Abstract

The present status of our knowledge of the structure of the spectra of the doubly and triply ionized spectra of the rare earths is derived partly from experimental data of the emission spectra of the free ions which provide the energy level scheme in great detail but are difficult and laborious to analyze. For the lower levels knowledge of the structure comes from the crystal absorption and fluoresence spectra. In all cases approximate theoretical calculations of the energies are essential.

© 1963 Optical Society of America

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References

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  1. G. H. Dieke, H. M. Crosswhite, B. Dunn, J. Opt. Soc. Am. 51, 820 (1961).
    [CrossRef]
  2. G. H. Dieke, D. Dimock, H. M. Crosswhite, J. Opt. Soc. Am. 46, 456 (1956).
    [CrossRef]
  3. G. H. Dieke, L. Heroux, Phys. Rev. 103, 1227 (1956), and subsequent papers on crystal spectra.
    [CrossRef]
  4. See for instance E. H. Carlson, G. H. Dieke, J. Chem. Phys. 29, 229 (1958); J. Chem. Phys. 34, 1602 (1961); H. M. Crosswhite, G. H. Dieke, ibid.35, 1535 (1961); G. H. Dieke, S. Singh, ibid.35, 555 (1961).
    [CrossRef]
  5. G. H. Dieke, L. A. Hall, J. Chem. Phys. 27, 465 (1957).
    [CrossRef]
  6. G. H. Dieke, Proc. First International Conference on Paramagnetic Resonance, Jerusalem, Israel (1962).
  7. G. H. Dieke, R. Sarup, J. Chem. Phys. 36, 371 (1962).
    [CrossRef]
  8. E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1951).
  9. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill, New York, 1960), two vols.
  10. G. Racah, Phys. Rev. 61, 186 (1942); Phys. Rev. 62, 438 (1942); Phys. Rev. 36, 367 (1942); Phys. Rev. 76, 1352 (1949).
    [CrossRef]
  11. Ce3+: R. Lang, Can. J. Res. A13, 1 (1935); Can. J. Res. A14, 127 (1936).
    [CrossRef]
  12. Er3+: F. L. Varsanyi, G. H. Dieke, J. Chem. Phys. 36, 2951 (1962); G. H. Dieke, S. Singh, ibid.35, 555 (1961); E. H. Carlson, H. M. Crosswhite, ref. 13;B. G. Wybourne, ref. 13.
    [CrossRef]
  13. Nd3+: E. H. Carlson, G. H. Dieke, J. Chem. Phys. 34, 1602 (1961); E. H. Carlson, H. M. Crosswhite, Johns Hopkins University Spectroscopy Report 19 (1960); B. G. Wybourne, J. Chem. Phys. 32, 639 (1960); J. Chem. Phys. 34, 279 (1961).
    [CrossRef]
  14. Pm3+: J. G. Conway, J. B. Gruber, J. Chem. Phys. 32, 1586 (1960); M. H. Crozier, W. A. Runciman, ibid.35, 1392 (1961).
    [CrossRef]
  15. Sm3+: M. S. Magno, G. H. Dieke, J. Chem. Phys. 37, 2354 (1962); J. D. Axe, G. H. Dieke, ibid.37, 2364 (1962); B. G. Wybourne, ibid.36, 2295 (1962).
    [CrossRef]
  16. Eu3+: L. G. DeShazer, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ibid.
  17. Gd3+: A. H. Piksis, G. H. Dieke, J. Chem. Phys. (to be published); W. A. Runciman, J. Chem. Phys. 30, 1632 (1959).
    [CrossRef]
  18. Tb3+: K. S. Thomas, S. Singh, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ref. 16.
  19. Dy3+: H. M. Crosswhite, G. H. Dieke, ref. 4; J. D. Axe, G. H. Dieke, ref. 15; B. G. Wybourne, ref. 15.
  20. Ho3+: G. H. Dieke, B. C. Pandey (to be published); M. H. Crozier, W. A. Runciman, ref. 14.
  21. Pr3+: G. H. Dieke, R. Sarup, J. Chem. Phys. 29, 741 (1958); J. S. Margolis, ibid.35, 1367 (1961).
    [CrossRef]
  22. Tm3+: J. B. Gruber, J. G. Conway, J. Chem. Phys. 32, 1178 (1960); J. Chem. Phys. 32, 1531(1960).
    [CrossRef]
  23. Yb3+: G. H. Dieke, H. M. Crosswhite, J. Opt. Soc. Am. 46, 885 (1956).
    [CrossRef]
  24. B. W. Bryant (to be published).
  25. W. R. Callahan, J. Opt. Soc. Am. (to be published).
  26. G. S. Ofelt, J. Chem. Phys. 37, 511 (1962); B. R. Judd, Phys. Rev. 127, 750 (1962).
    [CrossRef]
  27. Z. J. Kiss, Phys. Rev. 127, 718 (1962).
    [CrossRef]
  28. J. Sugar (to be published).
  29. G. Racah, J. Opt. Soc. Am. 50, 408 (1960).
  30. H. N. Russell, W. F. Meggers, J. Res. Natl. Bur. Std. 9, 625 (1932).
  31. W. A. Hovis, J. Opt. Soc. Am. 52, 649 (1962).
    [CrossRef]
  32. A. J. Freeman, R. E. Watson, Phys. Rev. 127, 2058 (1962).
    [CrossRef]

