Metastable states of atomic hydrogen in an ideal linearly polarized laser have been shown to exist. These states, in the laboratory frame, have the electron oscillating with a large amplitude. The electron will radiate both even and odd harmonics of the laser frequency at a rate calculated here. The electron may also radiate nonharmonic radiation, thereby leaving the atom in an excited state. This process contributes to the width of the ground state. Both processes are evaluated at an upper limit of intensity imposed upon the theory by the dipole approximation.
This paper discusses the general theory of two-photon ionization of a hydrogenic state in the nonrelativistic dipole approximation. An application is made to the photoionization of the metastable
2S state of atomic hydrogen by optical radiation, for example, by the light from a ruby laser. The sum over intermediate states is carried out exactly by means of an implicit technique. The results are given for a range of wave-lengths from the threshold at 7290 down to 4556 \AA{}. At 6943 \AA{}, the total cross section per unit intensity is found to be 5.35\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}29}$
cm4 ${\mathrm{W}}^{\ensuremath{-}1}$. The lowest order damping corrections to the perturbation-theory results are worked out.
In view of the possibilities of laser spectroscopy with very short pulses and relatively high frequencies, we examine aspects of the theory of atom-field interactions that are related to violation of the condition of the long-wavelength approximation (LWA) according to which
kr⪡1, where
r is ``of the order of atomic dimensions'' and
k is the magnitude of the wave vector. On- and off-resonance transitions are considered, with
kr being larger than unity due to the large extent of the two wave functions involved in the coupling matrix element. The implementation of the analysis uses bound-free transition matrix elements with the
n=50 and 80 hydrogenic functions as initial states and values of
k up to
27eV, which is sufficient to produce
kr>1, thereby rendering the LWA inoperative. In spite of this, it is shown that, for on-resonance transitions, the results from the use of the well-known multipole operators resulting from the LWA [e.g., the electric dipole approximation (EDA)] agree with those from the exact expressions derived here from the application of the multipolar Hamiltonian. This numerical agreement is proven analytically. As a test of the kind of convergence of the multipole series expansion for small values of
k and large
r, it is shown that the lowest-order ratio of electric dipole to quadrupole matrix elements decreases rapidly within 1.0 atomic unit above threshold. Finally, it is shown that off-resonance couplings lead to differences between the full-interaction operator and the EDA which cannot be neglected. In the extreme case of intrashell couplings for the
n=50 shell, calculation shows that the
50p state is coupled to angular momentum states up to $\ensuremath{\ell}=21$, compared to the electric dipole coupling of $\ensuremath{\Delta}\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$.
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.