Exact quantum-mechanical calculations of the transition probabilities for the collinear collision of an atom with a diatomic molecule are performed. The diatomic molecule is treated as a harmonic oscillator. A range of interaction potentials from very hard to very soft are considered. It is found that for ``realistic'' interaction potentials the approximate calculations of Jackson and Mott are consistently high, even when the transition probabilities are low and good approximate results are expected. In some cases double and even triple quantum jumps are more important than single quantum jumps. Comparisons are made with exact classical calculations. A semiempirical formula is given for computing quantum-mechanical transition probabilities from classical calculations.

A broad compound state (closed channel) resonance in the argon–methane system is investigated using a realistic model potential, and approximations are developed which allow one to search for such resonances easily. Methane is treated as a rigid rotor and the energy of the resonance is such that there are only three rotational states with open channels. The coupled states approximation proved invaluable in characterizing the resonances. A perturbation technique was developed which allows one to predict accurately the position of the peaks due to the resonance. Fully converged close coupled differential and integral cross sections are presented.

Articles you may be interested inQuantum functional sensitivity analysis within the logderivative Kohn variational method for reactive scattering J. Chem. Phys. 97, 6226 (1992); 10.1063/1.463706 Application of the logderivative method to variational calculations for inelastic and reactive scattering A symmetrized generalized logderivative method for inelastic and reactive scattering J. Chem. Phys. 79, 5960 (1983); 10.1063/1.445778 Erratum: The generalized logderivative method for inelastic and reactive collisions [J.A generalization of the log-derivative method is presented which is useful for both reactive and nonreactive scattering problems. In the coupled system of radial equations for this problem a first derivative term is included for complete generality. Thus, this method may be used when, as is often the case in reactive or curve crossing problems, the equations contain a first derivative term. When no first derivative term is present and no reactive channels are present, the method reduces to the standard log-derivative method. A reactive scattering problem is solved as an example.,,=(~~:) 5954

A numerical method is presented for rapidly calculating the energy eigenvalues of one-dimensional Schrödinger equations. It is applicable to systems for which the potential is either analytic or has no pole of order greater than two. The method is based on a power-series expansion of the wave function at large distances. With the use of high-speed computing machines the large number of terms required in the power series can be computed easily. The method is illustrated by obtaining energy eigenvalues for a number of one-dimensional systems with potentials of the type V=kx2n/2n. It is also applicable to a variety of systems of physical interest. As an example, an exact energy eigenvalue for a rotating Morse oscillator has been calculated. This is compared with that obtained from Pekeris' approximate analytical solution.

The Ar-HCl potential energy surface from a global map-facilitated inversion of state-to-state rotationally resolved differential scattering cross sections and rovibrational spectral dataThe rotational and vibrational dynamics of argon-methane. II. Experiment and comparison with theoryThe rotational and vibrational dynamics of argon-methane. I. A theoretical study J. Chem. Phys. 110, 5639 (1999); 10.1063/1.478462Neon-methane and argon-methane isotropic interaction potentials from total differential cross sections Total differential cross sections have been measured for Ar-CH. at E = 90.1 meV in the center of mass angular range from 5° to 55°. The well resolved rainbow m~ximum and .the s~perimposed rapid oscillations are used to establish a reliable isotropic interaction potentIal Vo(R). WIth thIS Vo(R). the torque and low temperature second virial coefficients are analyzed to establish constr~nts on the ~isotrop~c potential V3(R) which obeys tetrahedral symmetry. In a final step a complete potentIal surface IS det~rml.ned based o~ all three data sets. The scattering calculations are performed in the coupled-states approxImation for rotational state-to-state transitions which are summed for the total differential cross section. Small variations of anisotropic parameters lead to dramatic changes in the inelastic differential cross sections. while only small effects are observed in the total differential cross section.where R is the vector between the atom and molecule