Abstract

A theoretical calculation of the even configurations 5d 6s2, 5d2 6s, 5d3 of La i is presented, which fits the known energy levels well, and predicts the unknown levels.

© 1967 Optical Society of America

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References

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  1. W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 239 (1932).
  2. H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 625 (1932).
  3. G. R. Harrison, N. Rosen, and J. R. McNally, J. Opt. Soc. Am. 35, 658 (1945).
    [Crossref]
  4. G. Racah (private communication).
  5. Let E be the energy of a certain combination in the range; then the probability of finding exactly N−1 combinations between E and E+ t is given by the Poisson formula: [xN−1/(N−1)!]e−x. If this probability is small enough and x/n≪1, we may neglect the probability of longer aggregations. This formula gives, therefore, the probability of finding an aggregation with length N or greater, which begins with the combination E; therefore the average number of the fortuitous aggregations is M[xN−1/(N−1)!]e−x. This assumes that the combinations are scattered at random, and that M≫N.
  6. A is the additive parameter defined in the next section.
  7. A. Sommerfeld and W. Heisenberg, Z. Physik 11, 131 (1922).
    [Crossref]
  8. E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1957).
  9. G. Racah, Phys. Rev. 62, 438 (1942).
    [Crossref]
  10. G. Racah, Bull Res. Council Israel 8, 1 (1959).
  11. S. Amiel, M.Sc. thesis submitted to the Hebrew University of Jerusalem, 1955.

1959 (1)

G. Racah, Bull Res. Council Israel 8, 1 (1959).

1945 (1)

1942 (1)

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

1932 (2)

W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 239 (1932).

H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 625 (1932).

1922 (1)

A. Sommerfeld and W. Heisenberg, Z. Physik 11, 131 (1922).
[Crossref]

Amiel, S.

S. Amiel, M.Sc. thesis submitted to the Hebrew University of Jerusalem, 1955.

Condon, E. U.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1957).

Harrison, G. R.

Heisenberg, W.

A. Sommerfeld and W. Heisenberg, Z. Physik 11, 131 (1922).
[Crossref]

McNally, J. R.

Meggers, W. F.

H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 625 (1932).

W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 239 (1932).

Racah, G.

G. Racah, Bull Res. Council Israel 8, 1 (1959).

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

G. Racah (private communication).

Rosen, N.

Russell, H. N.

H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 625 (1932).

Shortley, G. H.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1957).

Sommerfeld, A.

A. Sommerfeld and W. Heisenberg, Z. Physik 11, 131 (1922).
[Crossref]

Bull Res. Council Israel (1)

G. Racah, Bull Res. Council Israel 8, 1 (1959).

J. Opt. Soc. Am. (1)

J. Res. Natl. Bur. Std. (U.S.) (2)

W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 239 (1932).

H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. (U.S.) 9, 625 (1932).

Phys. Rev. (1)

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

Z. Physik (1)

A. Sommerfeld and W. Heisenberg, Z. Physik 11, 131 (1922).
[Crossref]

Other (5)

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1957).

G. Racah (private communication).

Let E be the energy of a certain combination in the range; then the probability of finding exactly N−1 combinations between E and E+ t is given by the Poisson formula: [xN−1/(N−1)!]e−x. If this probability is small enough and x/n≪1, we may neglect the probability of longer aggregations. This formula gives, therefore, the probability of finding an aggregation with length N or greater, which begins with the combination E; therefore the average number of the fortuitous aggregations is M[xN−1/(N−1)!]e−x. This assumes that the combinations are scattered at random, and that M≫N.

A is the additive parameter defined in the next section.

S. Amiel, M.Sc. thesis submitted to the Hebrew University of Jerusalem, 1955.

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Tables (3)

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Table I The new levels of 5d3 4F and their connections to the known odd levels.

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Table II Parameters of La i (5d6s2, 5d26s, 5d3).

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Table III Energy-levels of La i (5d6s2, 5d26s 5d3).

Equations (6)

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E 1 + L 1 = E 2 + L 2 = E 3 + L 3 = E 4 + L 4 = E .
K = M [ x N - 1 / ( N - 1 ) ! ] e - x ,
K = M ( L - 1 N - 1 ) ( x / L ) N - 1 e - x .
A ( 5 d 2 ) - A ( 5 d 6 s ) A ( 5 d 6 s ) - A ( 6 s 2 )
A ( 5 d 3 ) - A ( 5 d 2 6 s ) A ( 5 d 2 6 s ) - A ( 5 d 6 s 2 )
B = B , C = C , G d s = G d s , H = H .