5 Data processing and results

The rotational analyses of the different bands raised no special difficulties since rotational constants for $X^2\Sigma^+$ and $B^2\Sigma^+$states were available, at least for v=0 and v=1. Thus, some 830 lines have been ascribed to the 0-0, 1-1, 2-1, 2-2, 3-2, 3-3, 4-3, 4-4, and 4-5 bands.

In order to reduce the observational data to a unique and consistent set of spectroscopic constants a simultaneous multiband, non-linear least-squares adjustment has been performed. Approximate values of the parameters are first entered in the model, producing series of level energies in the upper and lower states from which line positions are calculated. Then, comparison between observations and model predictions allows corrections to these values to be determined. The process is iteratively continued until the standard deviations of successive fits differ by less than a small, preset value. Three or four iterations are generally sufficient for convergence to be achieved.

The rotational energies for the levels v=0 to 5 of $X^2\Sigma^+$ and v=0 to 4 of $B^2\Sigma^+$ are given by the formulae (1) to (4), where each parameter is expressed at equilibrium as a polynomial expansion in $v+\frac{1}{2}$. The signs of the coefficients are defined as usual [7, (Huber & Herzberg 1979)]. Thus, the wavenumbers of all 830 lines belonging to the nine above-mentioned bands could be directly reduced to the set of effective equilibrium constants given in Table 2.

  

Table 2: Equilibrium spectroscopic constants ^(a) for the $X^2\Sigma^+$ and $B^2\Sigma^+$ states of LaO

It has been verified that the values found for the rotational constants in the ground state are consistent, within $\pm$ one standard deviation limits or better, with the values from [13, Törring et al. (1988)]. In the final fit, the parameters were kept fixed at these values, which were determined very accurately from the study of the microwave absorption spectrum. The b parameter in $X^2\Sigma^+$ and spin-rotation parameters in $B^2\Sigma^+$ were left free to vary, since they appear as effective in the present model which does not include hyperfine terms (except bI.S). Thus, small deviations are observed between the present values and the true values reported previously for these parameters [2, (Bacis et al. 1973]; [5, Childs et al. 1986]; [13, Törring et al. 1988)]. The dependence with v and N of the effective spin-rotation constant in the upper state is found to be significant.

Values of the vibrational constants in $X^2\Sigma^+$ and $B^2\Sigma^+$ states, and of the rotational constants in $B^2\Sigma^+$ are obtained, one or two orders of magnitude more precise than earlier values. This set of spectroscopic constants allows the positions of the observed lines to be calculated to nearly the experimental precision (the standard deviation of the fit is 0.009 cm^-1). It is expected to yield a realistic representation of the band spectrum up to N's of about 90 in the range of the v's considered, and thus to be useful for high resolution syntheses of S-type stellar spectra. Line wavenumbers corresponding to the 14 bands with Franck-Condon intensity factors greater than 0.10 have been calculated. These data are available in electronic form (see footnote to the title).

Work is in progress at the LASIM concerning the red $A^2\Pi{\rightarrow}X^2\Sigma^+$ and infrared $A^2\Pi{\rightarrow}A'^2\Delta$transitions.