A Theoretical Investigation of the Configurations (3d + 4s)⁸ 4p in Neutral Cobalt (Co I)

Abstract

Experimental levels of the configurations (3d + 4s)⁸ 4p were compared with corresponding calculated values. On fitting 154 levels by means of 19 free parameters an rms error of only 164 cm⁻¹ was obtained.

1. Introduction

Theoretical investigations of odd configurations 3d”4p for trebly and doubly ionized atoms of the iron group have been published by the author [1, 2]^1,2. In the calculations of doubly ionized Sc, Ti, and V the configurations 3dⁿ⁻¹4s4p were added [3], and for Cu II other odd configurations were also included [4].

The configurations (3d + 4s)³4p were considered previously for the arc spectrum of titanium by Rohrlich [5], as well as by Smith and Siddall [6]. The configurations 3d⁹4s4p in Cu I were investigated by Martin and Sugar [7]. Wilson [8] derived from a Hartree-Fock procedure a set of radial parameters for Cu I 3d⁹4s4p, which predicted satisfactorily the positions of seventeen low levels of Cu I. The configurations (3d + 4s)ⁿ 4p were investigated for the arc spectra of calcium, scandium, titanium, vanadium, chromium, manganese, and iron by the author [9 –13].

For the configurations (3d + 4s)³ 4p of Ti I, Rohrlich obtained an rms error of 1109 cm ⁻¹ before the advent of high-speed computers. He found it necessary to reject several terms which, however, fit very nicely in the recent investigations of Ti I, [6], [9]. Smith and Siddall obtained an rms error of 355 cm⁻¹, whereas in the author’s investigation the rms error was further reduced to 261 cm ⁻¹. One main reason for this considerable improvement is due to the fact that the author was able to identify experimental levels of the configuration 3d4s²4p and thus consider explicitly the interactions of this configuration with the configurations 3d²4s4p and 3d³4p. Secondly, Smith and Siddall restricted their analysis to the electrostatic approximation, whereas the author included the spin-orbit interactions.

The configurations (d + s)⁸p comprise 165 terms splitting into 438 levels. In AEL [14], 50 terms splitting into 139 levels are assigned to the configurations 3d⁸4p + 3d⁷4s4p, 8 terms splitting into 19 levels are given without configuration assignments, and in addition, there are 37 undesignated odd levels.

Since only the parameters³ B′,C, C′. and α vary monotonically from Ca I to Fe I, only the initial values of these parameters were obtained by linear extrapolation. Then, neglecting C and α for Sc I we obtain initially:

$$\begin{gathered} B^{\prime }=1,000 \\ C=3,660 \\ {C}^{\prime }=3,770 \\ {\alpha }^{\prime }=\alpha =85 \end{gathered}$$ (1)

The initial values of the other parameters were assumed to be equal to the final values for Fe I [13].

The initial value for the height of the configuration 3d⁷4s4p can be obtained either from ⁶F_{c. g.} or ⁶G_C. _G. (they differ only by $4F_2^{\prime }$). Then, from the electrostatic matrix of ⁶F [15],

$${}^6{\text{F}}_{\text{C}.\text{\hspace{0.17em}G.}}=A^{\prime }-15B^{\prime }-3G_{ds}^{\prime }-3F_2^{\prime }-G_{ps}^{\prime }+12{\alpha }^{\prime }=24180$$ (2)

and

$$A^{\prime }=50800$$ (3)

The initial value for the height of 3d⁸4p was obtained from the terms ²D of 3d⁸4p. By using the fact that the trace of a matrix equals the sum of its eigenvalues we obtain, [16,14]

$$\begin{array}{ll}3A-4B+2C+4F_2+10G_3+20\alpha \hfill & =3d^8\left(a^3\text{F}\right)4p{y}^2{\text{D}}_{\text{C}.\text{G}.}+3d^8\left({}^1\text{D}\right)4p{x}^2{\text{D}}_{\text{C}.\text{G}.}+3d^8\left({}^3\text{P}\right)4p{x}^2{\text{D}}_{\text{C}.\text{G}.}\hfill \\ \hfill & \text{= 126318}\hfill \end{array}$$ (4)

From the previously determined values of the other parameters, we obtain

$$\text{A = 39790}$$ (5)

Racah and Shadmi [17], found that the parameter D”, the difference between the weighted averages of the terms 3d^n-24s² and 3d^n-14s in the second spectra of the iron group, was a linear function of the atomic number with a quadratic correction. By assuming that D”[(d + s) ⁿp] in the first spectra obeys a similar relationship as a function of atomic number, a parabola is drawn to pass through the points determined by D”(Sc I), D”(Ti I) [9] and D” (Fe I) [13], and extrapolated for Co I, (Sc I and Fe I have experimental levels belonging to 3dⁿ⁻²4s²4p, whereas in Ti I, eigenfunctions of some of the higher levels to which experimental levels are assigned contain considerable contributions of 3d4s²4p so that the standard deviation in A” was only 234).

