Stephen L. Davis

M dependence in rotationally inelastic collisions in cell experiments: Implications of an irreducible tensor expansion for molecules in 1Σ electronic states

The tensorial coupling of initial and final angular momenta, commonly used in atomic collisions and attributed to Grawert, is here applied to M dependent collisions of molecules in 1Σ electronic states under conditions where the relative velocity vectors of the collision partners are uniformly distributed with respect to a laboratory fixed z axis. The integral inelastic cross sections are given by sums over tensor opacities, weighted by squares of vector coupling coefficients. The resulting expressions differ from those obtained within the tensorial treatment usually applied to molecular collisions. One can rigorously show that strict M conservation will not occur and, furthermore, that the complete matrix of M → M′ cross sections can be related to the smaller set of tensor opacities. In the energy sudden limit the JM → J′M′ cross sections can be related to the degeneracy‐averaged J″ → 0 cross sections. Accurate close‐coupling cross sections for the He–CO system due to Green are used to obtain the relevan...

Symmetry selection rules in rotationally inelastic collisions of open‐shell diatomic molecules and polyatomic tops: Implications of an irreducible tensor expansion

An irreducible tensor formalism due to Grawert is applied to collisions of open‐shell diatomics and polyatomic tops. Explicit examination of the reduced T‐matrix elements within the infinite‐order sudden and first‐order Born limits allows the derivation of several general symmetry selection rules for a rotationally inelastic process. In particular, both differential and integral cross sections will vanish unless the symmetry indices of the initial and final states satisfy certain conditions, for the following types of transitions: J=0→J′M′; J,M=0→J′,M′=0; and JM→J,−M. The M=0→M′=0 selection rule represents the extension, to an arbitrary orientation of the quantization axis, of a selection rule we have derived earlier. A comparison with results of fully quantum studies of collisions of NH3 and H2CO with He confirms the predictive accuracy of these rules. We discuss how both the M=0→M′=0 and JM→J,−M selection rules could be directly verified, in experiments involving laser excitation of a particular symmetr...

Inelastic collisions of CaCl(X 2Σ+) with Ar: A collaborative theoretical and experimental study

We investigate rotationally inelastic cross sections of CaCl(X 2Σ+) with Ar at a collision energy of 0.24 eV. Theoretical cross sections, determined by coupled states calculations based on an electron‐gas description of the potential surface, are compared with experimental cross sections, determined in a molecular beam apparatus involving initial state selection by an electric quadrupole field and final state detection by laser‐induced fluorescence. The agreement between theoretical and experimental cross sections is excellent, except for the e → e transitions with ΔN=even, which suggests a residual inaccuracy in the theoretical description of the second Legendre moment of the anisotropy in the potential. Both the theoretical and experimental cross sections clearly confirm a propensity toward conservation of the spectroscopic e/ f label. The sets of experimental and theoretical cross sections can be well fit by the sudden scaling relation, although the entire set of base cross sections can not be well rep...

A selection rule for M‐dependent transitions in collisional excitation of open shell diatomics

A selection rule is derived within the collision frame for M=0→M′=0 transitions in collisions between an open shell diatomic of odd multiplicity, e.g., 1Π or 3Σ, and a structureless particle. For 1Π and 3Σ states, the scattering amplitude for the J→J′ transition vanishes unless e/f symmetry is conserved. We then discuss how this selection rule for a 1Π state could be observed experimentally by measurement of the polarized fluorescence intensity ratio I⊥/I∥ in an optical–optical double resonance experiment. This raises the possibility of exploiting our selection rule to study the comparability of cross sections in the collision and laboratory frames.A selection rule is derived within the collision frame for M=0→M′=0 transitions in collisions between an open shell diatomic of odd multiplicity, e.g., 1Π or 3Σ, and a structureless particle. For 1Π and 3Σ states, the scattering amplitude for the J→J′ transition vanishes unless e/f symmetry is conserved. We then discuss how this selection rule for a 1Π state could be observed experimentally by measurement of the polarized fluorescence intensity ratio I⊥/I∥ in an optical–optical double resonance experiment. This raises the possibility of exploiting our selection rule to study the comparability of cross sections in the collision and laboratory frames.

The rotational excitation by helium of methanol in its ground and first excited torsional states

We have improved and extended our previous calculations of cross sections for the rotational excitation of methanol by helium. In the case of methanol in its torsional ground state, we extended our coupled states computations of the cross sections to higher collision energies and larger rotational basis sets. The accuracy of the rotational energy levels and eigenfunctions has been reviewed and improved for A-type methanol. The calculations have been extended to A- and E-type methanol in their first excited torsional states by averaging the CH3OH-He interaction potential over the excited state torsional eigenfunctions. Thermal rate coefficients have been calculated at low temperatures. Predictions are made of line intensity ratios which are sensitive to the density of the He perturber and which lend themselves to the determination of the perturber densities in the dark molecular clouds of the interstellar medium.

