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Journal of Physics B Atomic and Molecular Physics

H(3s) beam production by laser excitation of metastable hydrogen atoms in an electric field. II. Theoretical approach

D. Fussen, W. Claeys, A Cornet, V. Lorent

Published Sep 28, 1985• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/18/18/008

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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 authors studied in an earlier paper (1985) the production of a fast beam of H(3s) atoms. They investigated the particular problem of a coherent laser excitation of the 3s 1/2 and 3p 1/2 Stark states from the 2s 1/2 metastable Stark state. They measured the 3s 1/2 fluorescence outside the electric field and quantal interference effects have been observed as a function of the electric field strength. A simple theoretical interpretation is proposed which takes into account the quasi-adiabatic evolution of the atom in the electric field under the authors' experimental conditions.
The authors describe a method for producing a fast atomic hydrogen beam with a large amount of population selected in 3l j, mod mj mod levels. This is realized by a one-step tunable laser excitation of the metastable component of the atomic beam inside a nonhomogeneous static electric field. The linear laser polarization is taken either parallel or perpendicular with respect to the external field. It allows the selective excitation of all the states of the n=3 Stark manifold (with the exception of the mod mj mod =5/2 state). The electric field strength vanishes immediately after the laser excitation. At this point the population of the excited states are better referred to the atomic basis. The shapes of the resonant lines show that two transient effects are leading the excitation process. The first is of an optical kind (i.e. Rabi oscillation and rapid adiabatic passage) and the second is the intra Stark manifold state mixing due to the nonadiabatic time evolution of the external field strength. The internal state of the atoms crossing these fields is completely described by the density matrix evolution calculated independently on two bases (the atomic basis and the Stark instantaneous basis).
The excitation of metastable hydrogen towards the n = 4 Stark manifold is investigated both theoretically and experimentally. The Stark Hamiltonian is diagonalized to obtain the energy levels, oscillator strengths and relaxation rates of the n = 2 and n = 4 Stark states. In a fast beam experiment, the transitions are excited by the blue line of a CW argon ion laser with appropriate Doppler detuning, and the measured transition frequencies agree well with the calculated values. The population of the 4s state, as measured by its fluorescence, is maximum for an electric field strength between 50 and 100 V cm/sup -1 /, and a laser polarization perpendicular to the static field.
Electron-impact excitation of the hydrogen metastable 2s state to the 3s, 4s, 3d, and 4d states is studied in the presence of a resonant laser field using the rotating-wave approximation. The frequency of the circularly polarized laser field is chosen to match the 2s-3p transition frequency in the hydrogen atom. The role of the laser field in individual magnetic substate (mf{\mathit{m}}_{\mathit{f}}mf​=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2) excitation is analyzed. It is found that for these optically forbidden transitions (s-s, s-d), a significant increase in the excitation cross sections is obtained through joint collisions with electrons and photons.
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 ns\mathrm{ns}ns and np1n{p}_{1}np1​ 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 2s2s2s level in HHH 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.
We derive a set of density matrix equations describing laser photo-excitation and ionization of atomic hydrogen in the presence of an external electric field. The equations are relevant as a description of multiphoton ionization of hydrogen (or deuterium) atoms in laser-produced transient plasmas. The laser wavelength is 243 nm, so that the photoionization is resonant with the 2 s 1/2 level. The electric field causes Stark mixing of the 2 s 1/2 level with the 2 p 1/2 and 2 p 3/2 levels. Because the electric field is taken in the same direction as the linear polarization of the laser, only states with equal m j are coupled, and the atom can be described with a four-level density matrix. The laser bandwidth is taken into account by using the stochastic model of a chaotic laser field introduced by Zoller [1]. We present a few calculations of the probabilities for ionization and excitation of a single hydrogen atom as a function of laser intensity and wavelength.