1962 (7)

G. H. Dieke, R. Sarup, J. Chem. Phys. 36, 371 (1962).
[CrossRef]

Er3+: F. L. Varsanyi, G. H. Dieke, J. Chem. Phys. 36, 2951 (1962); G. H. Dieke, S. Singh, ibid.35, 555 (1961); E. H. Carlson, H. M. Crosswhite, ref. 13;B. G. Wybourne, ref. 13.
[CrossRef]

Sm3+: M. S. Magno, G. H. Dieke, J. Chem. Phys. 37, 2354 (1962); J. D. Axe, G. H. Dieke, ibid.37, 2364 (1962); B. G. Wybourne, ibid.36, 2295 (1962).
[CrossRef]

G. S. Ofelt, J. Chem. Phys. 37, 511 (1962); B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

Z. J. Kiss, Phys. Rev. 127, 718 (1962).
[CrossRef]

A. J. Freeman, R. E. Watson, Phys. Rev. 127, 2058 (1962).
[CrossRef]

W. A. Hovis, J. Opt. Soc. Am. 52, 649 (1962).
[CrossRef]

1961 (2)

G. H. Dieke, H. M. Crosswhite, B. Dunn, J. Opt. Soc. Am. 51, 820 (1961).
[CrossRef]

Nd3+: E. H. Carlson, G. H. Dieke, J. Chem. Phys. 34, 1602 (1961); E. H. Carlson, H. M. Crosswhite, Johns Hopkins University Spectroscopy Report 19 (1960); B. G. Wybourne, J. Chem. Phys. 32, 639 (1960); J. Chem. Phys. 34, 279 (1961).
[CrossRef]

1960 (3)

Pm3+: J. G. Conway, J. B. Gruber, J. Chem. Phys. 32, 1586 (1960); M. H. Crozier, W. A. Runciman, ibid.35, 1392 (1961).
[CrossRef]

Tm3+: J. B. Gruber, J. G. Conway, J. Chem. Phys. 32, 1178 (1960); J. Chem. Phys. 32, 1531(1960).
[CrossRef]

G. Racah, J. Opt. Soc. Am. 50, 408 (1960).

1958 (2)

Pr3+: G. H. Dieke, R. Sarup, J. Chem. Phys. 29, 741 (1958); J. S. Margolis, ibid.35, 1367 (1961).
[CrossRef]

See for instance E. H. Carlson, G. H. Dieke, J. Chem. Phys. 29, 229 (1958); J. Chem. Phys. 34, 1602 (1961); H. M. Crosswhite, G. H. Dieke, ibid.35, 1535 (1961); G. H. Dieke, S. Singh, ibid.35, 555 (1961).
[CrossRef]

1957 (1)

G. H. Dieke, L. A. Hall, J. Chem. Phys. 27, 465 (1957).
[CrossRef]

1956 (3)

1942 (1)

G. Racah, Phys. Rev. 61, 186 (1942); Phys. Rev. 62, 438 (1942); Phys. Rev. 36, 367 (1942); Phys. Rev. 76, 1352 (1949).
[CrossRef]

1935 (1)

Ce3+: R. Lang, Can. J. Res. A13, 1 (1935); Can. J. Res. A14, 127 (1936).
[CrossRef]

1932 (1)

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

Bryant, B. W.

B. W. Bryant (to be published).

Callahan, W. R.

W. R. Callahan, J. Opt. Soc. Am. (to be published).

Carlson, E. H.

Nd3+: E. H. Carlson, G. H. Dieke, J. Chem. Phys. 34, 1602 (1961); E. H. Carlson, H. M. Crosswhite, Johns Hopkins University Spectroscopy Report 19 (1960); B. G. Wybourne, J. Chem. Phys. 32, 639 (1960); J. Chem. Phys. 34, 279 (1961).
[CrossRef]

See for instance E. H. Carlson, G. H. Dieke, J. Chem. Phys. 29, 229 (1958); J. Chem. Phys. 34, 1602 (1961); H. M. Crosswhite, G. H. Dieke, ibid.35, 1535 (1961); G. H. Dieke, S. Singh, ibid.35, 555 (1961).
[CrossRef]

Condon, E. U.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1951).

