4 Reliability of the data

4.1 gf-values

One of the major purposes of performing these calculations is to apply them in the determination of REE abundances in CP stars. Given the high quality of modern spectroscopic observations and the increasing sophistication of stellar model atmosphere codes, the limiting factor in producing accurate abundances for many heavy and REE is the uncertainty in their atomic parameters, particularly the transition probabilities and/or gf-values. On the logarithmic scale typically used to report stellar abundances, the errors in element abundances scale directly with those in the log(gf) values. Consequently, it is important to assess the reliability of the gf-values presented here.

Based on previous experience, as well as on comparisons with data released since the appearance of some of our earlier work, we expect that, for lines with cancellation factors substantially greater than 0.1 in absolute value (cf. Cowan [1981], Eq. 14.107), and discounting core polarization effects, the oscillator strengths should be accurate to $\pm0.15$ dex. For transition arrays in which core polarization is important, most notably those involving p-electrons, we have found that our calculated radiative lifetimes can be up to a factor of 2 too small when compared with experiment (cf. Bord et al. [1997]); in these cases, the calculated log(gf) values are likely to be systematically too large by some 0.25 dex or more on average. As noted above, for the data reported here which do not involve configurations containing p-electrons, we do not anticipate that core polarization effects will contribute significantly to producing uncertainties in the gf-values beyond the quoted limits.

Since no experimental or theoretical gf-values exist for this ion to the author's knowledge, indirect evaluations of our computations must be made. In support of our assessment of the data, the following comparisions may be relevant. For Laii, our recommended formula for computing gf-values, based on a calibration of NBS Monograph 145 (Meggers et al. [1975]) intensities using Cowan-code oscillator strengths (Bord et al. [1996]), produces agreement with values computed by Gratton & Sneden ([1994]) from experimental lifetime data to within 0.02 dex on average, with a scatter of only $\pm0.08$ dex. Similarly, for Luii, comparison of results found using our log(gf) formula, again derived from Cowan-code calibrated Monograph 145 intensities (Bord et al. [1998]), with recently published experimental gf-values (Quinet et al. [1999]) for 10 lines yields a mean and standard deviation of only -0.026 $\pm$ 0.177 dex. Finally, an examination of the gf-values recently published by Wyart & Palmeri ([1998]) in their comprehensive study of Ceiii finds remarkably good agreement with those appearing in Bord et al. ([1997]), especially given that the former study incorporated ten new and/or revised energy levels and included more than twice the number of even and odd configurations used by us; neither investigation, however, includes corrections for core polarization effects. In particular, for the 30 lines held in common in the published lists with cancellation factors large enough to make the theoretical transition probabilities reliable, the mean difference and standard error in the log(gf)'s between the two investigations (taken in the sense $\log(gf_{{\rm BCM}}) - \log(gf_{{\rm WP}})$) is only $-0.014\pm0.133$.

4.2 g-factors

To the author's knowledge, no experimental measures of the g-factors for Ndiii have been made. To assess the expected accuracy of the values reported in this paper, appeal is again made to comparisons involving our prior work with other published studies. For example, for Laii where our term assignments and leading percentages are in excellent agreement with those given in MZH, we find similarly good agreement between our theoretical g-factors and the experimental ones compiled by MZH from Harrison et al. ([1945]); for 96 measures spanning both even and odd parity states, the average percent difference between the two sets of data is under 2%, while the mean and standard deviation of the difference $\Delta\,g\,\equiv\,\mid g_{{\rm meas}} - g_{{\rm theory}}\mid = 0.015\pm0.018$. For reference, the internal agreement between independent measurements of the same g-factor is $\pm0.004$.

Similarly, in Ceiii, for 34 levels with measured g-factors where the Cowan code term assignments agree with those presented in MZH, the average difference between the measured values and those computed is 3.25%. In six other cases where term mixing leads to disagreements between the Cowan-code designations and those reported by MZH, the average deviations never exceeded 25%. It may be worth noting in connection with this ion that the six measured g-factors considered uncertain (and marked with colons [:]) by MZH due to incomplete or unresolved Zeeman patterns are included in the first group of 34 levels mentioned above, and all agree with our calculated values to within the estimated errors of measurement, viz., $\pm0.02$.

Finally, for Luii, eliminating dubious measures and those possibly affected by hfs and/or unaccounted for term interactions (see discussion in MZH, p. 404), the absolute difference, $\Delta$g, taken in the same sense as above, between the NIST-compiled values and our calculations is $0.034\pm0.024$, or about 3% on average. This may be compared with the stated uncertainties in the measurements of $\pm$0.02 - 0.03. In the light of these results, we can expect that the g-factors for Ndiii reported here should be good to better than 5% overall, and that in cases of significant term mixing where the theoretical designations are uncertain, errors of under 25% may be anticipated.