Showing papers on "Stark effect published in 1978"

Atomic and Molecular Polarizabilities-A Review of Recent Advances

Abstract: Publisher Summary This chapter focuses on the recent developments in the experimental and theoretical determination of the polarizabilities of simple atoms and molecules. Polarizability values (related to the “quadratic Stark effect”) are accurately known for the noble gas atoms and for hydrogen, in theory, but the remainder of the periodic table has proven much more difficult to deal with, both theoretically and experimentally. The static electric dipole polarizability of the ground-state hydrogen atom is almost exactly 4.5a30, where a0 is the Bohr radius. Across rows of the periodic table, polarizabilities range from hundreds (of a30 units) for the alkali metal atoms generally monotonically down to a few for noble gas atoms. Excited atoms have much larger polarizabilities; recent polarizability measurements for atoms in Rydberg orbits have yielded values on the order of 1010a30. Further research on molecular polarizabilities can help in the determination of polarizability anisotropies whether through state selection or with beams of different temperatures. Supersonic molecular beams are found to have low internal energies, and the internal energy can be controlled somewhat in “seeded” beams.

Electronic resonance enhancement of coherent anti-Stokes Raman scattering

Abstract: We analyze the enhancement of the coherent anti-Stokes Raman-scattering (CARS) susceptibility when the frequencies of the waves involved are tuned into resonance with discrete and continuum one-photon absorptions, and discuss the applications. We first derive the expression for the susceptibility by means of the usual iterative treatment of density-matrix perturbations. We then show that this derivation can be done in a straightforward manner by means of a time-ordered diagrammatic representation, which brings novel physical insight into CARS mechanisms. This representation can also be used to analyze the transient behavior of CARS as the pump fields are turned on and off. In addition, we discuss resonant CARS spectroscopy in the gas phase. The spectrum is composed of the expected enhanced Raman lines and also of double-electronic-resonance lines. All these lines occur as doublets. We derive their relative intensities based on detunings, collisional broadening, Franck-Condon overlap integrals, and rotational transition moments. The line contours are predicted by representing the susceptibility in the complex plane. The problems arising from saturation and the optical Stark effect are also considered; all should be small below pump densities of 100 MW/${\mathrm{cm}}^{2}$ in gas mixtures near STP. Fluorescence interference is negligible, except at power densities high enough for the Stark effect to be large. Beam absorption is also negligible at STP if the resonant species' concentration is less than 1000 ppm; phase matching is then satisfied. Finally, an experimental resonant CARS spectrum of ${\mathrm{I}}_{2}$ at 1 mb in air near STP is presented and interpreted; the susceptibility is about 400 times larger than that of ${\mathrm{O}}_{2}$ off resonance and under the same thermodynamic conditions.

Stark Effect Revisited

Abstract: We extend the rigorous theory of complex scaling to atoms in constant electric field. This allows one to give a precise mathematical definition of resonance and leads to several results about the perturbation series: Borel summability at nonreal field and a relation between the asymptotics of the perturbation coefficients for large $n$ and the width of the resonance for small field.

Stark profile calculations for Lyman series lines of one-electron ions in dense plasmas. Interim report

Abstract: The frequency distributions of the first six Lyman lines of hydrogen-like carbon, oxygen, neon, magnesium, aluminum, and silicon ions broadened by the local fields of both ions and electrons are calculated for dense plasmas. The electron collisions are treated by an impact theory allowing (approximately) for level splittings caused by the ion fields, finite duration of the collisions, and screening of the electron fields. Ion effects are calculated in the quasistatic, linear Stark-effect approximation, using distribution functions of Hooper and Tighe which include correlation and shielding effects. Theoretical uncertainties from the various approximations are estimated, and the scaling of the profiles with density, temperature and nuclear charge is discussed. A correction for the effects caused by low frequency field fluctuations is suggested.

