REFLECTION AND INTERFERENCE STRUCTURE IN DIATOMIC FRANCK-CONDON DISTRIBUTIONS∗{^{*}}

Author Institution: Department of Chemistry, Vanderbilt UniversityLoosely speaking, the Franck-Condon distributions for diatonic radiative transitions from a single vibrational level of a given electronic state to all possible levels (bound and free) of a second electronic state exhibit either ``reflection"" or ``Interference"" structure. In reflection structure there is a one-to-one mapping of peaks in the initial state probability distribution into peaks in the spectrum. No such simple relationship is known for interference structure (originally called ``internal diffraction"" by $Condon^{1}$). It can be shown that the condition for reflection structure is a monotonic difference potential in the range of internuclear distance R sampled by the initial wavefunction, whereas interference structure occurs when the initial wavefunction samples extrema in the difference potential$^{2}$. These conditions are discussed with application to a number of diatomic transitions. ${^{*}}$ Work supported by the Air Force Office of Scientific Research. $^{1}$ E. U. Condon, Phys. Rev. 32. 858 (1928). $^{2}$ J. Tellinghuisen, et al., Chen. Phys. 50. 313 (1980

LEAST-SQUARES ERROR PROPAGATION: NEGLECTED ASPECTS

Author Institution: Department of Chemistry, Vanderbilt UniversityThe usual outcome of a detailed analysis of a body of spectroscopic data is a set of spectroscopic parameters aud their associated variances and covariances. While it is standard procedure to report the parameters and their errors (and sometimes the covariances or correlation coefficients), it is much less common to see errors reported for important derived functions of the parameters, even though the calculation of such propagated errors is quite straightforward. For example, in the analysis of diatomic data, one should really be more interested in the propagated error in the rotational constant $B_{v}$ as a function of v than in the errors in the various expansion coefficients ($B_{e}$, $\sigma_{e}$ etc.).In the high-order polynomial expansions that are often required to represent $B_{v}$, or the vibrational energy $G_{v}$, over a large range of v, the highest-order coefficients are seldom physically significant. Thus the errors in these parameters are not very informative, while the errors in the functions they help represent certainly are The present talk will illustrate error propagation in a number of examples, ranging from the simple cases mentioned above to more complex applications, such as (1) the calculation of RKR potentials, aud (2) the extraction of population distributions from emission spectra

SPECTROSCOPY OF AND WITH LASER POINTERS

Author Institution: Department of Chemistry, Vanderbilt University, Nashville, TN 37235The most common laser in everyday life is probably the ubiquitous laser pointer. Yet surprisingly, little specific information about the spectral properties of laser pointers seems to be available in the published literature. That lack will be addressed in this largely pedagogical presentation. By way of illustration, the relatively high spectral purity of the output from a green laser pointer facilitates a "flashy" demonstration of laser-induced fluorescence when the beam is directed through a cell containing I$_2$ vapor. In a novel experiment, the same properties permit a precise measurement of the continuous $C \leftarrow X$ absorption underlying the stronger $B \leftarrow X$ absorption near 532 nm in the spectrum of I$_2$

BOUND-FREE EMISSION FROM XeBr, XeI, AND KrF

$^{1}$J. J. Ewing and C. A. Brau, Phys. Rev. A12, 129 (1975).Author Institution: Department of Chemistry, NashvilleThe e-beam-excited emission bands of XeBr (2700-2850 {\AA}), XeI (2400-2550 {\AA}), and KrF (2400-2525 {\AA}) display a diffuse structure characteristic of bound-free emission from a near thermal (at $T \sim 360^\circ K$ ) distribution of $(v^{\prime}, J^{\prime})$ Levels to a relatively Hat lower potential curve. The nature of this structure is discussed. Spectral simulations are used to obtain approximate potential curves for the electronic states involved in these transitions

COMBINATION DIFFERENCES: VICTIM OF A ``BUM RAP''?

Author Institution: Department of Chemistry, Vanderbilt UniversityThe problem of correlation in data is considered for spectroscopic difference techniques. In the application of the method of combination differences to diatomic rotational structure with R and P branches only, there is no correlation problem, because each line is used only once in computing the differences. Under best circumstances the combination difference method can match the statistically optimum direct fit method exactly in the more limited goal of estimating the rotational and distortional constants for a given level. The correlation problem arises when a Q branch is added to a combination difference treatment, as it does also in the method of successive differences. Treatment of these cases by correlated least squares can again achieve exact agreement with the direct fit