3 Results

Table 1 lists the known energy levels for Ndiii from MZH and the Landé g-factors calculated using the Cowan code.

 

 

Table 1: Landé g-factors for Nd III^a

Configuration	Term	J	Energy	g-factor
			(cm-1)
4f4	5I	4	0.0	0.605
		5	1137.8	0.902
		6	2387.6	1.071
		7	3714.9	1.176
		8	5093.3	1.246
4f3(4I$^\circ$)5d	5K$^\circ$	5	15262.2	0.683
		6	16938.1	0.909
		7	18656.3	1.052
		8	20410.9	1.149
		9	22197.0	1.217
4f3(4I$^\circ$)5d	5I$^\circ$	4	18883.7	0.621
		5	20388.9	0.930
		6	22047.8	1.079
		7	22702.9	1.153
		8	24686.4	1.232
4f3(4I$^\circ$)5d	5H$^\circ$	3	19211.0	0.538
		4	20144.3	0.873
		5	21886.8	1.026
		6	23819.3	1.073
4f3(4I$^\circ$)5d		7	24003.2	1.184:
4f3(4I$^\circ$)5d		6	26503.2	1.183:
4f3(4I$^\circ$)5d	3K$^\circ$	8	27391.4	1.137
4f3(4F$^\circ$)5d		3	27569.8	1.146:
4f3(4F$^\circ$)5d	5H$^\circ$	3	27788.2	0.807
		4	28745.3	1.074
		5	30232.3	1.126
		6	31394.6	1.208
		7	32832.6	1.158
4f3(4F$^\circ$)5d		5	29297.3	1.126:

^a Energies and term designations are from Martin et al.(1978); g-factors followed by a colon are uncertain due to term mixing.

Log(gf) values were computed for all electric dipole transitions with wavelengths in the range 2000-7000 Å. A total of 9469 lines and associated gf-values exist in our data files. To present a complete list of the calculations is beyond the scope of this note. Table 2 shows the calculated gf-values, as well as the cancellation factors (CF, see Sect. 4), for the 54 predicted lines arising from the known energy levels after employing the usual selection rules; the gf-values have been scaled appropriately for the differences between the calculated wavelengths and the predicted ones.

Fewer than half of these lines appear in unpublished lists of the strongest laboratory lines of Ndiii provided by Crosswhite ([1976]), but many of these have been identified in RE-rich stars like HR465 (Bidelman et al. [1995]) and HD101065 (Cowley et al. [1998], [2000]). Hundreds of additional strong lines exist in the Crosswhite data, but it is difficult, if not impossible, given the uncertainties in the calculated energy levels, to unambiguously classify them using our data. The full set of computed wavelengths, energy levels, and log(gf) values will be released to the Vienna Atomic Line Database (VALD, Piskunov et al. [1995]; Kupka et al. [1999]) for the purpose of computing opacities for heavily line-blanketed stellar model atmospheres where especially high precision in the wavelengths is not required and where the f-sum rule for the oscillator strengths mitigates somewhat the uncertainties in the individual values.

 

 

