Stark Manifold Research Articles

Molecular quantum defect orbital study of the Stark effect in theH3molecule

Stark maps and the distribution of oscillator strengths within a Stark manifold in the ${\mathrm{H}}_{3}$ molecule have been calculated by diagonalization of the Hamiltonian matrix using a molecular quantum defect orbital (MQDO) basis set. Our perturbative treatment, in which only experimental quantum defects have been used and no fitting parameters are required, explicitly accounts for the coupling between the rotation of the molecular core and the Rydberg-electron motion. A pure Hund's case (d) has been adopted for all the Rydberg states except for the $np$ series, for which Hund's case (b) is considered to be more realistic. A mixing of some of the $np$ Stark states with those belonging to other Rydberg series appears to occur. The presently achieved results conform very well with other reliable theoretical values, in the absence of experimental data. The adequacy of the MQDO procedure for accurately dealing with properties related to the Stark effect in molecules is suggested.

Features of Er3+ luminescence in fluorine-doped amorphous silicon dioxide fabricated by low-temperature plasma CVD

Spectra and photoluminescence kinetics of Er3+ ions incorporated in an amorphous host of fluorine-doped silicon dioxide synthesized by surface plasma chemical vapor deposition (SPCVD) are investigated at temperatures of 27–300K. Luminescence is excited with an Ar+ laser at a wavelength of 514.5nm and with a diode laser at a wavelength of 975nm. Narrow and well-defined components of Stark manifolds with a small contribution from inhomogeneous broadening intrinsic to Er3+ ions in crystalline, but not amorphous, hosts are revealed and identified in photoluminescence spectra. The structure of the Stark manifolds is well-resolved at low temperatures. The presence of the well-resolved Stark structure in the spectra is indicative of stable anion complexes formating the Er3+ local neighborhood presumably associated with fluorine incorporation. This neighborhood is formed during the low temperature plasma chemical synthesis and is destroyed upon glass fusion.

Initial anticrossing between Stark manifold n and n+1 in Na

We present the theoretical results for the positions and widths of the initial anticrossing between Stark manifold n and n + 1 in sodium, obtained by using the method of diagonalization in which zero-field wave functions are chosen from a kind of atomic potential model. These results can provide the quantitative information for understanding the microwave ionization process, whose rate-limiting step is probably the n to n + 1 transition performed at the first crossing between the outermost states of these two manifolds.

Charge-transfer rates for xenon Rydberg atoms at a metal surface

The ionization of xenon Rydberg atoms excited to the lowest states in the $n=17$ and $n=20$ Stark manifolds at a flat $\mathrm{Au}(111)$ surface is investigated. Despite the strong perturbations in the energies and structure of the atomic states that occur as the surface is approached, it is shown that, under appropriate conditions, each incident atom can be detected as an ion and that the experimental data can be well fit by assuming that the ionization rate on average increases exponentially as the surface is approached. The ionization rates are compared to theoretical predictions.

The experimental study of Ba 6p jnk | M| = 0, 1 autoionizing series

The spectra of the Ba 6p nk autoionizing Stark states with | M| = 0, 1, converging to the 6p 1/2 + and 6p 3/2 + ionization thresholds, are measured as a function of the electric field strength F. Several 6p j nk Stark manifolds with n = 13–15 have been systematically studied in order to explore their characteristics of configuration interaction. Experimental results are analyzed by fitting them to the Lorentzian profile, from which the positions and widths are determined. Different spectroscopic properties between the Ba 6p 1/2 nk and 6p 3/2 nk autoionizing Stark states are investigated. Comparison between the Ba 6p j nk autoionizing Stark states with | M| = 0 and those with | M| = 1 are made.

