Ronald J. Bieniek

Collisional rates for vibrational-rotational transitions in circumstellar SiO masers

Calculations for rotational population inversion in circumstellar SiO masers require collisional rates for vibrational-rotational transitions. This paper reports quantum mechanical, state-to-state collisional rate coefficients for pure rotational and vibrational-rotational transitions among the first three vibrational states of SiO. These are expressed in terms of simple two-parameter power-law fits accurate in the temperature range 1000-3000 K.

An improved and extended examination of the adiabatic distorted‐wave infinite‐order sudden approximation (ADWIOSA)

Eno and Balint‐Kurti recently presented an adiabatic distorted‐wave formulation of the infinite‐order sudden approximation (ADWIOSA) that has a number of appealing qualities for calculating vibrot excitations and de‐excitations in atom–diatom collisions. The numerical values they determined for a limited number of He+H2 (nj)→He+H2 (n′j′) cross sections compared favorably to close‐coupled results. However, they employed spectroscopic diatomic eigenenergies while the exact calculations were based on harmonic eigenenergies. This paper reports extended ADWIOSA cross sections for (0j)→(1j′), (1j)→(2j′), and (0j)→(2j′) transitions using harmonic eigenenergies, and also gives corrected versions of ADWIOSA formulas. The small change in eigenenergy lowers cross sections to 1/2–1/4 their previous values. The comparison to exact results is then not quite as favorable, which is generally due to limitations in the basic sudden approximation rather than the distorted‐wave technique. The extended analysis also reveals c...

Electron-gas He-sio potential hypersurface for vibrational- rotational excitations through collisions

Abstract The Gordon-Kim electron-gas method was used to compute an ab initio potential hypersurface for the He-SiO interaction. The results are reported in the form of potential parameters associated with an accurate analytic fit of the electron-gas values.

Collisional Redistribution of Polarized Radiation for Sr - Ar(He) Systems: A Numerical Comparison of the Semiclassical Decoupling/Locking Model to Exact Results

Semiclassical formulations of collisional redistribution of polarized radiation are presented at several levels of approximation, from full classical path coupled equations to the locking/decoupling model. These are numerically tested against the results of a quantum mechanical coupled-channels formalism, by the comparison of polarization curves in both spectral wings of the Sr(1S0-1P1) transition, with Ar and He as collisional perturbers. It is found that the locking/decoupling model can often produce good agreement with exact results if the effects due to trajectories and multiple Condon points are treated properly. Significant discrepancies due to the Condon approximation used by the model are seen in the near blue wing of the spectra and attributed to antistatic effects.

Vibrational‐rotational deexcitation of HF in collision with He

State‐to‐state cross sections are reported for vibrational‐rotational transitions for HF in collisions with He, at collisional energies of 0.5 and 1.0 eV. These were computed within the infinite‐order sudden (IOS) approximation using adiabatic, distorted‐wave techniques. Values are tabulated for the vibrational‐rotational deexcitation sequences (v, j) → (v–1, 0), with v=1, 2, 3, 4 and j=0 – 40. These quenching cross sections can be used in conjunction with IOS factorization formulas to compute VRT cross sections for final rotational states other than jf=0. In addition to IOS results, vibrational quenching cross sections were computed using the much more simple breathing‐sphere technique. The breathing‐sphere results compare favorably to the more accurate IOS results, particularly as to energy dependence. This suggests a simple method of utilizing known quenching cross sections to predict values for different vibrational levels and/or collisional energies.

Semiquantal modeling of thermal vibrational relaxation of diatomic molecules

Abstract Vibrationally excited molecules play an important role in the spectroscopy, energetics, and chemical behavior of a wide range of gaseous systems of scientific and applied interest. Unfortunately, many desired collisional relaxation rates have not yet been experimentally measured, and current theoretical methods are often inadequate or too cumbersome for practical application. We report a semiquantal two-parameter scaling method for predicting relaxation rates that is very simple to employ, and impressively fits the temperature and vibrational dependencies of quantum mechanical and experimental collisional relaxation rates for several diatomic molecules (e.g., N 2 , HF, OH, NO) over many orders of magnitude.

Uniform stationary-phase methods for energy spectra resulting from collisions in a complex potential: Penning and associative ionization of He*(23S)+He*(23S)

Heavy-particle collisions involving strong electronic coupling can be conveniently described by using a complex (optical) potential in the entrance channel. Uniform JWKB stationary-phase techniques are used to evaluate T-matrix elements for transitions where an electron is ejected. The semi-analytic expressions for the resulting electron energy spectra are no more difficult to implement than corresponding ones for totally real potentials. Numerical results are reported for Penning and associative ionization from subthermal He*(23S)+He*(23S) collisions. These are in excellent agreement with fully quantal, complex-potential computations. The stationary-phase expressions for T-matrix elements and differential cross sections are employed to elucidate the rapid and slow rainbow interference oscillations in the spectra, including the significant effects of turning points and the imaginary width of the entrance-channel potential.

Evolution of the Two Cultures Controversy.

The Two Cultures schism is a persistent problem in our society. For over a century, scientific spokesmen and literary critics, from T. H. Huxley and M. Arnold to C. P. Snow and F. R. Leavis, have been involved in the Two Cultures issue. This article examines the evolution of the controversy between the ’’scientific’’ and ’’humanistic’’ elements of Western culture and its relation to educational policies. The division and antagonism between these two cultures appears to have arisen from differences in the human attitudes that they are preceived to engender. ’’Scientific’’ professionalism has been associated with a progressive optimism and self‐assurance that nurture a broad humanitarianism, while the ’’literary’’ tradition is characterized by restraint, acceptance, and a more selective humanism.

Uniform JWKB amplitudes and phases for turning-point problems

Semiclassical wave functions written in the form A (E,R)  sin[Φ (E,R)] can be used in conjunction with the method of stationary phase to obtain analytic expressions for T‐matrix elements. Such expressions are functions of the amplitudes, phases, and their derivatives at the points of stationary phase. Generally, simple JWKB formulas for amplitude [As(E,R) =k (R)−1/2] and phase [Φs(E,R) =FRRtk (r) dr+1/4π] have been used. Unfortunately these become invalid for stationary‐phase points that are near a classical turning point. This occurs at a crucial time, since T‐matrix elements are often unusually large under these circumstances. To preserve the advantages of semiclassical stationary‐phase methods, expressions for modified amplitudes, phases, and their derivatives are presented that remain uniformly valid both near to and far from the turning points in the three most commonly encountered problems: the single turning‐point of a simple free state, the double set of a bound state, and the triple set associate...

Stationary phase analysis of inelastic atomic collisions: Penning ionization

Analytica semi-classical expressions, based on a stationary phase analysis, are presented for the energy distribution of particles ejected in inelastic processes. The tabulation of basic functions yields a considerable savings of computer time. Numerical comparisons with quantal calculations are made for the Penning ionization process involving metastable helium and atomic hydrogen, using two different potentials proposed for the He*H(2Σ) state.