Conway, J. G.

Pm3+: J. G. Conway, J. B. Gruber, J. Chem. Phys. 32, 1586 (1960); M. H. Crozier, W. A. Runciman, ibid.35, 1392 (1961).
[CrossRef]

Tm3+: J. B. Gruber, J. G. Conway, J. Chem. Phys. 32, 1178 (1960); J. Chem. Phys. 32, 1531(1960).
[CrossRef]

Crosswhite, H. M.

DeShazer, L. G.

Eu3+: L. G. DeShazer, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ibid.

Dieke, G. H.

Er3+: F. L. Varsanyi, G. H. Dieke, J. Chem. Phys. 36, 2951 (1962); G. H. Dieke, S. Singh, ibid.35, 555 (1961); E. H. Carlson, H. M. Crosswhite, ref. 13;B. G. Wybourne, ref. 13.
[CrossRef]

Sm3+: M. S. Magno, G. H. Dieke, J. Chem. Phys. 37, 2354 (1962); J. D. Axe, G. H. Dieke, ibid.37, 2364 (1962); B. G. Wybourne, ibid.36, 2295 (1962).
[CrossRef]

G. H. Dieke, R. Sarup, J. Chem. Phys. 36, 371 (1962).
[CrossRef]

Nd3+: E. H. Carlson, G. H. Dieke, J. Chem. Phys. 34, 1602 (1961); E. H. Carlson, H. M. Crosswhite, Johns Hopkins University Spectroscopy Report 19 (1960); B. G. Wybourne, J. Chem. Phys. 32, 639 (1960); J. Chem. Phys. 34, 279 (1961).
[CrossRef]

G. H. Dieke, H. M. Crosswhite, B. Dunn, J. Opt. Soc. Am. 51, 820 (1961).
[CrossRef]

See for instance E. H. Carlson, G. H. Dieke, J. Chem. Phys. 29, 229 (1958); J. Chem. Phys. 34, 1602 (1961); H. M. Crosswhite, G. H. Dieke, ibid.35, 1535 (1961); G. H. Dieke, S. Singh, ibid.35, 555 (1961).
[CrossRef]

Pr3+: G. H. Dieke, R. Sarup, J. Chem. Phys. 29, 741 (1958); J. S. Margolis, ibid.35, 1367 (1961).
[CrossRef]

G. H. Dieke, L. A. Hall, J. Chem. Phys. 27, 465 (1957).
[CrossRef]

G. H. Dieke, L. Heroux, Phys. Rev. 103, 1227 (1956), and subsequent papers on crystal spectra.
[CrossRef]

Yb3+: G. H. Dieke, H. M. Crosswhite, J. Opt. Soc. Am. 46, 885 (1956).
[CrossRef]

G. H. Dieke, D. Dimock, H. M. Crosswhite, J. Opt. Soc. Am. 46, 456 (1956).
[CrossRef]

G. H. Dieke, Proc. First International Conference on Paramagnetic Resonance, Jerusalem, Israel (1962).

Tb3+: K. S. Thomas, S. Singh, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ref. 16.

Dy3+: H. M. Crosswhite, G. H. Dieke, ref. 4; J. D. Axe, G. H. Dieke, ref. 15; B. G. Wybourne, ref. 15.

Ho3+: G. H. Dieke, B. C. Pandey (to be published); M. H. Crozier, W. A. Runciman, ref. 14.

Eu3+: L. G. DeShazer, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ibid.

Gd3+: A. H. Piksis, G. H. Dieke, J. Chem. Phys. (to be published); W. A. Runciman, J. Chem. Phys. 30, 1632 (1959).
[CrossRef]

Dimock, D.

Dunn, B.

Freeman, A. J.

A. J. Freeman, R. E. Watson, Phys. Rev. 127, 2058 (1962).
[CrossRef]

Gruber, J. B.

Tm3+: J. B. Gruber, J. G. Conway, J. Chem. Phys. 32, 1178 (1960); J. Chem. Phys. 32, 1531(1960).
[CrossRef]

Pm3+: J. G. Conway, J. B. Gruber, J. Chem. Phys. 32, 1586 (1960); M. H. Crozier, W. A. Runciman, ibid.35, 1392 (1961).
[CrossRef]

Hall, L. A.