By substituting into eqs (8) and (9) of reference [12] the final values of the parameters for Fe I [13], and adding $-10G_1^{\prime \prime }-35G_3^{\prime \prime }$ to eq (9) (see ref. [12]) since the matrices of d⁶s²p, i.e., d⁶p, on tape are those calculated by Ishidzu and Obi [18], who did not use the convention that for the case of an almost complete shell and an electron outside the shell, one subtracts from the energy matrix the interaction of the outer electron with the closed shell (see section 3, [19]), we obtain

$$D^{″}(\text{Fe})=36420$$ (6)

By using the values of D”(Ti) and D”(Sc) given by eqs (11) and (14) of reference [10], with the above value for D”(Fe) to obtain the parabola through these three points, and extrapolating

$$D^{″}(\text{Co})=42410$$ (7)

From eqs (8) and (9) of reference [12] and again adding $-10G_1^{\prime \prime }-35G_3^{\prime \prime }$ to eq (9), reference [12], we obtain

$$A^{″}=87980$$ (8)

2. Discussion and Results

Although the configuration 3d⁶4s²4p is very high, it markedly influences the results. In the calculations of 3d⁸4p + 3d⁷4s⁴p the rms error was 209 cm⁻¹, whereas the inclusion of 3d⁶4s²4p reduced the rms error in the uniform treatment⁴ to 164 cm⁻¹. Furthermore, the terms obtained from (4F) + ¹P⁵ had very high deviations when considering only 3d⁸4p + 3d⁷4s4p. In particular, in 3d⁸4p + 3d⁷4s4p the mean deviation of the term ⁴F(¹P)x⁴D was — 643, whereas with the three configurations the mean deviation was only — 50. This great improvement can be attributed to the fact that when (3d + 4s) ⁸4p was considered $G_{ps}^{\prime }$assumed a much higher value (7038 ± 5 6 cm⁻¹ versus 6571 ± 62 cm⁻¹).

The experimental data for Co I are not sufficient to permit A”, the height of 3d⁶4s²4p, to change freely. Thus in the final variation the value of A” was held fixed at 85220 so that with the final values of the parameters, D” should approximately equal its original value of 42410. The final parameters in the uniform treatment are given in table 1.

Table 1.

Parameters for Co I (3d + 4 s)⁸4p (in units of cm^−l)

Parameter	Initial Value	Final Value
A	39790	39264 ± 122
A′	50800	50677 ± 69
A″	87980	85220 (Fixed)
B	740	833 ± 8
B′	1000	956 ± 6
B″	1260	1079 (Arith. Progress.)
C	3660	3744 ± 63
C′	3770	3875 ± 18
C″	3880	4006 (Arith. Progress.)
$G_{ds}^{\prime }=G$	1540	1607 ± 33
F2	170	218 ± 10
$F_2^{\prime }$	300	303 ± 7
$F_2^{\prime \prime }$	430	388 (Arith. Progress.)
G1	200	196 ± 9
$G_1^{\prime }$	240	199 ± 7
$G_1^{\prime \prime }$	280	202 (Arith. Progress.)
$G_3=G_3^{\prime }=G_3^{\prime \prime }$	20	14 ± 2
$G_{ps}^{\prime }$	7120	7038 ± 56
α= α′= α″	85	71 ± 3
H = H′	85	72 ± 6
J = J′	1180	1245 ± 50
K	2460	2331 ± 55
K′	3352	3223 (Fixed Diff.)
${\zeta }_d={\zeta }_d^{\prime }={\zeta }_d^{\prime \prime }$	410	517 ± 17
${\zeta }_p={\zeta }_p^{\prime }={\zeta }_p^{\prime \prime }$	200	236 ± 53
rms error		164.2 cm−1

The comparison of the experimental and calculated values of the levels and g-factors obtained from the final least-squares of the uniform treatment is given in table A of the Appendix. The calculated values, percentage compositions, and g-factors of all the 258 predicted levels of 3d⁸4p + 3d⁷4s4p are given in table A. The 25 lowest levels of 3d⁶4s²4p, based on 3d⁶(⁵D) are also quoted. However, the latter values as well as those higher levels of 3d⁸4p + 3d⁷4s4p containing significant contributions of 3d⁶4s²4p must be considered as only approximate.

Of the unclassified odd levels only the levels 1°, 2°, 3°, 7°, 10°, 11°, 12°, 15°, and 23° were included. Besides the 28 unclassified odd levels, the following 13 levels were also neglected in the least-squares:

1. The level 3d⁸ (³P)4p: y²S_1/2

2. The level 3d⁸ (³P)4p: x²P_1/2

3. The level 3d⁸(³P)4p: w²P_1/2

4. The four levels of 3d⁷4s(³D)4p: s ⁴D

5. The level t²F_7/2:

6. The level s²F_5/2:

7. The four levels of v⁴F

It is evident from table A that one of the terms y²S and x²S cannot be assigned to a corresponding theoretical term ²S. The theoretical term ²S, calculated at 48010, contains contributions with the same assignments as y²S and x²S, and the experimental values of the two terms are very close. However, x²S was accepted since the correspondence between the calculated and experimental g-factors is better for x²S than for y²S.

The levels of the term ⁴P(³P)²P are calculated at 48966 and 48453. Thus, when the experimental level x²P_3/2 is assigned to ⁴P(³P)²P_3/2, the deviation is only — 119. However, the level x²P_1/2, which is given as uncertain in AEL, would yield a deviation of around — 800, which is incompatible with the results for the other levels. Furthermore, the level w²S, which cannot be assigned to a theoretical level ²S, fits with a deviation of only — 128 when assigned to ⁴P(³P)²P_1/2. Although the agreement between the experimental and calculated g-factors is not very good here, it should be noted that the experimental g-factor of 1.50 for w²S is given as uncertain in AEL.

