Table I
Calculated energy levels, compositions, and g factors for 4f 3 configuration.
J Observed energy (cm−1 ) Calculated minus observed energy with 5, 6, and 7 parameters Percentage composition Predicted g factor Five Six Seven 1/2 18 694 316 −303 −240 2 P (95)0.637 23 465 66 127 −12 4 D (95)0.030 3/2 9 371 −7 −197 23 4 F (95)0.426 10 950 −229 −649 −118 4 S (95)1.961 17 096 469 −111 −87 a 2 D (46),2 P (44)1.069 20 857 390 −186 −110 2 P (49)a 2 D (45)1.075 23 092 125 141 −57 4 D (82)1.135 26 921 558 246 −71 b 2 D (81)0.868 5/2 10 138 −49 −221 28 4 F (98)1.032 14 187 −121 8 −147 4 G (99)0.574 19 046 298 99 −76 a 2 D (98)1.196 23 246 181 174 −34 4 D (81)1.334 27 597 967 542 258 b 2 D (72)1.203 (34 193) −1483 −2011 −1870 a 2 F (57),b 2 F (32)0.889 7/2 10 859 −41 −203 45 4 F (94)1.216 13 888 181 112 6 a 2 G (37),4 G (30),b 2 G (28)0.935 15 443 −36 3 −104 4 G (70)0.961 24 887 −89 6 −116 4 D (99)1.427 39 941 133 336 373 b 2 G (58),a 2 G (41)0.891 9/2 0 94 292 142 4 I (97)0.732 10 033 436 295 114 a 2 H (60)0.990 11 762 37 −111 51 4 F (78)1.247 15 705 −15 35 −59 4 G (62)1.143 16 764 74 13 −35 4 G (35),a 2 G (33),b 2 G (33)1.139 26 979 226 b 2 H (88)0.912 39 226 178 376 405 b 2 G (58),a 2 G (42)1.110 11/2 1 398 36 249 133 4 I (99)0.966 12 495 404 302 81 a 2 H (82)1.098 17 410 −195 −46 −125 4 G (94)1.263 24 358 −767 −457 −155 2 I (87)0.946 28 102 −257 −226 59 b 2 H (72)1.070 13/2 2 893 −12 213 129 4 I (100)1.107 16 089 −510 −2 −94 2 K (99)0.935 25 392 −888 −531 −202 2 I (99)1.076 15/2 4 454 −51 184 130 4 I (99)1.199 17 642 −586 −60 −121 2 K (96)1.064 25 245 −1085 −229 −144 2 L (97)0.945 17/2 26 448 −1161 −288 −180 2 L (100)1.059
Table II
Radial parameters for 4f 3 (cm−1 ).
Parameter Number of parameters Five Six Seven E 0 11 024. ±130 10 615. ±100 11 182. ±110 E 1 4 212.4 ± 60 4 160.4 ± 40 4 264.6 ± 30 E 2 02.82 ± 0.8 20.52 ± 0.5 20.57 ± 0.3 E 3 400.9 ± 5 412.5 ± 4 416.8 ± 3 ζf 642.6 ± 45 646.2 ± 30 659.6 ± 20 α 20.84 ± 3 28.67 ± 2 γ −63.84± 10 rms error ±484 ±292 ±168
Table III
Radial parameters for f 2 d (cm−1 ).
Parameter Number of parameters Eleven Twelve Thirteen E 0 25 407. ±60 25 107. ±55 25 371. ±160 E 1 5 102.2 ±51 4 938.1 ±41 4 982.0 ± 48 E 2 22.05± 0.4 22.60± 0.3 22.72± 0.3 E 3 467.4 ± 3 477.3 ± 2 479.4 ± 3 F 2 181.4 ± 3 181.2 ± 2 181.0 ± 2 F 4 16.91± 0.9 17.75± 0.7 17.73± 0.7 G 1 270.6 ± 4 277.5 ± 3 275.1 ± 3 G 3 25.48± 2 27.00± 1 27.50± 1 G 5 4.75± 0.4 4.55± 0.3 4.68± 0.3 ζf 765.8 ±21 771.6 ±15 775.4 ± 15 ζd 718.7 ±41 723.7 ±30 721.4 ± 30 α 20.74± 2.3 22.17± 2.4 γ −28.15± 16 rms error ±255 ±184 ±182
Table IV
Calculated energy levels, compositions, and g factors for 4f 2 5d configuration.