Model polarizabilities and multipoles for ionic compounds. Alkali halides

Various dipole interaction models were compared with one another and with literature values for dissociation energies, multipole moments (u, Q, and Ω), and polarizabilities α for the alkali halide molecules. A displaced‐shell (D‐shell) model, which takes account of the overlap repulsion as in the shell model but also uses the effective electron shell displacements in calculating the electrostatic interactions, gives slightly better dissociation energies and as good or better dipole and quadrupole moments than the other models. All of the models considered here give mean polarizabilities in fairly good agreement with published SCF values; however, none gives consistently good polarizability anisotropies. It is found that both the overlap repulsion (as treated in the shell model) and the effective displacements of the electron shells (as treated in the D‐shell model) have large effects on the calculated polarizability anisotropies relative to the DID model.

M dependence in the analysis of NH3–He microwave double resonance experiments

New close‐coupled calculations of laboratory‐frame, m‐dependent cross sections for rotational excitation in NH3–He collisions are used to examine the validity of using degeneracy averaged values in the analysis of four‐level double resonance experiments. It is found that the proper use of m‐dependent cross sections and absorption probabilities produces only minor changes in the calculated ΔI/I and does not, therefore, resolve the discrepancies between theoretical and experimental values that were noted in previous studies.

Electron-gas interaction potentials for collisions of CaCl(X 2Σ+) and KCl(X 1Σ+) with Ar

Abstract Interaction potentials for CaCl(X 2 Σ + )-Ar and KCl(X 1 Σ + )-Ar have been determined. They include a Gordon-Kim electron-gas repulsive part smoothly joined to the long-range van der Waals potential. The van der waals potential for KClAr was taken from Meyer and Toennies. For CaClAr, the necessary molecular parameter were estimated from the Rittner model, which predicts both the dipole and quadrupole moments fairly accurately. The CaClAr interaction potential is quite different from that of KClAr. Due to the outer 4s electron on the Ca + ion. the CaClAr potential exhibits a deep minimum in the odd-order Legendre terms which is expected to have a large effect on the cross sections for collisional rotational excitation. The KClAr potential determined here also shows significant differences in the repulsive and well regions from that predicted by Meyer and Toennies using a site-site model for the repulsive contribution.

The torsional dependence of an interaction potential: the CH3OHHe system

Abstract An interaction potential for the methanol-helium system was calculated, consisting of an SCF part plus a damped dispersion contribution. A double-zeta basis set was used for the methanol, augmented with one set of polarization functions on each atom. The He basis was a ( 6s 3s ) set augmented with two p-functions. The counterpoise method was used to help correct the basis set superposition error. Interaction energies were computed as a function of the relative position of the HE (R, θ, φ) as well as of the methanol conformation, described by the single angle γ. The SCF potential was found to be relatively more repulsive at the methyl end of the molecule compared to the Billing site-site potential. A φ-shift approximation was found to predict fairly accurately the γ-dependence of the potential from the staggered conformation interaction alone. The anisotropy of the potential was analyzed using an expansion in products of spherical harmonics in θ, φ and exp(inγ) functions, in which it was shown that only n values which are multiples of three appear. The resulting expansion coefficients are those needed for the matrix elements of the potential between two rotational-torsional states in the close-coupling formation of the scattering problem. It was found that the torsional anisotropy is much weaker than the overall anisotropy and that the φ and γ anisotropies are strongly coupled.

M-preserving propensities for rotationally inelastic NH3-He collisions. In the kinematic apse frame

Abstract Semiclassical calculations are used to obtain integral cross sections in both the initial velocity, or collision-fixed, frame and the kinematic apse frame (defined by Khare et al.) for rotational excitation in the NH 3 -He system at a collision energy of 100 cm − . A comparison with earlier close-coupling calculations in the initial velocity frame. using the same interaction potential, shows that the semiclassical method predicts relative M -dependence quite accurately. The kinematic apse cross sections, unlike those in the initial velocity frame, are highly diagonal in the quantum number M . An examination of the M -dependent transition probabilities as a function of impact parameter indicates that the propensity for conservation of M in the kinematic apse frame is due to the dominance of backward, or high-angle, scattering in the cross section. The propensity for conservation of M breaks down for large impact parameters where the interaction is attractive.