The theoretical term ²P following ⁴P(³P)²P in height, is the term ²P(³P)²P to which the levels of v²P correspond. Thus, the experimental levels of w²P cannot be assigned to a theoretical term ²P. The level w²P_3/2 is assigned to the previously vacant theoretical level ²P(³P)²D_3/2 yielding a deviation of only — 60. The experimental g-factor of 1.099 corresponds to the calculated value of 0.991. The only theoretical level to which w²P_1/2 could conceivably be assigned is ²P(³P)²S. However, as the resulting deviation would then be greater than 600, and since the agreement between the experimental g-factor of 1.365 and the calculated g-factor of 1.882 is also very poor, the level w²P_1/2 was not inserted into the least-squares.

It is immediately evident from table A that the experimental levels of s ⁴D have no corresponding vacant theoretical levels to which they could be assigned.

The levels of the term A²D(³P)²F are calculated at 52491 and 52784. Thus, it is evident that the experimental levels t²F_5/2 and s²F_7/2 should be grouped together and assigned to the theoretical term, A²D(³P)²F. The resulting deviations are 305 and 320 with excellent agreement between the experimental and calculated g-factors of both levels. The two remaining levels t²F_7/2 and s²F_5/2, both of which are given as uncertain in AEL, have no corresponding theoretical levels to which they could be assigned.

The experimental levels v ⁴F cannot be assigned to a theoretical term ⁴F. Conceivably, the levels v ⁴F_3/2,_5/2,_7/2 could be fitted to the theoretical levels ⁴P(¹P)⁴D_3/2,_5/2,_7/2 and the level v ⁴F_9/2 could be assigned to ²H(³P)²H_9/2. Besides the danger of performing changes in term designations for such high levels, it is important to note that in the paper of Russell, King, and Moore [20], these levels are considered as doubtful.

The following table indicates how the nine unclassified odd levels were assigned:

The unclassified levels 4°, 5°, 8°, 13°, 14°, 16°, 17°, 18°, 19°, 20°, 21°, and 22° have no corresponding theoretical levels to which they could be assigned.

For the level 6° the J-value is questioned. For J equal to 9/2 the level 6°_7/2? could be assigned to either ²H(³P)⁴I_9/2 or ²H(³P)⁴G_9/2. ‘

The level 9° probably should be assigned to A²D(³P)⁴F_9/2 to complete with 10°, 11°, and 12° the term A²D(³P)⁴F. However, unlike the levels 10°, 11°, and 12°, the level 9° is given as uncertain in AEL, and there is no experimental g-factor to confirm this assignment. Furthermore, the levels 10°, 11°, and 12° have combinations with levels of 9 even terms, whereas 9° is based on combinations with the levels of only 2 even terms [20]. Although the level 9° was not included in the least-squares calculations, it is inserted in parentheses adjacent to the calculated value of A²D(³P)⁴F_9/2 in table A.

The following changes in assignment were performed:

1. AEL3d⁷4s(a⁵P)4pz⁴P→ (³P)⁴P

2. ²G(³P)²F↔ (¹D)²F

3. AEL 3d⁸(³P)4py⁴P)→ ²P(³P)⁴P

4. AEL 3d⁷4s(³P)4px⁴P_3/2→ (³P)⁴S_3/2

5. AEL 3d⁸(³P)4pv⁴D_3/2→ ⁴P(³P)⁴P_3/2

6. AEL 3d⁷4s(³P)4py⁴S_3/2→ (³P)⁴D_3/2

7. AEL 3d⁷4s(³P)4pv²D_3/2→ (³P)²D_3/2

8. AEL 3d⁸(³P)4pw²D_3/2→ ⁴P(³P)²D_3/2

9. AEL 3d⁷4s(³P)4py²P→ (³P)²p

10. AEL 3d⁷4s(³P)4px²S→ (³P)²S

11. AEL v ²F_5/2,_7/2 → ²H(³P)⁴G_5/2,7/2

12. AEL 3d⁸(³P)4px⁴S→ ²P(³P)⁴S

13. AEL 3d⁷4s(³P)4pt ⁴D→ A²D(³P)⁴D

14. AEL w²S_1/2 → ⁴P(³P)²P_1/2

15. AEL 3d⁸(³P)4px²P_3/2 → ⁴P(³P)²P_3/2

16. AEL 3d⁷4s(³P)4pw²P_3/2→ ²P(³P)²D_3/2

17. ²H(³P)²G↔ (^lG)²G

18. AEL 3d⁷4s(³H)4px²H_9/2,_11/2→ ²H(³P)⁴H_9/2,_11/2

Although in most changes of assignment the theoretical eigenfunctions are mixed strongly, in the changes 1, 2, 3, 9, 10, 12, 13, and 15 the compositions of the theoretical levels contain only small contributions of the experimental assignments (see table A).

The experimental g-factor of y⁴S is 1.273. Since the theoretical g-factor of ⁴S is 2.000, y ⁴S could be assigned to a theoretical term ⁴S if the latter would have significant contributions of terms with low theoretical g-factors (such as ⁴F_3/2, ²D_3/2). However, this is not so in the present case and thus after several variations it was ascertained that the best agreement in the values and g-factors of the levels ⁴P(³P)⁴P, (³P)⁴D and (³P)⁴S is obtained after performing the changes 4, 5, and 6.

The grouping of the levels of w²D and v²D as given in AEL, is incongruous with the calculated values of the levels of (³P)w²D and ⁴P (³P)v²D. Thus, the changes 7 and 8 were performed.

