Chifuru Noda

Relation between classical and quantum formulations of the Franck-Condon principle: The generalized r-centroid approximation

Abstract The classical transition point r v′v″ ∗ for the (v′, v″) band is introduced as the point where the kinetic energy does not change during the transition (classical statement of the Franck-Condon principle). It is shown that when the r-centroid approximation is valid, it implies that the r centroid r v′v″ equals r v′v″ ∗ , allowing a new connection to be made between the classical and quantum statements of the Franck-Condon principle. The r-centroid approximation fails for some classically allowed bands having large Franck-Condon factors. This occurs when the (v′, v″) band has more than one classical transition point. A generalization of the r-centroid approximation permits such bands to be used in determining the variation of the electronic transition moment with internuclear distance.

Information on the impact parameter dependence of the Ba+HI → BaI(ν=8)+H reaction

Using selectively detected laser‐induced fluorescence, the rotational state distribution of the BaI product has been measured for the beam–gas reaction Ba+HI → BaI(ν=8)+H. Owing to the highly constrained kinematics for this system, these measurements can be used to derive the reaction probability as a function of the impact parameter for this channel, called the ‘‘specific’’ opacity function, once the reaction probability as a function of velocity has been determined. Unfortunately, lack of knowledge of the exoergicity and the height of any energy barrier prevents a conclusive determination of the specific opacity function for this reaction. Instead, various approximate opacity functions are estimated based on different models of the velocity dependence of the reaction channel studied. If the reaction probability is the same for all relative collision velocities, then the BaI(ν=8) specific opacity function peaks strongly near 2.6 A with a full width at half‐maximum of 1.0 A. However, the possible presence of a small energy barrier in the entrance channel causes a cutoff in the relative collision velocity distribution, and this type of velocity dependence would significantly affect the shape of the specific opacity function.

Dynamics of kinematically constrained bimolecular reactions having constant product recoil energy

A model is presented for kinematically constrained reactions in which the product recoil energy is assumed constant (CPR approximation). It is further assumed that the reaction probability is independent of both the impact parameter and the collision energy for all collisions that lead to products. This model predicts that (1) the product vibrational distribution is bell‐shaped, peaking at the vibrational level with an energy equal to the reaction exoergicity minus the product recoil energy, (2) small values of the impact parameters produce high vibrational excitation while large values produced low vibrational excitation, the specific opacity function for the most populated vibrational level being sharply peaked at the impact parameter equal to the equilibrium internuclear distance of the product diatomic, (3) the product rotational distribution for each vibrational level differs but has the form of a sharp leading edge for some J value followed by a falloff whose shape depends on the form of the collisi...

Hyperfine structure of the BaI X 2Σ+ and C 2Π states

Optical‐microwave double resonance measurements were carried out to find the hyperfine structure constants of the v=0 level of the BaI X 2Σ+ state. These were combined with sub‐Doppler optical measurements of the BaI C 2Π–X 2Σ+(0,0) band in order to derive the hyperfine structure constants of the excited state. We have determined the following molecular constants (in MHz) where the numbers in parentheses represent one standard deviation in a least squares fit: for the BaI X 2Σ+ state, γ‘=75.8501(33), b‘=93.117(19), c‘=52.170(54), and eQq‘=−33.62(12), and for the BaI C 2Π state, a’=263(53), b’+c’=−430(212), d’=−66.7(1.4), and eQq’=−214(11). The Fermi contact interaction and the electric quadrupole coupling constants for both the BaI X and C states appear to arise from the distortion of closed‐shell I− orbitals by the field of the Ba+ ion. In the BaI X state, the charge distribution on the Ba+ center is directed away from I− while in the C state toward I−.

Rotational analysis of the BaI C2Π-X2Σ+ (8,8) band

Abstract The BaI C2Π-X2Σ+ (8,8) band has been measured and rotationally assigned using techniques of population-labeling optical-optical double resonance (PLOODR) and selectively detected laser-induced fluoresence (SDLIF). A weighted nonlinear least-squares fit has been carried out to model the positions of 891 transitions with J″ ranging from 13.5 to 271.5 to a 2Π-2Σ+ Hamiltonian which has 10 spectroscopic constants. Despite the fact that most of our data is from 6 out of the possible 12 rotational branches and is biased in favor of the C 2 Π 1 2 -X 2 Σ + subband, we are able to assign J″ quantum numbers unambiguously for all the observed transitions as well as derive the principal spectroscopic constants of the BaI C2Π and X2Σ+ states for the (8,8) band.