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 3d^{8}, 3d^{7}4s, 3d^{7}5s, 3d^{7}4d, 3d^{7}5d, 3d^{6}4s^{2}, 3d^{6}4p^{2}, 3d^{6}4d^{2} and 3d^{6}4s4d. 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 3d^{8} and 3d^{7}4s configurations of Co II with the experimental energy levels compiled by Sugar & Corliss (1985). In the absence of CI, the 3d^{8} configuration is described by four parameters, , F^{2}(3d, 3d), F^{4}(3d, 3d) and , while for the the 3d^{7}4s, also the G^{2}(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 3d^{8} and 3d^{7}4s. All the parameters of these two configurations were adjusted except the effective interaction parameter corresponding to 3d^{8}. Indeed, for this configuration, only four electrostatic parameters (, F^{2}(3d, 3d), F^{4}(3d, 3d) and ) can be optimized due to the fact that only the four terms ^{3}F, ^{3}P, ^{1}D and ^{1}G have been determined experimentally (the ^{1}S is missing). The average energy of the 3d^{6}4s^{2} configuration was also adjusted using the a^{5}D 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 3d^{8}, 3d^{7}4s and 3d^{6}4s^{2} 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 3d^{7}(^{2}G)4s a^{3}G_{3} 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} | |
3d^{8} | E | 12516. | ||
F^{2}(3d,3d) | 71848. | 0.8541 | ||
F^{4}(3d,3d) | 45288. | 0.8731 | ||
79. | ||||
469. | 0.9915 | |||
3d^{7}4s | E | 27557. | ||
F^{2}(3d,3d) | 78543. | 0.8527 | ||
F^{4}(3d,3d) | 51650. | 0.9038 | ||
91. | ||||
-1035. | ||||
G^{2}(3d,4s) | 8467. | 0.8652 | ||
507. | 0.9657 | |||
3d^{6}4s^{2} | E | 78765. | ||
F^{2}(3d,3d) | 84612.^{a} | 0.8500 | ||
F^{4}(3d,3d) | 52787.^{a} | 0.8500 | ||
581.^{a} | 1.0000 |
Configuration | Term | J | E^{a} | g^{a} | E | g | E^{b} |
3d^{8} | a^{3}F | 4 | 0. | 0. | 1.250 | 0. | |
3 | 951. | 948. | 1.084 | 3. | |||
2 | 1597. | 1598. | 0.668 | -1. | |||
3d^{7}(^{4}F)4s | a^{5}F | 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. | ||
3d^{7}(^{4}F)4s | b^{3}F | 4 | 9813. | 1.243 | 9820. | 1.250 | -7. |
3 | 10708. | 1.082 | 10681. | 1.084 | 27. | ||
2 | 11322. | 0.68 | 11272. | 0.679 | 50. | ||
3d^{8} | a^{1}D | 2 | 11651. | 1.111 | 11648. | 1.096 | 3. |
3d^{8} | a^{3}P | 2 | 13261. | 1.415 | 13275. | 1.392 | -14. |
1 | 13404. | 1.484 | 13390. | 1.502 | 14. | ||
0 | 13593. | 13584. | 9. | ||||
3d^{7}(^{4}P)4s | a^{5}P | 3 | 17772. | 1.68 | 17786. | 1.668 | -14. |
2 | 18032. | 1.839 | 18064. | 1.829 | -32. | ||
1 | 18339. | 2.510 | 18372. | 2.493 | -33. | ||
3d^{8} | a^{1}G | 4 | 19190. | 19193. | 1.000 | -3. | |
3d^{7}(^{2}G)4s | a^{3}G | 5 | 21625. | 1.186 | 21390. | 1.199 | 235. |
4 | 22009. | 1.066 | 21754. | 1.048 | 255. | ||
3 | 22415. | 0.75 | 22126. | 0.750 | 289. | ||
3d^{7}(^{4}P)4s | b^{3}P | 2 | 24075. | 1.500 | 23998. | 1.497 | 77. |
1 | 24268. | 1.498 | 24260. | 1.471 | 8. | ||
0 | 24411. | 24468. | -57. | ||||
3d^{7}(^{2}P)4s | c^{3}P | 2 | 24887. | 1.49 | 25149. | 1.482 | -262. |
1 | 25318. | 1.47 | 25525. | 1.451 | -207. | ||
0 | 25862. | 26004. | -142. | ||||
3d^{7}(^{2}G)4s | b^{1}G | 4 | 25147. | 0.997 | 25100. | 0.994 | 47. |
3d^{7}(^{2}H)4s | a^{3}H | 6 | 27106. | 1.172 | 27316. | 1.167 | -210. |
5 | 27469. | 1.041 | 27644. | 1.034 | -175. | ||
4 | 27902. | 0.803 | 28037. | 0.809 | -135. | ||
3d^{7}(^{2}D)4s | a^{3}D | 3 | 27485. | 1.36 | 27495. | 1.334 | -10. |
2 | 28112. | 1.18 | 28071. | 1.182 | 41. | ||
1 | 29269. | 0.77 | 29229. | 0.791 | 40. | ||
3d^{7}(^{2}P)4s | a^{1}P | 1 | 27585. | 0.83 | 27626. | 0.798 | -41. |
3d^{7}(^{2}H)4s | a^{1}H | 5 | 30567. | 1.027 | 30782. | 1.001 | -215. |
3d^{7}(^{2}D)4s | b^{1}D | 2 | 31199. | 1.02 | 31196. | 1.012 | 3. |
3d^{6}4s^{2} | a^{5}D | 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. | ||||||
3d^{7}(^{2}F)4s | c^{3}F | 2 | 40771. | 40649. | 0.666 | 122. | |
3 | 40879. | 40780. | 1.084 | 99. | |||
4 | 41047. | 40982. | 1.252 | 105. | |||
3d^{7}(^{2}F)4s | a^{1}F | 3 | 44091. | 43974. | 1.000 | 117. |