The levels of v ²F cannot be assigned to a theoretical term ²F. However, when the two levels of v ²F are assigned to the two lowest levels of ²H (³P)⁴G, not only is there excellent agreement between the experimental and calculated values of the levels (for each level the deviation is only — 24), but there is also a close correspondence between the experimental and calculated g-factors (the experimental g-factors of 0.619 and 1.173 correspond to the calculated values of 0.619 and 1.008, respectively). This change is indicated by 11.

The changes 14 and 16 were discussed previously.

The change 18 is similar to change 11. Although there is no corresponding theoretical term ²H to which the levels of x ²H could be assigned, there is excellent agreement between the calculated and experimental values of the levels and g-factors when the levels x ²H are assigned to the theoretical levels ²H(³P)⁴H_9/2,_11/2. To the theoretical level ²H(³P)⁴H_7/2, the level ${\text{15}}_{7/2}^0$ (based on 10 combinations with even levels, [20]), is assigned to yield a deviation of only — 48.

Below the limit of the experimental levels inserted, there are 21 theoretical levels with no corresponding experimental levels. The lowest of these is the level ⁴P(³P)⁶S calculated at 34642.

With very few exceptions the agreement between the experimental and calculated g-factors is excellent.

Table 2.

Unclassified Odd Levels of Co I

Level	Assignment	Deviation	Observed g-Factor	Calculated g-Factor
$1_{7/2}^{°}$	4P(3P)6P7/2	205	1.40	1.709
$2_{5/2}^{°}$	4P(3P)6P5/2	165	1.863	1.866
$3_{7/2}^{°}$	2G(3P)4H7/2	−1		0.680
$7_{5/2}^{°}$	2P(3P)2P5/2	−218		1.163
${10}_{7/2}^{°}$	A2D (3P)4F7/2	58	1.260	1.257
${11}_{5/2}^{°}$	A2D (3P)4F5/2	−7	1.079	1.107
${12}_{3/2}^{°}$	A2D (3P)4F3/2	87	0.569	0.680
${15}_{7/2}^{°}$	2H (3P)4H7/2	−48		0.690
${23}_{3/2}^{°}$	A2D (3P)4P3/2	180	1.353	1.363

Appendix Table A. Observed and Calculated Levels and g-Factors

In the column “Name” the calculated designation of the term is given. Whenever the terms of the parent dⁿ have different seniorities these are denoted by the letters A and B, the lower calculated term being designated by A. The terms of d⁷sp are denoted by d⁷v₁S₁L₁(sp^1,3P)SL. The terms of d⁸p are differentiated from those of d⁶s²p by using a star for the latter terms.

The entries in the columns “j”, “Obs. Level (cm⁻¹)”, “ Calc. Level (cm⁻¹)”, “ Obs. g-Factor” and “ Calc. g-Factor” are self-evident. In the column “Percentage”, for each calculated level either the three highest contributions or all those contributions exceeding five percent are given.

Whenever the experimental and calculated term designations differ, the experimental designation is entered in the column “AEL” using the notation of C. E. Moore, [14]. In many instances the exchanges involve complete terms rather than isolated levels. Unless specified otherwise, the entries in the column “AEL” pertain to exchanges in terms.

The column “O-C” gives the difference between the observed and calculated values of the levels.

The entries are in increasing energy of the calculated levels.

Table A.

