Graphical methods for deperturbation

There are many extremely useful graphical presentations of spectral data. Most are based on several of the following ideas (1) straight-line plots, (2) scale 

Several other kinds of information are available from the information in Fig. 5.7. Two consecutive vibrational levels of A1 are crossed by the same vibrational level of e3 . The Q branch (F2) crossing occurs in va = 1 and 0 at J = 48.9 and 61.5. Since the deperturbed A1 term energies at these two J-values are known by interpolation, accurate values for B(e3 ) and F(e3 ) can respectively be determined from the slope and intercept of the straight line drawn through these va = 1, J = 48.9 and va == 0, J = 61.5 term values. Alternatively, the J-values of all three 1II 3 (Fi,F2,F3) crossings are determined accurately at many perturbations, for example, (56.5, 61.5, 66.0) in Si160 A1 v = 0. Each 3X TV-level consists of three near-degenerate J components. The perturbation selection rule is A J = 0, thus the F3 and F3 

Finally, the absence of a detectable perturbation at a crossing point predicted by drawing nearly horizontal tie lines between corresponding perturbations on Fig. 5.7 (no unfilled A on v = 1 of Si160 near J = 70) implies that either the expected perturbing state would have v = —1 or that the matrix element is less than 

If (AR + AP)/4J or AQ/2J is plotted versus J2 for an unperturbed band, a straight line is obtained with intercept and slope, respectively, of B — B and D - D.  

The center of gravity rule can be useful for obtaining parameter estimates, locating extra lines, and detecting the presence of an unsuspected second per-turber. When main and extra lines are observed for more than two J-values at 

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