Abstract

Eight low-lying levels of Er ii 4f12 6s have been observed to be grouped according to their energy in four close pairs. The centers of gravity of the pairs correspond to the energies of the four lowest levels of the core 4f12; the spacings between the two components of the pairs depend on the Coulomb interaction between the s electron and core and are determined by the single Slater integral G3(4f,6s). The levels of the core can be fitted very closely with integrals Fk(4f,4f) whose ratios one to another are the same as those for a hydrogenic 4f eigenfunction. The integral F2(4f,4f) is found to be 427 cm−1 and ζf the spin-orbit coupling constant, 2237 cm−1. The spacings are fitted moderately well by a value of 1580 cm−1 for G3; discrepancies are ascribed to configuration interaction. The g values of the levels are found to agree closely with those calculated on the basis of perfect Jj coupling.

© 1962 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. R. Harrison, W. E. Albertson, and N. F. Hosford, J. Opt. Soc. Am. 31, 439 (1941).
    [CrossRef]
  2. N. Rosen, G. R. Harrison, and J. R. McNally, Phys. Rev. 60, 722 (1941).
    [CrossRef]
  3. W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
    [CrossRef]
  4. W. E. Albertson, Astrophys. J. 84, 26 (1936).
    [CrossRef]
  5. W. F. Meggers, J. Opt. Soc. Am. 31, 157 (1941).
    [CrossRef]
  6. J. R. McNally and K. L. Vander Sluis, J. Opt. Soc. Am. 49, 200 (1959).
    [CrossRef]
  7. B. G. Wybourne and W. A. Runciman, J. Chem. Phys. 30, 1154 (1959).
  8. E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1935).
  9. F. H. Spedding, Phys. Rev. 58, 255 (1940).
    [CrossRef]
  10. B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
    [CrossRef]
  11. B. R. Judd, Phys. Rev. 125, 613 (1962).
    [CrossRef]
  12. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Publishing Company, New York, 1960), Vol. II.
  13. J. C. Van den Bosch, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1957), Vol. 28, p. 305.
  14. J. W. Lindner and S. P. Davis, J. Opt. Soc. Am. 48, 542 (1958).
    [CrossRef]

1962 (1)

B. R. Judd, Phys. Rev. 125, 613 (1962).
[CrossRef]

1961 (1)

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
[CrossRef]

1959 (2)

B. G. Wybourne and W. A. Runciman, J. Chem. Phys. 30, 1154 (1959).

J. R. McNally and K. L. Vander Sluis, J. Opt. Soc. Am. 49, 200 (1959).
[CrossRef]

1958 (1)

1942 (1)

W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
[CrossRef]

1941 (3)

1940 (1)

F. H. Spedding, Phys. Rev. 58, 255 (1940).
[CrossRef]

1936 (1)

W. E. Albertson, Astrophys. J. 84, 26 (1936).
[CrossRef]

Albertson, W. E.

W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
[CrossRef]

G. R. Harrison, W. E. Albertson, and N. F. Hosford, J. Opt. Soc. Am. 31, 439 (1941).
[CrossRef]

W. E. Albertson, Astrophys. J. 84, 26 (1936).
[CrossRef]

Condon, E. U.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1935).

Davis, S. P.

Harrison, G. R.

W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
[CrossRef]

G. R. Harrison, W. E. Albertson, and N. F. Hosford, J. Opt. Soc. Am. 31, 439 (1941).
[CrossRef]

N. Rosen, G. R. Harrison, and J. R. McNally, Phys. Rev. 60, 722 (1941).
[CrossRef]

Hosford, N. F.

Judd, B. R.

B. R. Judd, Phys. Rev. 125, 613 (1962).
[CrossRef]

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
[CrossRef]

Lindgren, I.

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
[CrossRef]

Lindner, J. W.

McNally, J. R.

J. R. McNally and K. L. Vander Sluis, J. Opt. Soc. Am. 49, 200 (1959).
[CrossRef]

W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
[CrossRef]

N. Rosen, G. R. Harrison, and J. R. McNally, Phys. Rev. 60, 722 (1941).
[CrossRef]

Meggers, W. F.

Rosen, N.

N. Rosen, G. R. Harrison, and J. R. McNally, Phys. Rev. 60, 722 (1941).
[CrossRef]

Runciman, W. A.

