Parabolic States Research Articles

Selective excitation of parabolic Stark states in ion-atom collisions via the Paul-trap mechanism

Excitation of atoms by ion impact is analyzed for such collisions where only the Coulomb field of the ion affects the excitation process. At intermediate energies, electrons bound to the atom are promoted on the saddle of a two-center Coulomb field, where they are dynamically stabilized by a Paul-trap-like mechanism. These excitation processes lead to transient atomic states with large electric dipole moments. By measuring the intensity of HeI spectral lines induced by 10–500-keV protonhelium and 65-MeV Arq +-helium (q = 6 and 13) collisions as a function of an electric field Fz applied to the collision volume, the electric dipole moments predicted by the Paul-trap model were detected.

Coherent states composed of Stark eigenfunctions of the hydrogen atom

It is well known that for the nonrelativistic hydrogen atom it is possible to separate the Schrödinger equation in parabolic as well as spherical coordinates. The eigenfunctions obtained in these coordinate systems are each a suitable basis set in the absence of an electric field, but only the parabolic states, the Stark eigenfunctions, retain their character in the presence of a weak field. The properties of coherent superpositions of these Stark states are investigated and the motion of the resulting wave packet described. It is shown that a properly constituted superposition will mimic classical motion. It is also shown that the constant energy separation between adjacent Stark states of a given principal quantum number leads to periodic motion. In general, they split into distinct “clumps” of probability, but revive to form a single packet after each period. It is, however, possible to construct a packet that maintains its shape for all time.

Internal photoemission on a-Si:H Schottky barrier structures revisited

Direct measurements of mobility gaps in hydrogenated amorphous silicon (a-Si:H) using internal photoemission (IPE) of electrons and holes have been carried out. The analysis used in the measurement of metal/a-Si:H Schottky barrier heights in the previous studies was based on the classical Fowler theory. More detailed treatment of IPE in a-Si:H Schottky barriers, however, shows that the IPE yields Y(hν) α (hν − E T ) 2+c rather than (hν − E T ) 2 , where E T is the threshold energy. In the case of parabolic extended band states, c = 1 2 and the exponent 5 2 in place of 2. The extrapolations of yield versus hν result in barrier heights lower than those determined by the Fowler theory but can be fitted over a larger energy range. The effects of the new analysis of experimental results on different a-Si:H materials are presented and discussed.

Interference oscillations in ionization of extreme Stark states by half-cycle pulses

We study the classical, semiclassical, and quantum dynamics of parabolic Rydberg states of hydrogen subject to half-cycle electromagnetic pulses as a function of the field strength and the duration of the pulses. We show that for the most ``red-shifted'' Stark state the quantum ionization probability oscillates around the classical value. These oscillations can be described semiclassically in terms of path interference. By contrast, the ionization probability of the extreme ``blue-shifted'' state is a smooth function of field strength. These predictions could be tested experimentally.

Selective excitation of parabolic Stark states of He I by proton impact.

Resonancelike intensity variations of the impact radiation were observed at electric-field anticrossings of 1[ital snl] [sup 1][ital L] and [sup 3][ital L] Stark sublevels ([ital n]=5, 6, 7; [ital l][ge]2), when investigating excitation of helilium atoms by 12.5 keV proton impact. The measured signal amplitudes provide strong evidence that the collision process excites the electron selectively to the ([ital n][sub 1] , [ital n][sub 2], [ital m]) hydrogenic Stark states (0, [ital n][minus]1, 0) and (0, [ital n][minus]2, [plus minus]1), indicating that the electron is promoted along in-saddle sequences of H[sub 2][sup +]-like molecular orbitals during the final phase of the collision.

Free-bound dipole transition in H-like atoms

The matrix elements for free-bound transitions between parabolic states are given by compact expressions which satisfy simple and real recurrence relations.

Atomic electron wave packets in an electrical field.

We have observed the periodic motion of a parabolic electron wave packet. The wave packet was created by coherent excitation with 7-ps laser pulses of several parabolic states of atomic rubidium in a dc electrical field. The dispersion of the wave packet was small because the spacing between subsequent energy levels of the Stark map is almost constant. By measuring the photoionization yield in a pump-probe experiment, as many as 10 oscillations were observed.

Ml=1 photoionization spectrum of hydrogen in strong dc electric fields.