G. H. Dieke, L. A. Hall, J. Chem. Phys. 27, 465 (1957).
[CrossRef]

Heroux, L.

G. H. Dieke, L. Heroux, Phys. Rev. 103, 1227 (1956), and subsequent papers on crystal spectra.
[CrossRef]

Hovis, W. A.

Kiss, Z. J.

Z. J. Kiss, Phys. Rev. 127, 718 (1962).
[CrossRef]

Lang, R.

Ce3+: R. Lang, Can. J. Res. A13, 1 (1935); Can. J. Res. A14, 127 (1936).
[CrossRef]

Magno, M. S.

Sm3+: M. S. Magno, G. H. Dieke, J. Chem. Phys. 37, 2354 (1962); J. D. Axe, G. H. Dieke, ibid.37, 2364 (1962); B. G. Wybourne, ibid.36, 2295 (1962).
[CrossRef]

Meggers, W. F.

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

Ofelt, G. S.

G. S. Ofelt, J. Chem. Phys. 37, 511 (1962); B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

Pandey, B. C.

Ho3+: G. H. Dieke, B. C. Pandey (to be published); M. H. Crozier, W. A. Runciman, ref. 14.

Piksis, A. H.

Gd3+: A. H. Piksis, G. H. Dieke, J. Chem. Phys. (to be published); W. A. Runciman, J. Chem. Phys. 30, 1632 (1959).
[CrossRef]

Racah, G.

G. Racah, J. Opt. Soc. Am. 50, 408 (1960).

G. Racah, Phys. Rev. 61, 186 (1942); Phys. Rev. 62, 438 (1942); Phys. Rev. 36, 367 (1942); Phys. Rev. 76, 1352 (1949).
[CrossRef]

Russell, H. N.

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

Sarup, R.

G. H. Dieke, R. Sarup, J. Chem. Phys. 36, 371 (1962).
[CrossRef]

Pr3+: G. H. Dieke, R. Sarup, J. Chem. Phys. 29, 741 (1958); J. S. Margolis, ibid.35, 1367 (1961).
[CrossRef]

Shortley, G. H.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1951).

Singh, S.

Tb3+: K. S. Thomas, S. Singh, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ref. 16.

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill, New York, 1960), two vols.

Sugar, J.

J. Sugar (to be published).

Thomas, K. S.

Tb3+: K. S. Thomas, S. Singh, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ref. 16.

Varsanyi, F. L.

Er3+: F. L. Varsanyi, G. H. Dieke, J. Chem. Phys. 36, 2951 (1962); G. H. Dieke, S. Singh, ibid.35, 555 (1961); E. H. Carlson, H. M. Crosswhite, ref. 13;B. G. Wybourne, ref. 13.
[CrossRef]

Watson, R. E.

A. J. Freeman, R. E. Watson, Phys. Rev. 127, 2058 (1962).
[CrossRef]

Can. J. Res. (1)

Ce3+: R. Lang, Can. J. Res. A13, 1 (1935); Can. J. Res. A14, 127 (1936).
[CrossRef]

J. Chem. Phys. (10)

Er3+: F. L. Varsanyi, G. H. Dieke, J. Chem. Phys. 36, 2951 (1962); G. H. Dieke, S. Singh, ibid.35, 555 (1961); E. H. Carlson, H. M. Crosswhite, ref. 13;B. G. Wybourne, ref. 13.
[CrossRef]

Nd3+: E. H. Carlson, G. H. Dieke, J. Chem. Phys. 34, 1602 (1961); E. H. Carlson, H. M. Crosswhite, Johns Hopkins University Spectroscopy Report 19 (1960); B. G. Wybourne, J. Chem. Phys. 32, 639 (1960); J. Chem. Phys. 34, 279 (1961).
[CrossRef]

Pm3+: J. G. Conway, J. B. Gruber, J. Chem. Phys. 32, 1586 (1960); M. H. Crozier, W. A. Runciman, ibid.35, 1392 (1961).
[CrossRef]

Sm3+: M. S. Magno, G. H. Dieke, J. Chem. Phys. 37, 2354 (1962); J. D. Axe, G. H. Dieke, ibid.37, 2364 (1962); B. G. Wybourne, ibid.36, 2295 (1962).
[CrossRef]

See for instance E. H. Carlson, G. H. Dieke, J. Chem. Phys. 29, 229 (1958); J. Chem. Phys. 34, 1602 (1961); H. M. Crosswhite, G. H. Dieke, ibid.35, 1535 (1961); G. H. Dieke, S. Singh, ibid.35, 555 (1961).
[CrossRef]