Table 2: gf-values for predicted lines in Nd III

$\lambda_{{\rm pred}}$	$\lambda_{{\rm exp}}$ a	Transition		log(gf)	$\mid$CF$\mid$
(Å)	(Å)
3283.67	.65	2387.66	$-$	32832.6$^\circ_7$	-3.23	0.120
3304.09		1137.85	$-$	31394.6$^\circ_6$	-3.24	0.268
3306.77		04	$-$	30232.3$^\circ_5$	-3.28	0.107
3400.70		04	$-$	29397.3$^\circ_5$	-4.98	0.015
3433.35	.33	3714.97	$-$	32832.6$^\circ_7$	-1.61	0.315
3436.09		1137.85	$-$	30232.3$^\circ_5$	-1.60	0.568
3446.46		2387.66	$-$	31394.6$^\circ_6$	-1.57	0.633
3477.83	.83	04	$-$	28745.3$^\circ_4$	-1.87	0.641
3537.62	.61	1137.85	$-$	29397.3$^\circ_5$	-3.29	0.107
3590.32	.33	2387.66	$-$	30232.3$^\circ_5$	-0.76	0.697
3597.62	.62	04	$-$	27788.2$^\circ_3$	-0.81	0.839
3603.97	.98	5093.38	$-$	32832.6$^\circ_7$	-0.63	0.697
3611.73	.72	3714.97	$-$	31394.6$^\circ_6$	-0.49	0.825
3621.17	.17	1137.85	$-$	28745.3$^\circ_4$	-0.74	0.836
3626.12	.12	04	$-$	27569.8$^\circ_3$	-1.24	0.730
3701.32	.29	2387.66	$-$	29397.3$^\circ_5$	-2.29	0.329
3941.26	.26	1137.85	$-$	26503.2$^\circ_6$	-3.81	0.035
4145.52	.50	2387.66	$-$	26503.2$^\circ_6$	-2.78	0.070
4222.41		3714.97	$-$	27391.4$^\circ_8$	-2.81	0.161
4386.98		3714.97	$-$	26503.2$^\circ_6$	-2.41	0.093
4407.64		1137.85	$-$	23819.3$^\circ_6$	-3.72	0.014
4483.43	.44	5093.38	$-$	27391.4$^\circ_8$	-1.43	0.219
4567.68		04	$-$	21886.8$^\circ_5$	-3.43	0.026
4624.99	.96	2387.66	$-$	24003.2$^\circ_7$	-2.01	0.387
4664.68		2387.66	$-$	23819.3$^\circ_6$	-3.22	0.013
4767.04		3714.97	$-$	24686.4$^\circ_8$	-1.72	0.623
4781.06		1137.85	$-$	22047.8$^\circ_6$	-1.71	0.455
4818.16		1137.85	$-$	21886.8$^\circ_5$	-3.70	0.003
4903.26		04	$-$	20388.9$^\circ_5$	-1.86	0.366
4921.02		2387.66	$-$	22702.9$^\circ_7$	-1.77	0.560
4927.57	.48?	3714.97	$-$	24003.2$^\circ_7$	-0.86	0.502
4962.80		04	$-$	20144.3$^\circ_4$	-6.08	0.000
4972.65		3714.97	$-$	23819.3$^\circ_6$	-1.27	0.225
5085.00		2387.66	$-$	22047.8$^\circ_6$	-0.68	0.583
5102.42	.43	5093.38	$-$	24686.4$^\circ_8$	-0.40	0.699
5126.99	7.00	2387.66	$-$	21886.8$^\circ_5$	-1.09	0.306
5193.06	.06	1137.85	$-$	20388.9$^\circ_5$	-0.77	0.597
5203.90	.91	04	$-$	19211.0$^\circ_3$	-1.19	0.328
5259.89		1137.85	$-$	20144.3$^\circ_4$	-1.15	0.350
5265.02	4.96?	3714.97	$-$	22702.9$^\circ_7$	-0.67	0.572
5286.76		5093.38	$-$	24003.2$^\circ_7$	-1.60	0.087
5294.10	.11	04	$-$	18883.7$^\circ_4$	-0.67	0.709
5453.16		3714.97	$-$	22047.8$^\circ_6$	-7.52	0.000
5553.61		2387.66	$-$	20388.9$^\circ_5$	-3.74	0.002
5633.54		1137.85	$-$	18883.7$^\circ_4$	-2.01	0.340
5677.15		5093.38	$-$	22702.9$^\circ_7$	-1.42	0.390
5845.07	.00?	5093.38	$-$	22197.0$^\circ_9$	-1.16	0.581
5987.80		3714.97	$-$	20410.9$^\circ_8$	-1.25	0.546
6145.07	.02?	2387.66	$-$	18656.3$^\circ_7$	-1.33	0.540
6327.24	.22	1137.85	$-$	16938.1$^\circ_6$	-1.40	0.551
6526.63		5093.38	$-$	20410.9$^\circ_8$	-2.34	0.552
6550.33	.21?	04	$-$	15262.2$^\circ_5$	-1.47	0.557
6690.97		3714.97	$-$	18656.3$^\circ_7$	-2.29	0.518
6870.72		2387.66	$-$	16938.1$^\circ_6$	-2.43	0.474

^a Based on data provided by Crosswhite (1976); entries with questions are possible identifications, although the wavelength differences are large.

No corrections to the gf-values given in Table 2 for core polarization effects have been made due to the fact that our current version of the multi-configuration Hartree-Fock-based code for doing so (see Vaeck et al. [1992]) will not handle configurations containing more than two f-electrons. We do not expect this to be a significant limitation on the accuracy of the data in Table 2 insofar as it contains no transitions into or out of any levels assigned to the 4f³6p configuration where such effects are most pronounced. A modified program to permit core polarization corrections to be made in configurations with greater than two f-electrons has been kindly made available to us by G. Gaigalas ([1998]) and awaits implimentation.

Based on the calculations, a re-evaluation of the ionization energy for Ndiii has been carried out following the approach of Sugar & Reader ([1973]). Using the computed energy for the lowest level of the 4f³6s configuration, 30776 cm^-1, and taking $\delta$ = 455 cm^-1 (as found from the formulae of Judd ([1962]) and the calculated Slater parameter G³(4f³6s) = 2125 cm^-1), we find the ionization energy to be 179031 $\pm$ 823 cm^-1. This result is only 0.2% higher than the published value, but it reduces the uncertainty by nearly a factor of three over the previous estimate. In this determination, we have applied the Sugar & Reader term value for the center of gravity of the 4f³6s configuration derived from the Rydberg-Ritz formula: T = 147800 cm^-1. The uncertainty in the ionization energy is the square root of the sum of the squares of the contributing uncertainites. We have adopted the value given in Sugar & Reader for $\Delta T$ and assumed the error in the energy for the 4f³6s ⁵I$^\circ_4$ term to be three times the mean deviation in the fitted energies for the odd parity levels.