B. G. Wybourne and W. A. Runciman, J. Chem. Phys. 30, 1154 (1959).

Shortley, G. H.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1935).

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Publishing Company, New York, 1960), Vol. II.

Spedding, F. H.

F. H. Spedding, Phys. Rev. 58, 255 (1940).
[CrossRef]

Van den Bosch, J. C.

J. C. Van den Bosch, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1957), Vol. 28, p. 305.

Vander Sluis, K. L.

Wybourne, B. G.

B. G. Wybourne and W. A. Runciman, J. Chem. Phys. 30, 1154 (1959).

Astrophys. J. (1)

W. E. Albertson, Astrophys. J. 84, 26 (1936).
[CrossRef]

J. Chem. Phys. (1)

B. G. Wybourne and W. A. Runciman, J. Chem. Phys. 30, 1154 (1959).

J. Opt. Soc. Am. (4)

Phys. Rev. (5)

N. Rosen, G. R. Harrison, and J. R. McNally, Phys. Rev. 60, 722 (1941).
[CrossRef]

W. E. Albertson, G. R. Harrison, and J. R. McNally, Phys. Rev. 61, 167 (1942).
[CrossRef]

F. H. Spedding, Phys. Rev. 58, 255 (1940).
[CrossRef]

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
[CrossRef]

B. R. Judd, Phys. Rev. 125, 613 (1962).
[CrossRef]

Other (3)

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Publishing Company, New York, 1960), Vol. II.

J. C. Van den Bosch, Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1957), Vol. 28, p. 305.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, New York, 1935).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Schematic representation of the low levels of Er II 4f12 6s. On the far left are the core levels of 4f12. They are split into pairs by the Coulomb interaction between the 6s electron and the core; the numbers outside the pairs give the appropriate values of J2 the numbers inside, the separations of the components in cm−1 as determined from first-order perturbation theory. The perturbing effects of levels with the same J2 on one another have been calculated by second-order perturbation theory, and the elevations and depressions (in cm−1) corresponding to pairs of interacting levels are indicated. Displacements shown are very much exaggerated. The final separations are given on the extreme right, and correspond to column 2 of Table III.

Tables (4)

Tables Icon

Table I Observed levels in Er ii.

Tables Icon

Table II Levels of the core f12.

Tables Icon

Table III Spacings between pairs of levels.

Tables Icon

Table IV Landé g values.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ζ i = 1 12 s i · 1 i
0.5541 | 3 F 4 , s , 9 2 ) 0.3322 | 1 G 4 , s , 9 2 ) + 0.7633 | 3 H 4 , s , 9 2 ) .
| f 12 S 1 L 1 J 1 , s , J 2 ) .
( f 12 S 1 L 1 J 1 , s , J 2 | H | f 12 S 3 L 3 J 1 , s , J 2 ) = ± δ ( S 1 , S 3 ) δ ( L 1 , L 3 ) × G 3 [ L 1 ( L 1 + 1 ) S 1 ( S 1 + 1 ) J 1 ( J 1 + 1 ) ] / 7 ( 2 J 2 + 1 ) ,
( f 12 S 1 L 1 J 2 + 1 2 , s , J 2 | H | f 12 S 3 L 3 J 2 1 2 , s , J 2 ) = δ ( S 1 , S 3 ) δ ( L 1 , L 3 ) [ G 3 / 7 ( 2 J 2 + 1 ) ] × [ ( S 1 + L 1 + J 2 + 3 2 ) ( S 1 + L 1 + 1 2 J 2 ) × ( L 1 + J 2 + 1 2 S 1 ) ( S 1 + J 2 + 1 2 L 1 ) ] 1 2
g = g ( J 1 ) J 2 ( J 2 + 1 ) + J 1 ( J 1 + 1 ) j ( j + 1 ) 2 J 2 ( J 2 + 1 ) + g ( j ) J 2 ( J 2 + 1 ) + j ( j + 1 ) J 1 ( J 1 + 1 ) 2 J 2 ( J 2 + 1 ) ,
g = [ ( 2 J 2 + 3 ) g ( J 1 ) 2 ] / ( 2 J 2 + 2 )
g = [ ( 2 J 2 1 ) g ( J 1 ) + 2 ] / 2 J 2