We present experimental and theoretical studies of the ${m}_{l}$=1 photoionization channel of H(n=2,${m}_{l}$=0) blue and red parabolic states in strong external electric fields in the energy region between the classical ionization threshold at E=-2 \ensuremath{\surd}F and the isolated-atom photoionization threshold at E=0. Our results indicate that the ionization from the rapidly ionizing channels is concentrated away from but between the two thresholds. We also find that the fractions of the nuclear charge ${Z}_{1}$=0, (1/2, and 1 define two regions that classify the properties of the states. These results are in contrast to our previous results for the ${m}_{l}$=0 channels where the ionization is concentrated at the two thresholds and the fractions ${Z}_{1}$=0, (1/4, (1/2, (3/4, and 1 define four quarters that classify the properties of these channels.

The stark effect in hydrogen: Properties of threshold resonances in the photoionization spectrum of excited parabolic states

Abstract We have performed exact numerical calculations of the photoionization of highly excited parabolic states of hydrogen in the region of the zero field ionization limit (E ∼ 0) in an external electric field. We present results for the photoionization of blueshifted m=0 initial states (n2=0) by both π and σ polarized light. For highly excited initial states, the effects of the overlap of the initial and final state charge distributions become dominant in determining which final states will be excited, leading to approximate selection rules. The broad resonances in the photoionization spectrum near E=0 are shown to be dramatically enhanced and narrowed, resulting in the appearance of essentially isolated resonances in π polarization. In contrast to the situation for photoionization of low-lying states, large resonances are also predicted to be present in σ polarization.

Spectroscopy between parabolic states in hydrogen: Enhancement of the Stark-induced resonances in its photoionization.

We present calculations of the photoionization spectrum of excited hydrogen using \ensuremath{\pi} polarization in the presence of a strong electric field as a function of the spherical (applicable to complex atoms) and parabolic quantum numbers of the excited state. We also present corresponding measurements of the photoionization yield from the individual parabolic states of n=2. Both the calculations and the measurements show an enhancement of the depth of the so-called ``Stark-induced modulation'' in the region E\ensuremath{\ge}0 when the initial excited state is a pure ${m}_{l}$=0 blue state, and disappear almost completely when the initial state is a pure ${m}_{l}$=0 red state. These results are understood using arguments based on the fact that the charge distribution of the Stark-induced states is tremendously extended up field. Because of the excellent signal to noise ratio of the enhanced modulations, we were able to measure the field dependence of the spacings with sufficient accuracy to confirm the (3/4) power law and rule out the recently suggested (2/3) power law.

Hidden symmetry, separation of variables and interbasis expansions in the two-dimensional hydrogen atom

Expansions for each fundamental basis of the hydrogen atom over two others are found and an additional integral of motion corresponding to an elliptic basis is determined. Representations of the elliptic basis as a superposition of polar and parabolic states are obtained. Certain interesting limiting cases are investigated.

Degenerate perturbative treatment of the hydrogenic Zeeman effect

Degenerate perturbation theory is applied to study the first 14 energy levels of the hydrogen atom in a uniform magnetic field up to the second order. The twofold degeneracy of all the levels among them in terms of the oscillator or parabolic states is completely removed. The results obtained with the use of the Pad\'e approximant are compared with those found in the literature. Level crossings are discussed.

Dc Conductivity, Optical Absorption, and Photoconductivity of Amorphous Arsenic Telluride Films

Conductivity, optical absorption, and photoconductivity experiments on amorphous ${\mathrm{As}}_{2}$${\mathrm{Te}}_{3}$ films are described. The films were prepared by condensation of the vapor on a cooled substrate. Over the temperature range from about 200 to 400\ifmmode^\circ\else\textdegree\fi{}K, the conductivity is of the form $\ensuremath{\sigma}={\ensuremath{\sigma}}_{0}{e}^{\ensuremath{-}\frac{\ensuremath{\Delta}E}{\mathrm{kT}}}$, with ${\ensuremath{\sigma}}_{0}=600$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{\Delta}E=0.4$ eV. This result is interpreted in terms of a "conductivity gap" of 0.8 eV. An analysis of the preexponental factor yields an average mobility between about 0.3 and 5 ${\mathrm{cm}}^{2}$/V sec, suggesting that the "mobility edges" which are responsible for the conductivity gap are on the borderline between localized and delocalized states. An "optical gap" is derived from a treatment of the optical-absorption data which suggests that for energies well above the conductivity gap the density of valence and conduction-band states have a parabolic dependence on energy. The optical gap of 0.95-0.98 eV is the energy difference between the edges of these parabolic states. Photoconductivity measurements indicate that the room-temperature life-time is less than 50 nsec. These measurements provide an estimate of 0.3 ${\mathrm{cm}}^{2}$/V sec for the lower limit of the mobility of carriers. The photoconductivity data also show the presence of trapping states.