible due to the Stark mixing with the optically allowed 1Po^{1}P^{o}1Po series, and their lifetime is strongly modified by the opening of the autoionization channel, not accessible in zero field. Although the electric field represents only a tiny perturbation of the atomic potential, a substantial shortening of the lifetimes below 100ps100\phantom{\rule{0.3em}{0ex}}\mathrm{ps}100ps is observed. This is the simplest quantum system where the ratio of autoionization to fluorescence decay probability can be effectively controlled by an electric field of moderate strength.
New features of the blackbody-induced radiation processes on Rydberg atoms were discovered on the basis of numerical data for the blackbody-induced decay P d nl ( T ), excitation P e nl ( T ) and ionization P ion nl ( T ) rates of n S, n P and n D Rydberg states calculated together with the spontaneous decay rates P sp nl in neutral hydrogen, and singlet and triplet helium atoms for some values of the principal quantum number n from 10 to 500 at temperatures from T = 100 K to 2000 K. The fractional rates R d ( e , ion) nl ( T ) = P nl d ( e , ion) ( T )/ P sp nl equal to the ratio of the induced decay (excitation, ionization) rates to the rate of spontaneous decay were determined as functions of T and n in every series of states with a given angular momentum l = 0, 1, 2. The calculated data reveal an essential difference between the asymptotic dependence of the ionization rate P ion nl ( T ) and the rates of decay and excitation P d ( e ) nl ( T )∝ T / n 2 . The departures appear in each Rydberg series for n > 100 and introduce appreciable corrections to the formula of Cooke and Gallagher. Two different approximation formulae are proposed on the basis of the numerical data, one for R d ( e ) nl ( T ) and another one for R ion nl ( T ), which reproduce the calculated values in wide ranges of principal quantum number from n = 10 to 1000 and temperatures between T = 100 K and T = 2000 K with an accuracy of 2% or better. Modified Fues' model potential approach was used for calculating matrix elements of bound–bound and bound–free radiation transitions in helium.
The linear-Stark-effect approximation is employed to investigate the effects of electric fields on autoionizing doubly excited atomic states corresponding to relatively large values of the outer-electron principal quantum number nnn. By assuming that a statistical distribution of the inner-electron magnetic sublevels has been established, simple expressions are derived which relate the autoionization and radiative transition rates in the presence of an electric field to the respective field-free rates. It is pointed out that the multiphoton laser excitation of the doubly excited states can give rise to a nonstatistical distribution of the magnetic sublevels and to complex interference terms involving transition amplitudes associated with different values of the outer-electron angular momentum quantum number lll. The results of calculations are presented for the autoionization and radiative-transition rates which play the most important role in the dielectronic recombination of the Li-like Fe+23{\mathrm{Fe}}^{+23}Fe+23 ion through the $2p\ensuremath{\rightarrow}2s$ inner-electron transition, where the contributions from large-nnn values are particularly important. In these calculations it is assumed that the magnetic sublevels are statistically populated and only the simple expressions for the transition rates are employed. The effects of the electric field on the dominant (inner-electron) radiative decay rate can be neglected, but the electric field mixing of the outer-electron lll substates substantially increases the autoionization rates from the higher-lll sublevels.
Photon emission by an atom in the metastable 2S2S2S state in a weak static electric field is examined within the context of bound-state quantum electrodynamics. Low's method is applied to obtain the expansion in terms of Coulomb wave functions of the propagation function for an electron interacting with the nuclear Coulomb field, the applied electric field, and the quantized radiation field. For a weak applied field, and to lowest relative order in $\frac{\ensuremath{\alpha}}{\ensuremath{\pi}}$, the 2S2S2S-state resonant contribution to the propagation function can be factorized to provide the basis for a calculation of the angular distribution of single-photon radiation and lifetime of the excited state. A numerical evaluation is given, which takes into account effects of electric dipole, magnetic dipole, and magnetic quadrupole emission, relativistic corrections, and finite level widths.