J Observed energy (cm)−1 Calculated minus observed energy with 11, 12, and 13 parameters Percentage composition Predicted g factor Eleven Twelve Thirteen 1/2 31 804 212 −143 −154 2 S (68)1.686 34 199 422 19 −4 b 2 P (69),2 S (25)1.002 36 683 33 115 97 b 4 P (61),c 2 P (31)1.896 38 550 −54 −43 −56 b 4 D (44),b 4 P (25),c 2 P (20)0.903 39 485 −171 −121 −119 b 4 D (48),c 2 P (41)0.506 3/2 20 160 −309 −129 −178 a 4 F (74)0.420 21 148 −130 −194 −93 a 4 P (73)1.557 22 278 260 162 233 a 4 D (50)1.049 23 051 −26 −72 −16 a 4 D (27),b 4 F (24),a 2 D (21)0.936 24 251 107 59 112 b 4 F (41),a 2 D (21)0.741 28 936 285 49 41 b 2 D (66)0.867 32 289 557 224 215 b 2 P (73)1.322 35 138 153 39 27 c 4 F (45),c 2 D (26)0.770 35 864 36 −9 −26 c 4 F (52)0.805 37 198 181 42 11 b 4 P (41),c 2 D (31)1.281 39 120 110 83 71 b 4 D (62)1.307 40 206 −80 −126 −141 c 2 P (36),b 4 D (22),1.293 48 401 6 42 63 d 2 D (90)0.805 5/2 15 046 197 243 236 a 4 G (54),b 4 G (29)0.622 18 212 663 634 628 a 2 F (32),b 2 F (21)0.890 20 848 −209 −138 −130 a 4 F (31),b 4 G (22)0.836 21 419 −194 −199 −159 b 4 G (38)0.866 21 611 87 33 101 a 4 P (57)1.332 23 533 −1 −23 22 a 4 D (55)1.224 24 309 −481 −543 −524 a 4 D (34),b 4 F (22)1.107 24 461 52 59 89 b 4 F (34),a 2 D (23)1.130 25 935 364 284 327 No state above 19% 1.073 27 452 143 −64 −65 b 2 D (57),a 2 D (25)1.184 29 268 187 −51 −72 c 2 F (57),b 2 F (21)0.884 34 520 330 17 22 d 2 F (54)0.926 36 652 61 −26 −30 c 4 F (80)0.017 37 012 230 80 44 b 4 P (44),c 2 D (37)1.352 38 695 148 63 26 b 4 P (47),c 2 D (24),b 4 D (22)1.417 40 099 250 154 143 b 4 D (68),c 2 D (21)1.337 44 903 −187 −67 −102 e 2 F (71)1.874 48 745 −203 −117 −103 d 2 D (88)1.185 7/2 16 136 −288 −55 −201 a 4 H (79)0.703 16 516 −46 60 43 a 4 G (59),b 4 G (29)0.967 18 990 −162 −298 −240 b 4 H (87)0.678 19 872 389 510 490 a 4 F (31),b 2 F (23),a 2 G (20)1.110 21 295 249 207 251 a 2 G (29),a 2 F (26)1.019 22 081 −212 −172 −154 b 4 G (32),a 4 G (24),a 4 F (21)1.078 22 528 19 71 74 a 2 G (23)1.051 23 652 301 188 168 b 2 G (23)1.106 24 471 21 −32 6 a 4 D (64)1.294 25 410 496 299 313 b 4 F (35),b 2 G (29)1.056 26 447 265 333 303 b 2 F (31),b 4 F (21)1.185 27 139 105 −54 −33 c 2 G (41)0.946 31 255 105 −41 −21 c 2 F (35),a 2 F (27)1.114 35 024 126 −98 −114 d 2 G (48)1.970 36 640 272 −16 −28 d 2 F (40),c 4 F (21)1.119 37 920 144 9 7 c 4 F (62),d 2 F (23)1.218 41 024 98 50 46 b 4 D (85)1.390 44 680 −190 −53 −76 e 2 F (78)1.138 46 674 −214 212 211 E 2 G (98)0.890 9/2 12 847 240 348 307 4 I (55),a 2 H (38)0.813 14 559 57 137 114 4 I (41),a 2 H (31)0.814 17 627 −279 −127 −162 a 4 H (77)0.994 18 063 −85 45 36 a 4 G (55),b 4 G (29)1.136 20 316 −157 −277 −217 b 4 H (87)0.972 21 535 87 −24 −18 b 2 H (28)1.070 22 748 −101 −17 −35 a 4 F (49)1.211 23 845 −7 −129 −91 b 4 G (46)1.098 24 788 −54 112 112 a 2 G (64)1.149 25 034 400 305 255 b 2 G (38),a 4 F (28)1.195 27 604 351 220 220 b 4 F (48),b 2 G (31)1.225 