The Stark spectroscopy of the hydrogen atom has been investigated near the ionization threshold in static homogeneous external electric fields from \ensuremath{\sim}1000 to \ensuremath{\sim}8000 V/cm with use of a two-step excitation H(n=1)+\ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{vuv}\ensuremath{\rightarrow}}$H(n=2)+\ensuremath{\Elzxh}\ensuremath{\omega} $_{\mathrm{uv}\ensuremath{\rightarrow}}$
H∗ with vuv and uv laser radiation, independently tunable and linearly polarized either parallel (\ensuremath{\pi}) or perpendicular (\ensuremath{\sigma}) with respect to the external field. Different from other, nonhydrogenic atoms, the hydrogen atom is a peculiar case insofar as the initial states of H(n=2), from which excitation takes place, are essentially of parabolic character at the field strengths employed in this study.Individual sublevels (
n1,
n2,\ensuremath{\Vert}
ml\ensuremath{\Vert}) have been prepared in the n=2 state with sub-Doppler resolution. Photoionization spectra have been obtained with \ensuremath{\pi}- and \ensuremath{\sigma}-polarized uv radiation from the four possible sublevels of the n=2 Stark manifold: \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,1,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, \ensuremath{\Vert}0,0,\ifmmode\pm\else\textpm\fi{}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉, and \ensuremath{\Vert}0,0,\ensuremath{\mp}1〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉. All spectra show sharp line structures of quasistable field-ionizing states superimposed on continua in the energy region between the classical saddle point, ${E}_{\mathrm{SP}=\mathrm{\ensuremath{-}}2\phantom{\rule{0ex}{0ex}}\mathrm{\ensuremath{\surd}}\mathrm{F}}$ a.u., and the zero-field ionization threshold E=0 a.u. Employing existing theoretical treatments, the quasistable spectral structures are quantitatively completely analyzed and accounted for, as long as their field ionization rate is less than \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}
1011 ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. Field-ionization rates of quasistable states have been measured and are compared with theory. Oscillatory resonance structures of the ionization cross section near the zero-field threshold are observed with pronounced modulation degree only in the spectrum from the \ensuremath{\Vert}1,0,0〉 \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}1/2〉 sublevel excited with the uv \ensuremath{\pi}-polarized. The energy spacing of the oscillations has been measured as a function of the electric field strength F and found to be nearly proportional to
F3/4, with slight but definite deviations. Theoretical analysis of the oscillations yields quantitative agreement with the experiment.
We observe strong energy-dependent quantum defects in the scaled-energy Stark spectra for | M | = 1 Rydberg states of barium atoms at three scaled energies: ε = –2.000, ε = –2.500 and ε = –3.000. In an attempt to explain the observations, theoretical calculations of closed orbit theory based on a model potential including core effect are performed for non-hydrogenic atoms. While such a potential has been uniformly successful for alkali atoms with a single valence electron, it fails to match experimental results for barium atoms in the 6snp Rydberg states with two valence electrons. Our study points out that this discrepancy is due to the strong perturbation from the 5d8p state, which voids the simple approximation for constant quantum defects of principle quantum number n.
A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\ensuremath{\epsilon}}_{r}$, widths ${\ensuremath{\Gamma}}_{r}$, and oscillator strengths
frF are derived in terms of matrices
HF and
hF, which represent the hydrogenic density of states in a Stark field
F. Core effects appear through zero-field quantum defects ${\ensuremath{\mu}}_{l}$ and dipole matrix elements
dl0. Normalized oscillator strengths
frF are defined which are independent of all
dl0 for $s\ensuremath{\rightarrow}p$ transitions. Isolated and interacting Stark manifolds with
m=0and1 are examined for systems with two nonnegligible ${\ensuremath{\mu}}_{l}$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields
F<3n51 level positions are given analytically with respect to H levels of fixed
n;
m=0 intensity distributions do not appear hydrogenic in Li since ${\ensuremath{\mu}}_{0}\ensuremath{\sim}\frac{1}{2}$. At
F>3n51, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at
m=1 anticrossings in Li, as observed in ZLKK. For
m=0 the lower levels usually vanish instead. A full Stark map of calculated intensities
frF is presented for Li (
m=0) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include
ls coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].
We have studied experimentally and theoretically two-step photoionization through the 3P state of sodium in an electric field of up to 3.90 kV/cm. The apparatus uses an atomic beam crossed by two pulsed laser beams, one at 589 nm for the first step, and the other swept through the zero field threshold Eo near 409 nm for the ionization. We observe broad undulations in the photocurrent above Eo that narrow with decreasing energy and eventually sharpen into well-defined but asymmetric transitions to Stark-shifted Rydberg states. We calculate the oscillator strength density for the appropriate transitions using modified hydrogenic wave functions and find excellent agreement for the position and relative strength of all the spectral features. We model the asymmetries as Fano-type interferences between quasi-discrete and continuum ionization channels. Using appropriate core potentials, and taking into account core-induced coupling of both discrete-to-continuum and continuum-to-continuum states, we obtain estimates of Fano's q and Ɖ that agree reasonably well with our measurements.
We observe strong energy-dependent quantum defects in the scaled-energy Stark spectra for vertical bar M vertical bar = 1 Rydberg states of barium atoms at three scaled energies: epsilon = -2.000, epsilon = -2.500 and epsilon = -3.000. In an attempt to explain the observations, theoretical calculations of closed orbit theory based on a model potential including core effect are performed for non-hydrogenic atoms. While such a potential has been uniformly successful for alkali atoms with a single valence electron, it fails to match experimental results for barium atoms in the 6snp Rydberg states with two valence electrons. Our study points out that this discrepancy is due to the strong perturbation from the 5d8p state, which voids the simple approximation for constant quantum defects of principle quantum number n.