Dipole polarization in coherently excited Stark manifolds

The dipole polarization of a coherently excited Stark manifold is studied for the simplest case of n = 2. In addition to the well-known observables (L⊥, γ) for coherent excitation of the 2p component, we explore the opportunities provided by the degeneracy of the 2s and 2p states in a purely Coulombic system. This degeneracy allows for additional observables (D, ε) that define the size and direction of the electron charge-cloud polarization. As an example, simultaneous ionization–excitation of He+(n = 2) by electron impact is discussed. Calculations of these observables for impact energies of 5640 eV and 1585 eV are shown, together with the corresponding polarized n = 2 charge-cloud densities. For ejection angles of the slow electron within 90° of the momentum-transfer direction, these calculations predict that the excited electron is preferably located on the side of the nucleus opposite to the ejected electron. For larger ejection angles, the situation is reversed.

Laser assisted excitation in electron–hydrogen-like ion collisions

An approach is developed for the study of the excitation of a ground-state hydrogenic ion under the simultaneous action of fast electron impact and a single mode, linearly polarized laser field in the framework of the Coulomb–Born approximation. The projectile–laser interaction is considered to all orders while the laser–ion interaction is considered to first order only. An elegant method is developed to construct the dressed excited states of a hydrogen-like ion target using the first-order perturbation theory in the parabolic coordinate representation which is the correct prescription for such laser assisted excitation processes. By virtue of this, the problem arising due to the l degeneracy of the excited states of a hydrogenic ion is overcome successfully. The differential (DCS) as well as total (TCS) cross sections are studied for the excitation to n = 2 level accompanied by the transfer of l photons with the field direction parallel to the incident momentum . The variations of the cross sections with respect to the target charge number Z are also studied. The overall effect of the laser field is to suppress the field free cross sections. Some numerical results are also presented for the excitation of He+ ion to individual Stark manifolds for the n = 2 level.

Study of the electric field and wall voltage in a high pressure ac-PDP cell by laser induced fluorescence spectroscopy

The electric field in a surface discharge type ac-PDP cell with He or He/Xe(0.1%) mixture has been measured over a wide range of pressure (5–50 kPa) using laser induced fluorescence detection. The wall voltage was estimated from the measured electric field. The Stark manifolds of triplet atomic helium Rydberg state (2s3S) with principal quantum numbers (n=8 and 9) have been used to measure the electric field, as the lifetime of 2s3S is longer than the single atomic helium Rydberg state (2s1S) in high pressure discharge. Comparison of the Stark manifolds between the n=9 and n=8 shows that the measurement accuracy of electric field can be increased by 10%. The maximum electric field strength during discharge and the wall voltage at the end of pulse decreases with the increase of pressure. The comparison of He and He/Xe(0.1%) discharge at 13 kPa showed that He/Xe gas mixture discharge can accumulate more wall charge on MgO surface and the electric field was somewhat higher than those of pure helium discharge during pulse off period under the same discharge conditions.

Characterization of quasi-one-dimensional Rydberg atoms using multiply directed half-cycle pulses

The characteristics of quasi-one-dimensional (1D) high-$n$ Rydberg atoms produced by photoexciting, in a weak dc field, extreme members of the $n=350$ Stark manifold are investigated by studying their ionization when subjected to unidirectional electric field pulses, termed half-cycle pulses (HCP's), of duration ${T}_{p}⪡{T}_{n}$ where ${T}_{n}$ is the classical electron orbital period, directed both parallel and perpendicular to the atomic axis. The observed differences in the ionization characteristics provide a measure of the anisotropy of the momentum distribution. It is shown that HCP's applied transverse to the atomic axis provide a particularly sensitive probe of the quasi-1D nature of the state. The experimental data are in good agreement with the results of classical trajectory Monte Carlo simulations.

Stark maps and Rydberg transitions in the presence of an electric field for Li, Na, and K. A quantum defect orbital approach

The Stark structure of the Rydberg states of the lighter alkali atoms, Li, Na, and K, and the Stark oscillator strength distribution for Li have been calculated by diagonalization of the quantum defect orbital (QDO) Hamiltonian matrix. The presently obtained Stark maps are in excellent agreement with those resulting from theory and experiment, as reported in the literature by other authors. Good accord is also found for the presently calculated oscillator strength distribution, within a Stark manifold, with that of other theoretical approach and experimental measurements. The adequacy of the QDO procedure for accurately dealing with properties related to the Stark effect in atoms is suggested.

