TABLE I
Constants for series formulas in Na i. These constants apply to the formula for δ = n − n* given in the text. The resulting values of n* yield energy levels based on the values 109 734.69 cm−1 for RNa and 41 449.44 cm−1 for the limit.
| Series | δ0 | a | b | c | d |
|---|
| ns 2S1/2(1) | 1.4 | 1.347 964 4 | 0.060 142 6 | 0.006 956 | 0.006 493 |
| ns 2S1/2(2) | 1.4 | 1.347 971 4 | 0.059 973 5 | 0.008 050 | 0.004 683 |
|
| 0.9 | 0.854 627 0 | 0.110 550 2 | 0.036 692 | 0.088 09 |
|
| 0.9 | 0.855 418 2 | 0.111 013 5 | 0.029 628 | 0.106 13 |
| nd 2D | 0 | 0.014 901 3 | −0.042 472 | 0.006 401 | 0 |
| nf 2F° | 0 | 0.001 629 0 | −0.006 850 | 0 | 0 |
| ng 2G | 0 | 0.000 435 7 | −0.002 984 | 0 | 0 |
| nh 2H° | 0 | 0.000 157 4 | −0.001 63 | 0 | 0 |
| ni 2I | 0 | 0.000 065 6 | −0.000 92 | 0 | 0 |
TABLE II
Differences between calculated and observed levels in Na i, Ecalc − Eobs (cm−1). The calculated levels were obtained with the formula constants in Table I. The observed levels were taken from Ref. 1 except for 4f 2F° from Ref. 3. Levels for which the differences are given in parentheses were fitted or taken into account in deriving the formula constants.
| n | 2S1/2(1) | 2S1/2(2) |
|
| 2D | 2F° |
|---|
| 3 | (0.000) | (+0.001) | (−0.001) | (−0.001) | (0.000) | |
| 4 | (0.000) | (0.000) | (0.00) | (0.00) | (0.000) | (−0.018) |
| 5 | (0.000) | (+0.002) | (0.00) | (0.00) | (0.000) | (+0.022) |
| 6 | (0.000) | (−0.003) | (+0.01) | (+0.01) | −0.003 | 0.00 |
| 7 | −0.004 | −0.007 | (−0.01) | (−0.01) | +0.02 | +0.02 |
| 8 | −0.01 | −0.01 | −0.01 | −0.01 | +0.02 | +0.02 |
| 9 | −0.01 | −0.01 | | | +0.04 | +0.04 |
| 10 | −0.02 | −0.02 | | | +0.08 | −0.02 |
| 11 | +0.01 | 0.00 | | | +0.07 | |
| 12 | +0.01 | +0.01 | | | | |
TABLE III
Frequency separations of some high levels of Na i. The formula values are predicted by the constants in Table I, the ns 2S levels being obtained with the 2S1/2(1) formula. The separations refer to 2P°, 2D, and 2F° term baricenters except for the 2P° levels listed with J values. Most of the original experimental values (references in text) have been rounded off to give uncertainties of a few units in the last place (numbers in parentheses).
| Separation | Frequency (GHz) (formula) | Frequency (GHz) (experiment) |
|---|
| 23s 2S–24s 2S | 605.91 | 605.81(6) |
| 23s 2S–23p 2P° | 308.95 | 308.91(6) |
| 23p 2P°–24s 2S | 296.96 | 296.93(6) |
| 33s 2S–34p 2P° | 289.17 | 289.10(6) |
| 32p 2P°–34s 2S | 305.83 | 305.88(6) |
| 38s 2S–40p 2P° | 301.99 | 301.91(6) |
| 39s 2S–41p 2P° | 279.27 | 279.27(6) |
| 29d 2D–31p 2P° | 295.52 | 295.58(6) |
|
| 38.763 | 38.774(4) |
|
| 38.572 | 38.574(4) |
|
| 35.141 | 35.147(5) |
|
| 34.968 | 34.970(5) |
|
| 31.956 | 31.965(4) |
|
| 31.800 | 31.803(4) |
| 28d 2D–29d 2D | 284.843 | 284.825(30) |
| 28d 2D–29f 2F° | 288.41 | 288.25(6) |
| 28f 2F°–29d 2D | 280.87 | 280.93(6) |
TABLE IV
Quantum defects for some high levels in Na i. The δ(formula) values were obtained with the constants for the appropriate series in Table I. The experimental defect for 36s is from data in Ref. 15 and all other experimental defects are from Ref. 4. The experimental uncertainties given in parentheses are in units of the last decimal place of the quoted values.
| Term | δ(formula) | δ(experiment) |
|---|
| 36s 2S1/2(1) | 1.348 0146 | |
| 36s 2S1/2(2) | 1.348 0215 | 1.348 0213(6) |
| 13d 2D | 1.465 0 × 10−2 | 1.465 3(5) × 10−2 |
| 14d | 1.468 5 | 1.468 8(5) |
| 15d | 1.471 3 | 1.471 9(6) |
| 16d | 1.473 6 | 1.475 1(6) |
| 17d | 1.475 4 | 1.475 9(7) |
| 13f 2F° | 1.588 × 10−3 | 1.585 (4) × 10−3 |
| 14f | 1.594 | 1.592 (4) |
| 15f | 1.599 | 1.601 (5) |
| 16f | 1.602 | 1.611 (5) |
| 17f | 1.605 | 1.603 (5) |
| 13g 2G | 4.180 × 10−4 | 4.155 (30) × 10−4 |
| 14g | 4.205 | 4.219 (33) |
| 15g | 4.224 | 4.242 (35) |
| 13h 2H° | 1.478 × 10−4 | 1.466 (15) × 10−4 |
| 14h | 1.491 | 1.479 (15) |
| 15h | 1.502 | 1.489 (15) |
TABLE V
Constants for linear formulas for two Na i series.
| Series | δ0 | a | b |
|---|
| ns 2S1/2 | 1.495 27 | 1.348 071 6 | 0.056 230 0 |
|
| 1.143 44 | 0.854 939 5 | 0.095 371 |
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