28 721 −80 −118 −70 c 2 G (54)1.062 29 835 76 −21 3 c 2 H (35),b 2 H (26)0.977 35 828 170 −50 −77 d 2 G (55),c 4 F (22)1.152 39 024 98 76 69 c 4 F (74)1.264 39 870 −249 44 69 d 2 H (84)0.933 45 806 −401 16 22 E 2 G (95)1.107 11/2 13 352 −205 −206 −231 4 K (83)0.080 14 860 219 338 306 4 I (66),a 2 H (24)1.004 15 526 −65 6 −15 4 I (30),a 2 H (25)1.009 18 242 −27 42 45 a 2 I (44)0.993 19 309 −308 −138 −176 a 4 I (83)1.123 19 701 14 132 144 a 4 G (47),b 4 G (30)1.229 21 756 −181 −280 −217 b 4 H (86)1.126 23 442 67 −47 −38 b 2 H (32),b 4 G (25),a 4 G (24)1.177 26 095 51 −87 −55 b 4 G (36),b 2 H (27)1.168 27 380 177 −78 −155 b 2 I (63)0.959 30 506 34 47 68 c 2 H (58)1.077 36 671 −445 −64 −36 c 2 I (92)0.935 39 733 −323 33 60 d 2 H (87)1.080 13/2 15 454 −283 −257 −280 4 K (96)0.969 17 113 −175 −17 −78 4 I (98)1.106 19 360 −180 −125 −119 a 2 I (47),a 4 H (23)1.119 21 239 −236 −70 −111 a 4 H (71)1.187 23 175 −226 −252 −199 b 4 H (73)1.176 23 648 −241 −57 −79 a 2 K (74)0.983 29 263 108 −75 −147 b 2 I (68),a 2 I (22)1.079 36 642 −336 42 56 c 2 I (70),b 2 K (25)1.036 38 702 −328 56 43 b 2 K (63),c 2 I (27)0.976 15/2 17 535 −310 −261 −280 4 K (100)1.090 18 921 −153 18 −35 4 I (98)1.197 25 979 −259 8 −12 a 2 K (87)1.069 38 786 −280 61 62 b 2 K (62),2 L (26)1.034 39 726 −429 −161 −117 2 L (73),b 2 K (25)0.975 17/2 19 650 −316 −252 −264 4 K (100)1.176 41 027 −429 −191 −125 2 L (100)1.059
Table V
Calculated energy levels not yet detected.
J 4f 3 Configuration Theoretical g factor Calculated energy (7 parameters) Percentage composition 5/2 58 227 b 2 F (64),a 2 F (36)0.857 7/2 33 470 a 2 F (70),b 2 F (29)1.144 57 430 b 2 F (70),a 2 F (29)1.142 4f 2 5d Configuration (13 parameters) 1/2 20 344 a 2 P (40),a 4 P (39)1.399 21 443 a 4 P (53),a 4 P (26)1.578 24 066 a 4 D (55),a 2 P (39)0.363 3/2 24 609 a 2 P (46)1.112 68 805 E 2 D (95)0.800 5/2 70 155 E 2 D (98)1.200
Table VI
Alternate designations for levels of f 2 d .
J Level Present work Sugara 1/2 31 804 2 S b 2 P 34 199 b 2 P 2 S 3/2 22 278 a 4 D a 4 D 23 051 a 2 D a 4 D 35 138 c 2 D c 4 F 35 864 c 4 F c 2 D 5/2 21 419 b 4 G a 4 P 21 611 a 4 P b 4 G 24 309 b 4 F a 2 D 24 461 a 2 D b 4 F 7/2 19 872 a 4 F a 2 F 21 295 a 2 F a 4 F 9/2 12 847 4 I a 2 H 14 559 a 2 H 4 I 11/2 14 860 4 I a 2 H 15 526 a 2 H 4 I
a Reference 1 .
Table VII
Matrix elements of configuration interaction between 4f 2 and 5d 2 . The squared values are obtained by use of R 1 = 9628.5, R 3 = 8662.5, and R 5 = 7135.1.
Term Matrix element Squared value 1 S
−
(
35
)
−
1
2
(
3
R
1
+
4
R
3
/
3
+
50
R
5
/
33
) 75.0336×106 3 P
−
(
70
)
−
1
2
(
4
R
1
+
2
R
3
/
3
−
50
R
5
/
33
) 16.0114×106 1 D
−
(
294
)
−
1
2
(
36
R
1
/
5
−
22
R
3
/
15
+
50
R
5
/
33
) 15.4657×106 3 F
−
(
735
)
−
1
2
(
9
R
1
−
8
R
3
/
3
−
25
R
5
/
33
) 4.6007×106 1 G
−
(
11
/
2205
)
+
1
2
(
3
R
1
+
4
R
3
/
3
+
25
R
5
/
363
) 8.3560×106
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