Doppler-detuned CW excitation of then = 4 Stark manifold of atomic hydrogen

The excitation of metastable hydrogen towards then = 4 Stark manifold is investigated both theoretically and experimentally. The Stark Hamiltonian isdiagonalized to obtain the energy levels, oscillator strengths and relaxation rates of then = 2 and n = 4 Stark states. In a fast beam experiment, the transitions are excited by the blue line of aCW argon ion laser with appropriate Doppler detuning, and the measured transitionfrequencies agree well with the calculated values. The population of the 4s state, asmeasured by its fluorescence, is maximum for an electric field strength between 50 and100 V cm−1, and a laser polarization perpendicular to the static field.

Behavior of Rydberg atoms at surfaces: energy level shifts and ionization

The ionization of xenon atoms excited to the extreme red and blue states in high-lying Xe( n) Stark manifolds at a metal surface is investigated. The data show that, despite their very different initial spatial characteristics, the extreme members of a given Stark manifold ionize at similar atom/surface separations. This is explained, with the aid of complex scaling calculations, in terms of the strong perturbations in the energies and structure of the atomic states induced by the presence of the surface which lead to avoided crossings between neighboring levels as the surface is approached.

Ionization of xenon Rydberg atoms at surfaces

Measurements of the ionization of the extreme red and blue states in high-lying Xe( n) Stark manifolds at a metal surface are reported. The data show that, despite their very different initial spatial characteristics, the extreme members of a given Stark manifold ionize at similar atom/surface separations. This is attributed to energy level shifts induced by the presence of the surface which lead to avoided crossings between states in adjacent n manifolds prior to ionization. These energy level shifts are examined using hydrogenic complex scaling theory.

First charge exchange recombination spectroscopy and motional Stark effect results from the Madison Symmetric Torus reversed field pinch

We report on the first results of charge exchange recombination spectroscopy (CHERS) and motional Stark effect (MSE) measurements in the Madison Symmetric Torus reversed field pinch. A 30 keV, 4 A neutral H beam is used in combination with visible and ultraviolet spectroscopy to make the measurements. For CHERS, we find that the C VI line at 3433.69 Å yields the largest charge-exchange signal/background ratio and is most clearly resolved from other nearby lines. Equilibrium ion temperature measurements have been made with an existing fast Doppler spectrometer and a higher throughput spectrometer is being designed to do velocity and temperature fluctuation measurements. MSE measurements are made by recording the Doppler shifted Hα spectrum emitted by the beam with a charge coupled device and imaging spectrometer. We have observed separation of the π components of the Stark manifold at magnetic fields of about 0.5 T and are considering options for increasing measurement accuracy.

Photo- versus pulsed field-ionization of individual high n (n≲57) Rydberg states: Resolved d,g series of benzene

Low l Rydberg states of the polyatomic molecule benzene in the range 37≲n≲56 are resolved for the first time by double resonance excitation using narrow-band ultraviolet (UV)-laser pulses. The short lived Rydberg states are detected by photoexcitation of the ionic core with the same laser pulses followed by fast autoionization of the Rydberg states. The Rydberg spectrum obtained shows clear substructure of individual high n Rydberg peaks with components of quantum defects δl=0.00, 0.015, and 0.04. It is compared with a delayed pulsed field ionization spectrum with a delay of 8 μs. The bright low l core-penetrating zero order states cannot be observed in the delayed pulsed field ionization experiment for n<50 since there is no mixing with the long-lived Stark manifold of noncore-penetrating high l Rydberg states in the residual electric stray fields present in our apparatus which is necessary to lengthen the lifetime to survive the delay of 8 μs. Our results for the observed low l Rydberg states agree with previous results from Rydberg spectroscopy of low n Rydberg states in benzene. This is an important step towards observation of continuous Rydberg series from n=3 up to n=56. Above n=56 the different n,l Rydberg states are mixed in the electric stray fields into a single n Stark manifold.