Perturbation theory of the Stark effect in hydrogen to arbitrarily high order

Abstract: The solution of the Stark effect in hydrogen to arbitrarily high orders of perturbation theory is made feasible by the explicit formula for the Nth-order energy in terms of the separation constants through Nth order, derived here. The Nth-order separation constant ..beta../sup( N/)/sub i/ is shown to be a polynomial of total degree N + 1 in the parabolic quantum number n/sub i/ and the magnetic quantum number m. The polynomial coefficients have been tabulated through seventeenth order and are listed here through tenth order. Similarly, the Nth-order energy is a polynomial in the quantum numbers n/sub 1/, n/sub 2/, and m. The polynomial coefficients (which are more numerous than for ..beta../sup( N/)/sub i/) have been tabulated through seventeenth order and are listed here through seventh order. Seventeenth order is high enough to permit a clear numerical demonstration of the asymptotic character of the perturbation series, and a ''maximum useful field strength'' is defined and illustrated. Energies calculated by perturbation theory for specific states are shown to be in excellent agreement with energies calculated nonperturbatively.

Photon Statistics and Spectrum of Transmitted Light in Optical Bistability

Abstract: A quantum description of the transmitted field is given. In the bistable situation, the stationary Glauber quasi probability distribution has two peaks thereby producing a first-order phase transition. For small incident field the linewidth of the transmitted light is proportional to the atomic density and becomes very narrow as the field approaches some critical value from below. Crossing this value the spectrum splits discontinuously into a triplet (dynamical Stark shift) where the central peak is as high as twice the side-bands.

Resonances in Stark effect and perturbation theory

Abstract: It is proved that the action of a weak electric field shifts the eigenvalues of the Hydrogen atom into resonances of the Stark effect, uniquely determined by the perturbation series through the Borel method. This is obtained by combining the Balslev-Combes technique of analytic dilatations with Simon's results on anharmonic oscillators.

Complex coordinates and the Stark effect

Abstract: The theories of the dilatation, r ..-->.. re/sup i theta/, and translation, x ..-->.. x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the /sup 1/P/sup 0/, 2s2p H/sup -/ shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation. 45 references.

An asymptotic approach to the Stark effect for the hydrogen atom

Abstract: An asymptotic method is presented for solving the problem of a hydrogen atom perturbed by a uniform electric field F considered as a weak field. An asymptotic expansion for the level width Gamma is obtained. A comparison is given of the values of Gamma obtained using the asymptotic formulae with exact numerical results.

Microwave spectrum, structure, dipole moment and centrifugal distortion of nitrosomethane. Dipole moment of acetaldehyde

Abstract: The microwave spectra of ten isotopic species of nitrosomethane have been measured enabling structures for CH3NO and CD3NO to be determined independently. The mean of these structures is found to be : NO = 1.211, C—N = 1.480, C—Hi(in plane)= 1.094, C—H0(out-of-plane)= 1.094 A, ∠CNO = 113.2, ∠HiCN = 111.0, ∠H0CN = 107.2 and ∠H0CH0= 109.2°. The methyl group is tilted by 2.5° away from the oxygen atom. The orientation of the dipole moment in nitrosomethane has been determined from isotopic measurements. For CH315NO, higher order Stark perturbation terms, arising through an accidental near degeneracy, had to be included to obtain an accurate dipole moment. The components of the dipole moment are; µa= 2.262, µb= 0.516 and µ= 2.320 ± 0.004 D. The orientation of the dipole moment in the related molecule acetaldehyde has been determined from isotopic work and previous Stark effect measurements have been refined to give µa= 2.537, µb= 1.062 and µ= 2.750 ± 0.006 D. A, E splittings in the microwave spectra of CH3NO and CD3NO have been analysed by both the principal axis method (PAM) and the internal axis method (IAM) for a rigid top–rigid frame model. An attempt to fit the spectrum of CD3NO was made using Woods' IAM treatment in conjunction with Watson's centrifugal distortion theory. More precise distortion constants were then obtained from the spectra of sym-CH2DNO and sym-CHD2NO and used to determine a preliminary harmonic force field for nitrosomethane. A few perturbations in the spectra of the symmetric species have been observed due to sym–asym interactions. The structure, bonding and vibrational properties of nitrosomethane are discussed.