Observed and calculated levels of Co I (3d + 4s)⁸4p

Name	J	Percentage	AEL		Obs. Level (cm−1)	Calc. Level (cm−1)	o-c	Obs. g-Factor	Calc. g-Factor
			Config.	Desig.
4F(3P)6F	1/2	99	3d74s(a5F)4p	z 6F	25233	25240	−7	−0.622	−0.631
	3/2	95			25041	25061	−20	1.118	1.080
	5/2	90 + 74F(3P)6D			24733	24775	−42	1.336	1.328
	7/2	84 + 124F(3P)6D			24326	24397	−71	1.436	1.412
	9/2	78 + 184F(3P)6D			23856	23961	−105	1.481	1.452
	11/2	97			23612	23635	−23	1.466	1.451
4F(3P)6D	1/2	94	3d74s(a5F)4p	z 6D	26250	26404	−154	3.286	3.297
	3/2	91			26063	26210	−147	1.812	1.810
	5/2	87 + 64F(3P)6F			25740	25881	−141	1.612	1.615
	7/2	83 + ll4F(3P)6F			25269	25407	−138	1.550	1.555
	9/2	78 + 174F(3P)6F			24628	24770	−142	1.569	1.529
4F(3P)6G	3/2	97	3d74s(a5F)4p	z 6G	26598	26425	173	0.006	0.042
	5/2	95			26450	26273	177	0.876	0.882
	7/2	94			26232	26049	183	1.150	1.156
	9/2	94			25938	25749	189	1.281	1.278
	11/2	96			25569	25375	194	1.354	1.344
	13/2	100			25139	24941	198	1.40	1.384
4F(3P)6F	3/2	85 + 13(3F)4F	3d74s(a5F)4p	z 4F	29563	29561	2	0.410	0.408
	5/2	82 + 13(3F)4F			29216	29217	−1	1.033	1.026
	7/2	80 + 13(3F)4F			28777	28779	−2	1.247	1.234
	9/2	82 + 15(3F)4F			28346	28328	18	1.330	1.331
4F(3P)4G	5/2	94	3d74s(a5F)4p	z 6G	30103	30044	59	0.577	0.583
	7/2	91			29735	29680	55	0.995	0.991
	9/2	90			29270	29219	51	1.175	1.175
	11/2	95			28845	28765	80	1.276	1.273
4F(3P)4D	1/2	65 + 31(3F)4D	3d74s(a5F)4p	z 4D	30743	30790	−47	−0.006	0.003
	3/2	62 + 33(3F)4D			30444	30482	−38	1.192	1.192
	5/2	57 + 36(3F)4D			29949	29969	−20	1.359	1.362
	7/2	53 + 42(3F)4D			29295	29289	6	1.425	1.425
4F(3P)2G	7/2	41 + 29(3F)4F + 11(3F)2G	3d74s(63F)4p	z 2G	32733	32850	−117	0.899	0.990
	9/2	47 + 29(3F)4G + 13(3F)4F			31700	31822	−122	1.126	1.121
4F(3P)2F	5/2	71 + 26(3F)2F	3d74s(63F)4p	z 2F	32782	32962	−180	0.870	0.863
	7/2	66 + 28(3F)2F			31871	32061	−190	1.177	1.153
(3F)4D	1/2	59 + 364F(1P)4D			33449	33533	−84	0.012	0.003
	3/2	56 + 374F(‘P)4D			33151	33209	−58	1.195	1.193
	5/2	51 + 414F(1P)4D			32654	32680	−26	1.366	1.364
	7/2	46 + 454F(1P)4D			32028	31982	44	1.395	1.416
(3F)4G	5/2	52 + 30(3F)4F			33674	33608	66	0.704	0.777
	7/2	34 + 31(3F)2G + 11(3F)4F			33173	33185	−12	1.039	1.040
	9/2	53 + 28(3F)2G + 84F(3P)2G			32465	32414	51	1.154	1.171
	11/2	94			32431	32296	135	1.287	1.273
4F(3P)2D	3/2	53 + 37(3F)2D	3d74s(b3F)4p	z 2D	34352	34423	−71	0.787	0.781
	5/2	53 + 42(3F)2D			33463	33497	−34	1.186	1.198
(3F)4F	3/2	67 + 244F(1P)4F			34196	34205	−9	0.430	0.430
	5/2	38 + 42(3F)4G			33946	33937	9	0.900	0.824
	7/2	25 + 33(3F)4G + 244F(3P)2G			33467	33445	22	1.155	1.055
	9/2	51 + 224F(3P)4F + 144F(3P)2G			32842	32791	51	1.313	1.278
(3F)2G	7/2	50 + 21(3F)4G + 214F(3P)2G			34134	34179	−45	0.917	0.921
	9/2	56 + 274F(3P)2G + 11(3F)4G			33440	33420	20	1.165	1.159
4P(3P)6S	5/2	99				34642			1.998
(3F)2F	5/2	53 + 18(3F)2D +164F(3P)2F			36330	36250	80	0.892	0.948
	7/2	61 + 254F(3P)2F			35451	35236	215	1.145	1.144
(3F)2D	3/2	53 + 404F(3P)2D			36875	36923	−48	0.794	0.805
	5/2	35 + 364F(3P)2D			36092	36049	43	1.186	1.118
4P(3P)6D	1/2	94				39184			3.314
	3/2	92				39093			1.846
	5/2	92				38991			1.655
	7/2	92				38902			1.583
	9/2	96				38847			1.555
4P(3P)4S	3/2	74 +10(3P)4S	3d74s(a 5P)4p	z 4S	40622	40240	382	2.017	1.918
4F(1P)4D	1/2	62 + 24(3P)4D	3d74s(b 3F)4p	x 4D	41102	41141	−39	0.026	0.012
	3/2	62 + 23(3P)4D			40828	40863	−35	1.240	1.204
	5/2	63 + 21(3P)4D			40346	40395	−49	1.370	1.369
	7/2	65 + 18(3P)4D			39649	39726	−77	1.428	1.428
