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The Astrophysical Journal

Metastability of Hydrogen and Helium Levels.

GREGORY A. BREIT, Edward Teller

Published Mar 1, 1940• 337 citations
Publisher

Abstract

The mean life of the 2S state of hydrogen in the absence of collisions is primarily determined by the simultaneous emission of two photons. Owing to this cause the mean life is `-*4 sec. It is expected that the mean life of is 2S `S of He i is of the same order of magnitude and is much shorter than that of is 2S 3S of He i. The non-adiabatic collisions with electrons are found to be more important than the static effects at small electron densities, leading to a transition probability `-*-`~h sec ` for an electron temper- ature `-.--`io,ooo° C and an electron density 30 cm3. The effect of static electric fields on the 2S state of hydrogen is worked out in more detail than previously by taking into account the hyperfine structure. The mean life in static electric fields which are strong enough to make double emission of little importance and yet weak enough to give a mean life > io7 sec is found to be the sum of two lives: (i) the mean life calculated neglecting hyperfine structure and (2) the mean life calculated neglecting radiation coupling. In both (i) and (2) the mixing of 2~ into 2S by the Stark effect is taken into account. Radiations due to quadrupole and magnetic dipole effects are considered qualita- tively for is 2S 3S of helium and quantitatively for 2S of hydrogen. For the latter there exists a small radiative magnetic dipole effect on Dirac's theory of the electron which is absent in the ordinary spin model

DOI
10.1086/144158

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•Jan 1, 2018•0 citations
The mean life of the 2S state of hydrogen in the absence of collisions is primarily determined by the simultaneous emission of two photons. Owing to this cause the mean life is -*4 sec. It is expected that the mean life of is 2S S of He i is of the same order of magnitude and is much shorter than that of is 2S 3S of He i. The non-adiabatic collisions with electrons are found to be more important than the static effects at small electron densities, leading to a transition probability -*-h sec for an electron temper- ature-.--`io,ooo° C and an electron density 30 cm3. The effect of static electric fields on the 2S state of hydrogen is worked out in more detail than previously by taking into account the hyperfine structure. The mean life in static electric fields which are strong enough to make double emission of little importance and yet weak enough to give a mean life > io7 sec is found to be the sum of two lives: (i) the mean life calculated neglecting hyperfine structure and (2) the mean life calculated neglecting radiation coupling. In both (i) and (2) the mixing of 2 into 2S by the Stark effect is taken into account. Radiations due to quadrupole and magnetic dipole effects are considered qualita- tively for is 2S 3S of helium and quantitatively for 2S of hydrogen. For the latter there exists a small radiative magnetic dipole effect on Dirac's theory of the electron which is absent in the ordinary spin model
It has been found by Breit and Teller that double photon emission is the principal cause of decay of interstellar hydrogen atoms from their metastable 2s2s2s state and the mean life corresponding to this decay was bracketed by them between upper and lower limits. In the present note an account is given of a more accurate evaluation of the transition probability ${A}_{\ensuremath{\tau}}=(8.226\ifmmode\pm\else\textpm\fi{}0.001){Z}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, where ZZZ is the atomic number. Relativistic effects on the atomic wave functions have been neglected in the calculations which are therefore accurate only for small ZZZ.
The time-dependent theory of the Stark quenching of 2S2S2S states in hydrogen and helium is developed for high electric fields, fields for which the Stark matrix element is large compared to the state separations. The metastable 2S2S2S state of an atom is mixed with two PPP states by the field, and the subsequent decay is described.
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.
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.
The hyperfine levels for the ground state of hydrogen are normally connected by magnetic dipole transitions. However, for astrophysical applications, it may be that two-photon electric dipole processes are also important over cosmological distances. This thesis sets up a general mathematical formalism for the calculation of two-photon processes within the hyperfine structure of an atom with spin 1/21/21/2, and applies it to the ground state of hydrogen. Rates are calculated for both spontaneous emission and absorption of radiation. Due to an extraordinary degree of cancellation in the matrix elements, the rates turn out to be too small to have a significant impact on astrophysical processes involving the absorption and emission of radiation. The results are nevertheless important in reducing the uncertainty due to possible contributions from these processes. Other two-photon processes involving Raman scattering are also considered and the relevant cross sections calculated. The calculations of the decay rate, absorption coefficient and Raman scattering cross section are extended to heavier hydrogenic ions as a function of the nuclear charge ZZZ, using an approximate interpolation formula for the hyperfine splitting in the ground state. Results are presented for the hydrogenlike ions from He+^++ to Pb81+^{81+}81+. Modifications for the case of isotopes with a nuclear spin greater than 1/21/21/2 are briefly considered