G. H. Dieke, L. A. Hall, J. Chem. Phys. 27, 465 (1957).
[CrossRef]

G. H. Dieke, R. Sarup, J. Chem. Phys. 36, 371 (1962).
[CrossRef]

Pr3+: G. H. Dieke, R. Sarup, J. Chem. Phys. 29, 741 (1958); J. S. Margolis, ibid.35, 1367 (1961).
[CrossRef]

Tm3+: J. B. Gruber, J. G. Conway, J. Chem. Phys. 32, 1178 (1960); J. Chem. Phys. 32, 1531(1960).
[CrossRef]

G. S. Ofelt, J. Chem. Phys. 37, 511 (1962); B. R. Judd, Phys. Rev. 127, 750 (1962).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Res. Natl. Bur. Std. (1)

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

Phys. Rev. (4)

A. J. Freeman, R. E. Watson, Phys. Rev. 127, 2058 (1962).
[CrossRef]

Z. J. Kiss, Phys. Rev. 127, 718 (1962).
[CrossRef]

G. H. Dieke, L. Heroux, Phys. Rev. 103, 1227 (1956), and subsequent papers on crystal spectra.
[CrossRef]

G. Racah, Phys. Rev. 61, 186 (1942); Phys. Rev. 62, 438 (1942); Phys. Rev. 36, 367 (1942); Phys. Rev. 76, 1352 (1949).
[CrossRef]

Other (11)

J. Sugar (to be published).

B. W. Bryant (to be published).

W. R. Callahan, J. Opt. Soc. Am. (to be published).

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, Cambridge, 1951).

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill, New York, 1960), two vols.

G. H. Dieke, Proc. First International Conference on Paramagnetic Resonance, Jerusalem, Israel (1962).

Eu3+: L. G. DeShazer, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ibid.

Gd3+: A. H. Piksis, G. H. Dieke, J. Chem. Phys. (to be published); W. A. Runciman, J. Chem. Phys. 30, 1632 (1959).
[CrossRef]

Tb3+: K. S. Thomas, S. Singh, G. H. Dieke, J. Chem. Phys. (to be published); G. S. Ofelt, ref. 16.

Dy3+: H. M. Crosswhite, G. H. Dieke, ref. 4; J. D. Axe, G. H. Dieke, ref. 15; B. G. Wybourne, ref. 15.

Ho3+: G. H. Dieke, B. C. Pandey (to be published); M. H. Crozier, W. A. Runciman, ref. 14.

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Figures (12)

Fig. 1
Fig. 1

Stages of ionization. Different excitation conditions in the gadolinium spectrum. Lines of Gd ii, iii, and iv are indicated by corresponding sets of dots. The 3-A spectrum is that of a dc are, the others are pulsed, critically damped discharges.

Fig. 2
Fig. 2

A—900-A peak current discharge (hot spark); B—50-A peak (mild spark). All spectrum regions were taken simultaneously. The short lines on the edges are from the Fe calibration tube.

Fig. 3
Fig. 3

Absorption and fluorescence spectra of 1 % Er3+ in Y2O3. Left: Absorption from Z group to A Group (4I15/24I11/2). Right: Fluorescence from P group to A group (2P3/24I11/2). See Fig. 7.

Fig. 4
Fig. 4

Block diagram of three-electron configurations Nd iv and Pr iii. Arrows indicate principal transitions. Parity is indicated by “odd” or “even.”

Fig. 5
Fig. 5

The same for Ce ii and La i.

Fig. 6
Fig. 6

Upper: Relative positions of the centers of the low configurations in third spectra (doubly ionized). The nl symbols refer to the optically active electron; e.g., 6s means 4fn−1 6s. Lower: Same for fourth spectra (triply ionized).

Fig. 7
Fig. 7

Observed and calculated levels of Er3+.

Fig. 8
Fig. 8

Observed energy levels of the trivalent rare-earth ions.

Fig. 9
Fig. 9

4f135d configuration of Yb2+.

Fig. 10
Fig. 10

Schematic diagram of the 4fn (white) and 4fn−15d (black) configurations of the divalent rare-earth ions.

Fig. 11
Fig. 11

The same for trivalent ions.

Fig. 12
Fig. 12

Hyperfine structure of holmium lines. A–D, Ho ii lines; E–G, Ho iii lines; H, Ho iv line in crystal spectra.

Tables (2)

Tables Icon

Table I Numerical Values of the Parameters F2 and ζ

Tables Icon

Table II The Four Lowest Configurations of the Trivalent Rare-Earth Ions

Equations (1)

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H 1 = ( e 2 / r i j ) and H 2 = Σ ζ i ( s i l i )

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