4P(3P)6P	3/2	90 + 64P(3P)4S				40992			2.291
	5/2	93		2°	41105	40940	165	1.863	1.866
	7/2	97		1°	41041	40836	205	1.40	1.709
4F(!P)4F	3/2	61 + 272G(3P)4F	3d74s(b 3F)4p	x 4F	42797	42396	401	0.406	0.408
	5/2	59 + 242G(3P)4F			42434	42046	388	1.024	1.052
	7/2	63 + 232G(3P)4F			41918	41571	347	1.248	1.234
	9/2	66 + 192G(3P)4F			41226	40917	309	1.319	1.330
(3P)4P	1/2	66 + 142P(3P)4P+ 114P(3P)4P	3d74s(a 5P)4p	Z 4P	41970	42048	−78	2.51	2.520
	3/2	64 + 124P(3P)4P + 92P(3P)4P			41983	41972	11	1.732	1.665
	5/2	65 + 124P(3P)4P + 92P(3P)4P			41969	41932	37	1.627	1.548
4F(1P)4G	5/2	93	3d74s(b 3F)4p	x 4G	43200	43350	−150	0.649	0.581
	7/2	92			42811	42962	−151	1.004	0.988
	9/2	93			42269	42439	−170	1.169	1.174
	11/2	95			41529	41747	−218	1.291	1.272
2G(3P)4H	7/2	95		3°	42988	42989	−1		0.680
	9/2	90				42775			0.977
	11/2	92				42632			1.135
	13/2	98				42565			1.229
(1D)2P	1/2	42 + 25(3P)2P + 72P(3P)2P			43130	43084	46	0.727	0.846
	3/2	31 + 23(1D)2D + 224P(3P)4D			43538	43544	−6	1.120	1.175
4P(3P)4D	1/2	75 + 92P(3P)4D	3d74s(a 5P)4p	w 4D	43436	43444	−8	0.169	0.101
	3/2	58 + 9(1D)2D			43264	43298	−34	1.191	1.186
	5/2	46 + 28(1D)2F			43243	43218	25	1.101	1.168
	7/2	88 + 3(1D)2F			43399	43346	53	1.334	1.417
(lD)2F	5/2	37 + 364P(3P)4D+102G(3P)2F	3d74s(3G)4p	x 2F	43426	43371	55	1.119	1.108
	7/2	45 + 202G(3P)4F + 162G(3P)2F			43555	43602	−47	1.229	1.174
(1D)2D	3/2	40 + 33(1D)2P + 5(3P)2P			43911	43957	−46	1.127	1.070
	5/2	52 + 202G(3P)4F			43922	44113	−191	1.230	1.147
4P(3P)2S	1/2	61 + 21(3P)2S	3d74s(3P)4p	z 2S	44455	44185	270	2.10	1.908
2P(3P)4F	3/2	68+184F(1P)4F + 7(3F)4F	3d74s(3G)4p	w 4F	44556	44745	−189	0.415	0.412
	5/2	29 + 232G(3P)4G + 23(1D)2D			44202	44333	−131	0.950	0.970
	7/2	39 + 23(1D)2F + 112G(3P)4G			43848	43979	−131	1.197	1.183
	9/2	71 + 154F(1P)4F + 5(3F)4F			43295	43523	−228	1.295	1.318
2G(3P)4G	5/2	69 + 192G(3P)4F	3d74s(3G)4p	w 4G	44568	44561	7	0.676	0.703
	7/2	77 + ll2G(3P)4F			44394	44343	51	1.004	1.013
	9/2	85 + 52G(3P)4F			44183	44100	83	1.163	1.169
	11/2	93			43952:	43851	101	1.279	1.266
2P(3P)4P	1/2	44 + 404P(1P)4P	3d8(3P)4p	x 2P	44858	45215	−357	2.371	2.523
	3/2	37 + 404P(1P)4P			44658	44948	−290	1.674	1.680
	5/2	33 + 424P(1P)4P			44480	44708	−228	1.557	1.565
2G(3P)2H	9/2	87	3d74s(3G)4p	x 2H	45111	44988	123	0.897	0.907
	11/2	90			45540	45380	160	1.097	1.091
(3P)2D	3/2	72 + 7(1D)2D + 64P(3P)2D	3d74s(3P)4p	v 2D	46186	46017	169	1.218	0.853
	5/2	70 + 84P(3P)2D	3d8(3P)4p	w 2D	45688	45397	291	1.219	1.170
(3P)4S	3/2	32 + 254P(3P)4S + 13(3P)2P	3d74s(3P)4p	x 4P	45905	45906	− 1	1.674	1.794
4P(3P)4P	1/2	44 + 22(3P)4P + 152P(3P)4P	3d74s(3P)4p	x 4P	45957	45864	93	2.522	2.613
	3/2	30 + 18(3P)4P + 162P(3P)4P	3d8(3P)4p	v 4P	46260	46151	109	1.508	1.714
	5/2	30 + 242P(3P)4P + 16(3P)4P	3d74s(3P)4p	x 4P	46003	46168	−165	1.543	1.566
2G(3P)2G	7/2	79 + 102H(3P)2G	3d74s(3G)4p	x 2G	45767	45931	−164	0.898	0.896
	9/2	80 + 102H(3P)2G			46032	46211	−179	1.131	1.113
(3P)4D	1/2	27 + 21A2D(3P)4D + 172P(3P)4D			46502	46489	13	0.161	0.149
	3/2	14 + 16(3P)2P + 12(1D)2P	3d74s(3P)4p	y 4S	46563	46654	−91	1.273	1.200
	5/2	28 + 252P(3P)4D + 114F(1P)4D			46330	46485	− 155	1.365	1.361
	7/2	44 + 222P(3P)4D + 114F(1P)4D			45971	46229	−258	1.424	1.406
4P(3P)2D	3/2	61 + 142P(3P)2D + 7(3P)4D	3d8(1P)4p	w 2F	46455	46803	−348	0.869	0.893
	5/2	45 + 202G(3P)2F + 9(3P)4D	3d74s (3P)4p	v 2D	46672	46695	−23	1.233	1.130
2G(3P)2F	5/2	33 + 224P(3P)2D + 14(1D)2F	3d8(1D)4p	w 2F	47129	46944	185	0.858	0.971
	7/2	36 + 312P(3P)4D + 11(1D)2F			47225	47062	163	1.229	1.310
