2 Methodology

The general methodology employed in making the calculations reported herein continues to be based on the Cowan code (Cowan [1981,1985]), and has been described in previous papers. Although some of the details of the Ndiii calculations have appeared before (Cowley & Bord [1998]), we review here the principal features of the analysis.

Single-particle radial wavefunctions were determined using a Hartree-plus-statistical-exchange interaction approximation for the following even and odd parity configurations, respectively: (4f⁴ + 4f²5d² + 4f²5d6s + 4f³6p), and (4f³5d + 4f³6s). An additional odd configuration, 4f²5d6p, was found to lie too high in energy to be of importance. Experimental energy levels exist for only two of these configurations (4f⁴ and 4f³5d), and neither is complete (Martin et al. [1978], hereafter MZH). The selected configurations comprise all of Goldschmidt's ([1978]) system A and B configurations (with the exception of 4f²6s²) and are well isolated from adjoining, higher ones which should minimize perturbations known to reduce the accuracy of the calculations. As in the past, relativistic and electron correlation corrections have been included in the calculations, and the eigenvectors were constructed using both LS- and jj-coupling basis sets. LS coupling is generally appropriate for the levels included in this study, except for those arising from the 4f³6s and 4f³6p configurations, where a J₁j-coupling scheme is preferred.

Ab initio values for the single-configuration center-of-gravity energies and the various radial and configuration interaction integrals were computed with uniform scaling applied to all spin-orbit and Slater parameters. Reducing the theoretical values of F^k and G^k in this manner, for example, roughly accounts for the effects of introducing additional two-body electrostatic operators for legal values of k (Cowan [1981], p. 478); no attempt to include effects due to "illegal-k" effective operators has been made.

The radial integrals were then optimized to fit the known energy levels using the method of least squares. Since experimental Landé factors are not available for Ndiii, additional improvements to the eigenvectors, particularly those not well described by LS-coupling, by including fits to the g-factors (Cowan [1981], p. 473) could not be performed.

For Ndiii, we computed a total of 1488 levels, of which only 28 (5 even and 23 odd) were fitted. One odd level at 24003 cm^-1 with J = 7 and no term designation in MZH was omitted from the fit. The adopted structure parameters yielded a mean deviation in energy of less than 1 cm^-1(0.02% over $\approx$ 5100 cm^-1) for the even levels and only 54 cm^-1 (about 0.2% over $\approx$ 33000 cm^-1) for the odd levels. Term designations and leading percentages for the known levels analyzed typically agreed with those given in MZH to within 10% in cases where the leading percentages were $\geq$50%. In instances where term mixing is severe and no assignment is given by MZH, the calculations usually identified the level with one of the two principal terms given in the NIST compilation. Exceptions were found for three terms: the ⁵I$^\circ_5$ at 20389 cm^-1 and ⁵H$^\circ_4$ at 28745 cm^-1 showed leading percentages $\approx$20% less than those given in MZH at 56% and 63%, respectively; and the ⁵H$^\circ_6$ at 31395 cm^-1 was computed to be substantially purer than indicated in MZH with a leading percentage of 72% as compared to 46%.