Autoionizing Rydberg states of NO in strong electric fields

We report on an investigation on autoionization of Rydberg electrons of the nitric oxide molecule in strong, static electric fields. The excitation was done via various rotational states of the A 2Σ+ intermediate state (v′=0) and with polarization parallel or perpendicular to the electric field. The splitting of the autoionizing Rydberg states into overlapping Stark manifolds is resolved for excitation above the saddlepoint created by the field. We observe that the competing decay between photoionization and predissociation can lead to an incorrect interpretation of threshold energy. The photoionization spectrum of NO Rydberg series attached to various rotational thresholds is very similar owing to weak rotational coupling. The experimental results are accurately simulated by quantum calculations based on multichannel quantum defect theory (MQDT). A more intuitive formulation of the average behavior of the photoionization cross section is developed that accounts for the suppression of ionization near the threshold due to competing predissociating channels.

Semiclassical formula for oscillator strengths in atomic spectra

A simple semiclassical formula is given for the oscillator strengths of high Rydberg states of a hydrogen atom in an electric field. The oscillator strength of a state is proportional to the square of the function representing the quantum angular distribution of outgoing waves, evaluated at the classical angle of ejection from the atom that sends the electron into a semiclassically quantized eigentrajectory. The formula gives an interpretation of the envelopes of Stark manifolds in photoabsorption spectra; it is in good agreement with quantum calculations. The formula may also be used for other integrable or near-integrable systems.

Very-high-n Stark wave packets generated by an electric-field step

Wave packets comprising a coherent superposition of n\ensuremath{\simeq}390 Stark states have been created in potassium by rapid application of a dc field. Their properties are examined using a half-cycle probe pulse that is applied following a variable time delay and that ionizes a fraction of the excited atoms. The survival probability exhibits pronounced oscillations (quantum beats) that are associated with the time evolution of the wave packet. Interestingly, even in the present regime of complete overlap of different Stark manifolds, a single dominant beat frequency is observed, and this is explained quantum mechanically in terms of energy-level statistics. Similar behavior is predicted by classical trajectory Monte Carlo simulations that reproduce well the experimental observations demonstrating classical-quantum correspondence in high-n systems.

INFLUENCE OF ENVIRONMENTAL RADIATION ON LIFETIMES OF STARK STATES IN HIGHLY EXCITED ATOM

The populations of n=17,m=0 Stark states of sodium atom in static electric fields have been obtained by two step excitation using tunable lasers. The lifetimes of some selected Stark states and the influences of blackbody radiation on the lifetimes were measured by using delayed electric field ionization. The measured data were compared with the calculated values. The experimental and theoretical results exhibit following behaviours: The total rates of stimulated emission and absorption transitions induced by environmental radiations are of the same order of magnitude in comparison to those of spontaneous transition for the observed n=17 Stark manifold states at room temperature. And this effect is more remarkable for longer lived states. It, along with the effect of the Stark mixing of l sublevels, will reduce the differences among lifetimes of Stark states in a manifold.

Electric field ionization of high Rydberg states of Ar with sequences of identical pulses.

Novel field-ionization behavior of very high Rydberg states of Ar ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}50--250$) is observed using sequential pulsed electric fields. Fast autoionization acts as a filter against adiabatic field ionization near the ${}^{2}{P}_{1/2}$ threshold, whereas both diabatic and adiabatic field ionization occur near the ${}^{2}{P}_{3/2}$ threshold. Sequences of up to 9 equivalent pulses yield recurrent field ionization signals near the ${}^{2}{P}_{3/2}$ threshold, provided that the field returns close to zero between pulses, demonstrating a statistical redistribution of the Rydberg population amongst all states of a given Stark manifold near zero field.