(3P)2P	1/2	46 + 30(1D)2P + 104P(3P)2P	3d74s (3P)4p	y 2P	47091	47215	−124	0.656	0.671
	3/2	27 + 12(1D)2P + 9(3P)4D			46685	46471	214	1.352	1.394
2P(3P)4D	1/2	37 + 21(3P)2S + 20(3P)4D		u 4D	47905	48010	−105	0.016	0.691
	3/2	47 + 18(3P)4D + 10A2D(3P)4F			47612	47554	58	1.122	1.105
	5/2	45 + 134P(3P)2D + 11(3P)4D			47394	47365	29	1.324	1.319
	7/2	26 + 23A2D(3P)4D + 212G(3P)2F			46873	46806	67	1.352	1.394
2H(3P)4I	9/2	94				48081			0.739
	11/2	94				47874			0.968
	13/2	97				47717			1.108
	15/2	100				47613			1.200
(3P)2S	1/2	35 + 262P(3P)4D + 154P(3P)2S	3d74s (3P)4p	x 4S	48026	48010	16	1.699	1.193
2H(3P)4G	5/2	81 + 72G(3P)2F		v 2F	48616:	48640	−24	0.619	0.619
	7/2	84 + 42G(3P)2F		v 2F	48317	48341	−24	1.173	1.008
	9/2	92				47996			1.171
	11/2	95				47626			1.272
A2D(3P)4D	1/2	52 + 16(3P)4D	3d74s(3P)4p	x 2D	48572	48893	−321	0.452	0.198
	3/2	21 + 222P(3P)4S + 12(3P)4D			48546	48742	−196	1.050	1.254
	5/2	52 + 19(3P)4D			48444	48796	−352	1.340	1.339
	7/2	51 + 18(3P)4D			48217	48573	−356	1.211	1.386
4P(3P)2P	1/2	69 + 122P(3P)2S + 10(3P)2P		w 2S	48838	48966	−128	1.50:	0.840
	3/2	40 + 152P(3P)4S + 11A2D(3P)4D	3d8(3P)4p	x 2P	48334	48453	−119	1.436	1.369
2P(3P)4S	3/2	48 + 26A2D(3P)4D + 8(3P)4D	3d8(3P)4p	x 2S	48754	48946	−192	1.728	1.623
2P(3P)2D	3/2	29 + 344P(3P)2P + 24A2D(3P)4F	3d74s(3P)4p	w 2P	49025	49085	−60	1.099	0.991
	5/2	32 + 34A2D(3P)4F + 102P(3P)4D		7°	48829	49047	−218		1.163
A2D(3P)4F	3/2	50 + 152P(3P)2D + 11A2D(3P)2D		12°	50105	50018	87	0.569	0.680
	5/2	43 + 242P(3P)2D		11°	49847	49854	−7	1.079	1.107
	7/2	75 + 62P(3P)4D		10°	49484	49426	58	1.260	1.257
	9/2	98		9°	(49198:)	49108	(90)		1.333
2H(3P)2I	11/2	90				50080			0.936
	13/2	67 + 312H(3P)4H				50435			1.126
(1G)2H	9/2	81 + 92H(3P)2H			50211	50124	87	0.899	0.915
	11/2	69 + 172H(3P)2H			50376	50389	−13	1.091	1.085
2P(3P)2S	1/2	68 + 134P(3P)2P				50417			1.882
(1G)2G	7/2	38 + 372H(3P)2G	3d74s(3H)4p	w 2D	50611	50556	55	0.82	0.908
	9/2	40 + 382H(3P)2G			50593	50616	−23	1.10	1.095
(1G)2F	5/2	57 + 17A2D(3P)2F			50712	50771	−59	0.905	0.909
	7/2	60 + 12A2D(3P)2F + 82G(3P)2F			50579	50693	−114	1.125	1.120
2P(3P)2P	1/2	71 + 13A2D(3P)4D		v 2P	50945	50972	−27	0.732	0.707
	3/2	53 +15A2D(3P)4D			50925	50861	64	1.340	1.331
2H(3P)4H	7/2	89 + 5(1G)2G		15°	51185	51233	−48		0.690
	9/2	86 + 5(1G)2G	3d74s(3H)4p	x 2H	50903	51048	−145	0.941	0.982
	11/2	86 + 11(1G)2H	3d74s(3H)4p	x 2H	50703	50828	−125	1.110	1.128
	13/2	68 + 302H(3P)2I				50573			1.184
A2D(3P)4P	1/2	66 + 122P(3P)4P	3d74s(3D)4p	w 2P	52355	52180	175	2.304	2.414
	3/2	57 + 172P(3P)2P			52014	51784	230	1.616	1.617
	5/2	73 + 132P(3P)2P			51160	50950	210	1.578	1.564
A2D(3P)2F	5/2	58 + 17(1G)2F		t 2H	52796	52491	305	0.883	0.897
	7/2	75 + 112G(3P)2F		s 2F	53104	52784	320	1.136	1.149
A2D(3P)2D	3/2	51 + 212P(3P)2D		u 2D	53075	52884	191	0.823	0.816
	5/2	49 +182P(3P)2D			53196	53964	232	1.206	1.180
2H(3P)2G	7/2	44 + 30(1G)2G + 222G(3P)2G	3d8(1G)4p	v 2G	53374	53288	86	0.888	0.889
	9/2	44 + 28(1G)2G + 242G(3P)2G			53276	53214	62	1.124	1.111
A2D(3P)2P	1/2	93				53764			0.750
	3/2	87		23°	54165	53985	180	1.353	1.363
2H(3P)2H	9/2	91 + 6(1G)2H				54608			0.910
	11/2	88 + 6(1G)2H				54821			1.092
4P(1P)4D	1/2	82 + 10(5D)4D*				55223			0.094
	3/2	80+10(5D)4D*				55057			1.224
	5/2	81 + 11(5D)4D*				54867			1.377
	7/2	85 +12(5D)4D*				54693			1.427
4P(1P)4S	3/2	58 + 27(3P)4S				55395			1.961
4P(1P)4P	1/2	70 + 19(5D)4P*				55825			2.561
	3/2	61 + 17(5D)4P*				55792			1.729
