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New spectroscopic data, spin-orbit functions, and global analysis of data on the and states of
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Image of FIG. 1.
FIG. 1.

Summary of the data used in this study. The observed term values are sorted according to the largest component in the calculated eigenvector.

Image of FIG. 2.
FIG. 2.

Adiabatic potentials for ungerade states in the energy region of this study, obtained by diagonalizing the DVR matrix for , for each value of . Vibrational quantum numbers are shown for the and states. The top plot shows the lower levels, with an inset showing the avoided crossing region. The bottom plot, also with an inset, shows levels and turning points closer to the dissociation limit. Eigenvalue calculations, however, used diabatic potentials and spin-orbit coupling functions.

Image of FIG. 3.
FIG. 3.

A schematic of the experimental setup for polarization spectroscopy. Lateral detection of the total fluorescence records a Doppler-limited laser excitation spectrum.

Image of FIG. 4.
FIG. 4.

A typical region of the polarization spectrum showing (top) the vernier etalon signal (VET) signal used to check that the laser scans continuously, (middle) the LES signal for calibration, (bottom) the Doppler-limited LES signal, and the polarization spectroscopy signal, which exhibits a sub-Doppler width.

Image of FIG. 5.
FIG. 5.

The range of the data for the and states from several of the individual data sets. The numbers in parentheses refer to the data source numbers listed in the first column of Table I.

Image of FIG. 6.
FIG. 6.

This plot shows relative band intensities, calculated from the product of the vibrational overlap, , including the transition moment from Ref. 66, times the Boltzmann factor, . Here, , .

Image of FIG. 7.
FIG. 7.

Residuals from (a) the data from Refs. 23 (dots) and 21 (crosses), (b) the new polarization spectroscopy data, and (c) all other data sets included in the fit. The energy in (a) is scaled as to expand the region near the dissociation limit, , so as to show systematic effects due to hyperfine structure above . Vibrational quantum numbers (smaller dots in a nearly straight line) are plotted with reference to the right axis. Data for (b) were selected to be within of the energy calculated from the fitted parameters.

Image of FIG. 8.
FIG. 8.

(a) The fitted short-range (dashed) and long-range (solid line) potentials near the transition point . (b) The difference between the short-range and long-range potentials (solid line), the theoretical exchange potential from Ref. 71 (dot-dashed line), and the fitted exchange potential (dashed line). In (a) and (b) the vertical bar denotes the value of the transition point, .

Image of FIG. 9.
FIG. 9.

(a) The sum of the contributions to as a function of , together with plots of the damping corrections to , , and , labeled 3, 6, and , respectively. (b) The individual components of plotted on a logarithmic scale.

Image of FIG. 10.
FIG. 10.

(a) The monotonically decreasing functions represent the logarithm of three estimates of for the state. From top to bottom, these are the experimental function, (dotted line), an ab initio function (from SK, dashed line), and the analytic exchange function from Ref. 71 (solid line). The peaked functions are the ratios of the first two to the last, plotted on the linear scale (right axis). (b) The logarithm of for the state obtained from one-half the difference , together with the ratio of this function to the corresponding analytic exchange function from Ref. 71. The inset in (b) shows the two potentials ( vs Å).

Image of FIG. 11.
FIG. 11.

Diagonal state spin-orbit function . The dashed line denotes results of a fit to a Taylor series expansion about that is made possible by the range of values of as a function of vibrational level as indicated below the curve. The solid line denotes the best fit to a Morse function [Eq. (7)] adjusted to match the Taylor series expansion as closely as possible. The filled circles and connecting line denote ab initio results. The inset shows an overview of the asymptotic region.

Image of FIG. 12.
FIG. 12.

Off-diagonal spin-orbit coupling functions. The solid-line curves show various fitted Morse function expressions. Each of these curves gives a comparably good fit to the experimental data. The inset shows that they cross within a small region near the crossing point of the and state potentials. The connected squares denote the ab initio results of SK which were used in the final fit.

Image of FIG. 13.
FIG. 13.

Calculated and observed term values showing the extent of the data in the region of perturbations for low levels of the state.

Image of FIG. 14.
FIG. 14.

Calculated (circles) and observed (crosses) term values for of the state with the deperturbed values subtracted. The quality of the fit is shown on an expanded scale relative to the previous figure. Divergences appear at the perturbation crossings.

Image of FIG. 15.
FIG. 15.

Calculated and observed term values over a larger region. In this figure, the filled dots represent experimental data from any of the sources.


Generic image for table
Table I.

Sources of the data used in the present work. The first number in parentheses after or denotes vibrational numbers, after the semicolon, the rotational quantum numbers. PW, present work; Abs. Spec., absorption spectroscopy; LS, laser spectroscopy; Mod. Pop. Spec., modulated population spectroscopy; LES, laser excitation specroscopy; Mod. Gain, modulated gain; Pol. Spec., polarization spectroscopy; AOTR, all-optical triple resonance; DR, double resonance; PFAOTR, perturbation-facilitated all-optical triple resonance; FT, Fourier transform; PFOODR, perturbation-facilitated optical-optical double resonance.

Generic image for table
Table II.

Fitted parameters for the potential function, for the and states. and are given in the following table. . The are in , while is dimensionless. Numbers in square brackets denote the power of 10. For the state, , the form applies, with values given below.

Generic image for table
Table III.

Potential parameters. and are in , in Å, and the parameters are in units . The parameters used in the exchange potential are dimensionless. work. Numbers in square brackets after a series of digits denote the power of 10, while parentheses denote uncertainty limits, which for the present work are discussed in the text.

Generic image for table
Table IV.

Deperturbed values, from previous studies and this one, perturbation shifts, values, and turning points for the state. eigenvalue for minus the deperturbed value, . The last two columns give the inner and outer turning points at the energies given in column 5. All quantities are in except for which are in Å.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: New spectroscopic data, spin-orbit functions, and global analysis of data on the AΣu+1 and bΠu3 states of Na2