Effects of an external electric field on /sup 1/P/sup o/ resonances of H/sup -/

Abstract: Positions, widths, and oscillator strengths for the $2s\ensuremath{-}2p$ "shape" resonance and the lowest Feshbach resonance in the $^{1}P^{o}$ spectrum of ${\mathrm{H}}^{\ensuremath{-}}$ have been computed via the method of complex coordinates. The dc Stark broadening of the shape resonance has been determined giving a quantitative estimate of the effects of plasma microfields on the resonance and explaining the negative observational results of Ott et al. [Phys. Rev. A 12, 2009 (1975)].

Stark structure of barium Rydberg states

Abstract: Observations of the Stark structure of barium for Rydberg states in the region of n=12 are presented. The Stark manifold includes a valence state which perturbs the 1D2 series. General features of the interaction of the valence and Rydberg states in the presence of the electric field are explained by simple arguments based on configuration mixing.

ac Stark Splitting in Resonant Multiphoton Ionization with Broadband Lasers

Abstract: An intense laser and a probe laser in near resonance with the sodium 3S/sub 1/2/ ..-->.. 3P/sub 1/2/ and 3P/sub 1/2/ ..-->.. 4D/sub 3/2/ transitions, respectively, produce a three-photon ionization current used to study the broadening and Rabi splitting of the 3P/sub 1/2/ intermediate state as a function of probe-laser tuning. We find a narrow, intense-laser detuning region where the peak heights ratio of the Rabi-split 3P/sub 1/2/ doublet is reversed from that predicted for a monochromatic laser field. This is attributed to the finite (approx. GHz) laser linewidth.

Resonant States in the Nonperturbative Regime: The Hydrogen Atom in an Intense Electric Field

Abstract: I present the first results of a precise measurement of the intense-field Stark effect in highly excited states of atomic hydrogen, a prototype system for experimental and theoretical studies of resonant states in the nonperturbative regime. I show that the quantity ${n}^{4}F$ (in atomic units), known to be important for field ionization, also governs the divergence properties of the perturbation series for the energy shift.

A simple formula for estimating Stark widths of neutral lines

Abstract: A simple formula for the prediction of Stark widths of neutral lines similar to the semiempirical method of Griem (1968) for ion lines is presented. This formula is a simplification of the quantum-mechanical classical path impact theory and can be used for complicated atoms for which detailed calculations are not readily available, provided that the effective position of the closest interacting level is known. The expression does not require the use of a computer. The formula has been applied to a limited number of neutral lines of interest, and the width obtained is compared with the much more complete calculations of Bennett and Griem (1971). The agreement generally is well within 50% of the published value for the lines investigated. Comparisons with other formulas are also made. In addition, a simple estimate for the ion-broadening parameter is given.

Complex scaling: An introduction

Abstract: The complex scaling method, also known as the complex coordinate or dilatation transformation method, is discussed in relation to the Stark effect and to the calculation of the position and width of resonant states of atoms or molecules. The significance of resonant scattering in atomic physics is briefly reviewed. 29 references.

Spectra of atomic Hamiltonians in DC fields: use of the numerical range to investigate the effect of a dilatation transformation

Abstract: Analysis of the numerical range of the atomic Stark Hamiltonian under the dilatation transformation r to rei theta gives sufficient information about the spectrum to justify use of the method for determination of atomic Stark shifting and broadening parameters in DC electric fields.