	5/2	70 + 21(5D)4P*				55421			1.587
2G(1P)2H	9/2	93				57733			0.914
	11/2	91				57103			1.088
(5D)6D*	1/2	99				58371			3.328
	3/2	99				58244			1.864
	5/2	98				58035			1.655
	7/2	97				57754			1.585
	9/2	99				57426			1.554
2G(1P)2F	5/2	84 + 4(1D)2F				58878			0.859
	7/2	80 + 4(‘D)2F				58189			1.138
2G(1P)2G	7/2	74 + 11(1G)2G				59402			0.892
	9/2	68 +132H(JP)2G				58698			1.105
2P(1P)2P	1/2	65 + 17A2D(1P)2P				60923			0.776
	3/2	65 + 13A2D(1P)2D				60947			1.231
(5D)6F*	1/2	99				61723			−0.659
	3/2	98				61647			1.066
	5/2	98				61517			1.312
	7/2	97				61332			1.394
	9/2	96				61091			1.432
	11/2	100				60812			1.455
2P(1P)2P	3/2	83 + 62P(1P)2P				61733			0.854
	5/2	79 + 8A2D(1P)2F				61014			1.175
2F(3P)4G	5/2	94				61635			0.579
	7/2	93				61764			0.990
	9/2	94				61941			1.175
	11/2	95				62174			1.270
2F(3P)4F	3/2	94				62192			0.416
	5/2	91				62335			1.035
	7/2	95				62483			1.232
	9/2	60 + 272H(1P)2G				62848			1.250
2H(1P)2I	11/2	96				62729			0.929
	13/2	98				62101			1.077
2F(3P)4D	1/2	93				62496			0.002
	3/2	92				62487			1.189
	5/2	89				62485			1.359
	7/2	87				62484			1.436
2P(1P)2S	1/2	70 +142P(3P)2P				62732			1.816
a2d(1p)2d	3/2	69 +102P(1P)2P				63531			0.862
	5/2	78 + 82F(3P)2D				62568			1.186
2H(1P)2G	7/2	60 + 11(5D)4F*				63467			0.949
	9/2	36 + 312F(3P)4F +17(5D)4F*				62864			1.221
(5D)6P*	3/2	97				63870			2.363
	5/2	98				63447			1.878
	7/2	93				62815			1.697
A2D(1P)2F	5/2	66 +162F(3P)2D				64160			0.970
	7/2	89				63306			1.141
(5D)4F*	3/2	93				63975			0.427
	5/2	89				63699			1.054
	7/2	77 + 82H(1P)2G				63330			1.209
	9/2	77 + 102H(1P)2G				62810			1.305
2F(3P)2D	3/2	68 + 12(5D)4D*				64398			0.857
	5/2	49 + 14(5D)4D*				64410			1.175
(5D)4D*	1/2	73 + 94P(1P)4D				64715			0.055
	3/2	61 + 132F(3P)2D				64573			1.131
	5/2	53 + 242F(3P)2D				64226			1.312
	7/2	68 + 7(5D)4F*				63916			1.415
2H(1P)2H	9/2	78 + 132F(1P)2G				64952			0.937
	11/2	90				64391			1.091
2F(3P)2G	7/2	85 +102H(1P)2G				64832			0.890
	9/2	78 + 142H(1P)2H				64886			1.088
A2D(1P)2P	1/2	66 + 122P(3P)2P				65449			0.694
	3/2	78				64135			1.347
2F(3P)2F	5/2	96				66808			0.859
	7/2	96				66717			1.143
(5D)4P*	1/2	78 + 204P(1P)4P				68813			2.662
	3/2	78 + 204P(1P)4P				68540			1.732
	5/2	77 + 214P(1P)4P				68061			1.599
	7/2	87 + 9(3H)2G*				75095			0.890
	9/2	87 + 9(3H)2G*				75389			1.111
2F(1P)2G	3/2	88				75783			0.801
2F(1P)2D	5/2	73 + 152F(3P)2F				75894			1.143
2F(1P)2F	5/2	75 + 152F(1P)2D				76244			0.915
	7/2	90 + 6(3G)2F*				76512			1.142
(1S)2P	1/2	89 + 9A2D(1P)2D				76561			0.667
	3/2	88 +10A2D(1P)2D				76836			1.333
B2D(3P)4P	1/2	97				79901			2.664
	3/2	95				79919			1.733
	5/2	96				79977			1.599
B2D(3P)4F	3/2	95				80762			0.401
	5/2	95				80885			1.028
	7/2	94				81057			1.237
	9/2	93				81278			1.332
B2D(3P)2P	1/2	65 + 17B2D(3P)4D + 9(A3P)4D*				84473			0.477
	3/2	79 + 12B2D(3P)4D				84186			1.298
B2D(3P)2F	5/2	75 + 13B2D(3P)4D				84381			0.945
	7/2	75 + 19B2D(3P)4D				84408			1.199
B2D(3P)4D	1/2	71 + 23B2D(3P)2P				84201			0.171
	3/2	73 + 10B2D(3P)2P				84393			1.183
	5/2	78 + 12B2D(3P)2F				84538			1.297
	7/2	45 + 18B2D(3P)2F				85100			1.387
B2D(3P)2D	3/2	96				86758			0.803
	5/2	96				86672			1.200
B2D(1P) 2P	1/2	56 + 32(3D)2P*				93582			0.669
	3/2	55 + 35(3D)2P*				93960			1.332
B2D(1P)2F	5/2	41 + 23(3G)2F* + 20(3D)2F*				96929			0.868
	7/2	42 + 22(3D)2F* + 20(3G)2F*				96971			1.142
B2D(1P)2D	3/2	49 + 41(3D)2D*				98049			0.805
	5/2	51 + 36(3D)2D*				98457			1.199