For the calculations, we used the suite of computer programs due to Cowan (1981) within the framework of the approximately relativistic Hartree-Fock (HFR) method originally introduced by Cowan & Griffin (1976). Considerable amount of CI effects were included explicitly in the calculations. These configurations are 3d⁸, 3d⁷4s, 3d⁷5s, 3d⁷4d, 3d⁷5d, 3d⁶4s², 3d⁶4p², 3d⁶4d² and 3d⁶4s4d. In order to reduce as much as possible the discrepancies between computed and observed energy levels, the HFR technique was used in combination with a well known least-squares optimization of the radial parameters.

The fitting procedure was applied to the 3d⁸ and 3d⁷4s configurations of Co II with the experimental energy levels compiled by Sugar & Corliss (1985). In the absence of CI, the 3d⁸ configuration is described by four parameters,

, F²(3d, 3d), F⁴(3d, 3d) and

, while for the the 3d⁷4s, also the G²(3d, 4s) parameter is required. In addition to the explicit introduction of CI mentioned above, effective interaction parameters such as

and

(see Trees 1951a,b; Racah 1952), associated with the excitation out of the 3s and 3p subshells into the 3d, can be used to describe the cumulative effects of distant configurations on 3d⁸ and 3d⁷4s. All the parameters of these two configurations were adjusted except the effective interaction parameter

corresponding to 3d⁸. Indeed, for this configuration, only four electrostatic parameters (

, F²(3d, 3d), F⁴(3d, 3d) and

) can be optimized due to the fact that only the four terms ³F, ³P, ¹D and ¹G have been determined experimentally (the ¹S is missing). The average energy of the 3d⁶4s² configuration was also adjusted using the a⁵D multiplet. The F^k, G^k and R^k integrals not optimized were arbitrarily scaled down by a factor 0.85 while ab initio values of the spin-orbit integrals,

, computed by the Blume-Watson method, were used without scaling.

The parameter values adopted for the 3d⁸, 3d⁷4s and 3d⁶4s² configurations of Co II are reported in Table 1 (click here) while calculated energy levels and Landé g-factors are compared with the experimental values in Table 2 (click here). In agreement with previous classifications, terms having the same LS notation are distinguished by the letters a, b and c in increasing energy order. As seen from Table 2 (click here), our calculated energy levels differ from the experimental data by amounts typically lower than 1%, the largest difference (289 cm^-1) being observed for 3d⁷(²G)4s a³G₃ at 22415 cm^-1. A very nice agreement is also observed when comparing the Landé g-factors obtained in our work with the measured values (when available).

Configuration	Parameter	Fitted value	Ratio^b
3d⁸	E	12516.
	F²(3d,3d)	71848.	0.8541
	F⁴(3d,3d)	45288.	0.8731
		79.
		469.	0.9915
3d⁷4s	E	27557.
	F²(3d,3d)	78543.	0.8527
	F⁴(3d,3d)	51650.	0.9038
		91.
		-1035.
	G²(3d,4s)	8467.	0.8652
		507.	0.9657
3d⁶4s²	E	78765.
	F²(3d,3d)	84612.^a	0.8500
	F⁴(3d,3d)	52787.^a	0.8500
		581.^a	1.0000

Table 1: Values of the parameters (in cm^-1) adopted in the HFR calculations for the 3d⁸, 3d⁷4s and 3d⁶4s² configurations of Co II. The ratios between fitted and ab initio HFR values are also indicated

Configuration	Term	J	E^a	g^a	E	g	E^b
3d⁸	a³F	4	0.		0.	1.250	0.
		3	951.		948.	1.084	3.
		2	1597.		1598.	0.668	-1.
3d⁷(⁴F)4s	a⁵F	5	3351.	1.413	3397.	1.401	-46.
		4	4029.	1.354	4035.	1.350	-6.
		3	4561.	1.258	4539.	1.250	22.
		2	4950.	0.997	4911.	1.000	39.
		1	5205.	0.00	5155.	0.000	50.
3d⁷(⁴F)4s	b³F	4	9813.	1.243	9820.	1.250	-7.
		3	10708.	1.082	10681.	1.084	27.
		2	11322.	0.68	11272.	0.679	50.
3d⁸	a¹D	2	11651.	1.111	11648.	1.096	3.
3d⁸	a³P	2	13261.	1.415	13275.	1.392	-14.
		1	13404.	1.484	13390.	1.502	14.
		0	13593.		13584.		9.
3d⁷(⁴P)4s	a⁵P	3	17772.	1.68	17786.	1.668	-14.
		2	18032.	1.839	18064.	1.829	-32.
		1	18339.	2.510	18372.	2.493	-33.
3d⁸	a¹G	4	19190.		19193.	1.000	-3.
3d⁷(²G)4s	a³G	5	21625.	1.186	21390.	1.199	235.
		4	22009.	1.066	21754.	1.048	255.
		3	22415.	0.75	22126.	0.750	289.
3d⁷(⁴P)4s	b³P	2	24075.	1.500	23998.	1.497	77.
		1	24268.	1.498	24260.	1.471	8.
		0	24411.		24468.		-57.
3d⁷(²P)4s	c³P	2	24887.	1.49	25149.	1.482	-262.
		1	25318.	1.47	25525.	1.451	-207.
		0	25862.		26004.		-142.
3d⁷(²G)4s	b¹G	4	25147.	0.997	25100.	0.994	47.
3d⁷(²H)4s	a³H	6	27106.	1.172	27316.	1.167	-210.
		5	27469.	1.041	27644.	1.034	-175.
		4	27902.	0.803	28037.	0.809	-135.
3d⁷(²D)4s	a³D	3	27485.	1.36	27495.	1.334	-10.
		2	28112.	1.18	28071.	1.182	41.
		1	29269.	0.77	29229.	0.791	40.
3d⁷(²P)4s	a¹P	1	27585.	0.83	27626.	0.798	-41.
3d⁷(²H)4s	a¹H	5	30567.	1.027	30782.	1.001	-215.
3d⁷(²D)4s	b¹D	2	31199.	1.02	31196.	1.012	3.
3d⁶4s²	a⁵D	4	40696.		40707.	1.499	-11.
		3	41314.		41314.	1.501	0.
		2	41738.		41734.	1.501	4.
		1	42009.		42004.	1.501	5.
		0			42136.
3d⁷(²F)4s	c³F	2	40771.		40649.	0.666	122.
		3	40879.		40780.	1.084	99.
		4	41047.		40982.	1.252	105.
3d⁷(²F)4s	a¹F	3	44091.		43974.	1.000	117.

Table 2: Calculated HFR energy levels (in cm^-1) and Landé g-factors and comparison with experiment for the 3d⁸, 3d⁷4s and 3d⁶4s² configurations of Co II

2. Method used