Effects of magnetic sublevel degeneracy on Rabi oscillations

Abstract: This paper describes the dynamics of multilevel excitation by coherent radiation, in the N-level rotating-wave approximation, when the levels have nonzero angular momentum J and consequent spatial-orientation degeneracy 2J + 1. Observable populations average over 2J + 1 independent sublevel excitation sequences. The phenomenon of inaccessible sublevels is noted, as is the effect of polarization. The paper illustrates how averaging over orientation can, in some cases, render illegible the Rabi oscillations and the ac Stark effect, whereas in other cases (J ..-->.. J, circular polarization on J ..-->.. J +- 1 linear polarization) appreciable structure remains.

Observation of second‐order Stark effects in silane, SiH4

Abstract: The Stark effect on rovibrational transitions of the tetrahedral molecule silane has been studied by laser Stark spectroscopy, i.e., by applying dc fields of up to 65 kV/cm and monitoring the absorption of fixed frequency ir laser lines. The coincidences observed occur between the ν4 fundamental of SiH4 and N2O laser lines. Using the inverse Lamb dip technique single M components of three high J transitions could be resolved, and two of these have been identified by rf–ir double resonance. In both cases the Stark shift is due to the second‐order Stark mixing of A1 with A2 rotational levels. The analysis of the Stark effects is consistent with the ground state centrifugal distortion moment ϑzxy=3.34×10−5 D measured previously by Kagann, Ozier, and Gerry. Experiments to measure the frequency offset Δν=νM−νL of the molecular absorption lines from the nearest laser line have also been performed, using the beat between two N2O lasers. Direct evidence of the second‐order Stark shift has been obtained by observi...

Microwave spectrum, dipole moment and internal rotation potential function of gauche-cyclopropanol

Abstract: The Microwave spectra of cyclopropanol and cyclopropan-[2H1]-ol slow the gauche-conformation is the dominant species present in the vapour at 293K. No evidence for the existence of the trans-conformation has been obtained. The spectra of this rotamer show transitions associated with dipole components in all three inertial axes, the b-type transitions, which form an appreciable part of the spectra, being split into doublets separated by ≈ 8200 MHz in the normal form and by ≈ 326 MHz in the [2H1] form an account of contributions of the torisonal frequence 0–â†� 0+ to these absorptions. Many lines of the normal form depart from rigid rotor behaviour. An analysis has been made in terms of nine parameters for this form, and confirmed by numerous double reasonances. The 0–â†� 0+ excitation energy for this species is 4115.25(42) MHz. Spectra of gauche-cyclopropan-[2H1]-ol can be fitted to a single set of rotational constants common to the 0+ and 0– states and a 0–â†� 0+ excitation energy of 163.74(1.80) MHz. The dipole moment components of the [2H12] from are determined from Stark effect measurements as : µa= 1.58(10)× 10–30 C m, [0.48(3)D]′µb= 3.75(50)× 10–30 C m, [1.12(15) D]; µc= 2.70(57)10–30 C m, [0.81(17) D]; and µtotal= 4.88(67)× 10–30 C m, [1.46(20) D];. Substitution coordinates of the hydroxyl hydrogen accord with an equilibrium dihedral angle of internal rotation, α, of 106°± 5° relative to a zero at the trans-conformation. The 0–â†� 0+ energy differences are used in conjunction with this value of α and the assumption that no stable trans-from occurs, to yield an approximate potential function for internal rotation. The cis-barrier separating the gauche-minima is 7.9(1.5)kJ mol–1, while the barrier via the trans-conformation is 17(6) kJ mol–1, while the barrier via the trans-conformation is 17(6) kJ mol–1.

Stark profile measurements on Lyman series lines of Al xiii

Abstract: Single shot photographic spectra of hydrogen‐like aluminum Lyman series lines are obtained from a low inductance vacuum spark. Corresponding pinhole pictures yield information on the source size. The observed line profiles are found to increase in width along the series and the higher series members Lγ and Lδ can be matched with convolved Stark and Gaussian profiles. The Gaussian profile includes the effects of source size, thermal Doppler broadening, and crystal resolution. The space and time‐averaged electron density determined from the profile analysis is 2.5×1021–1×1022 cm−3.