Abstract

The ionization energies of the neutral rare earths have been derived by means of interpolated values for the energy differences between the 4fN6s2, 4fN6s7s, and 4fN6s8s configurations and the difference in the effective quantum numbers of the 4fN6s7s and 4fN6s8s configurations. In Ce i the 4f5d2ns series was used. The results in eV are:

Ce i5.65
Pr i5.42
Nd i5.49
Pm i5.55
Sm i5.63
Eu i5.68
Dy i5.93
Ho i6.02
Er i6.10
Tm i6.18
Yb i6.25.
The uncertainty is estimated to be ±0.02 eV in all cases but Ce i for which the estimated uncertainty is ±0.06 eV. Values for La i and Gd i obtained spectroscopically by other workers are also tabulated. The present results are compared with those obtained by means of surface ionization. The calculated result for Tb i was inconclusive because of the lack of sufficient knowledge of the energy-level structure.

© 1966 Optical Society of America

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References

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  1. J. Sugar and J. Reader, J. Opt. Soc. Am. 55, 1286 (1965).
    [CrossRef]
  2. G. Risberg, Arkiv. Fysik 28, 381 (1965).
  3. I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
    [CrossRef]
  4. P. F. A. Klinkenberg, Z. Physik 180, 174 (1964).
    [CrossRef]
  5. H. N. Russell, J. Opt. Soc. Am. 40, 550 (1950).
    [CrossRef]
  6. W. C. Martin, J. Opt. Soc. Am. 53, 1047 (1963).
    [CrossRef]
  7. It should be noted that this terminology is a departure from that used in Ref. 1. In that paper these unperturbed centers of gravity were referred to as parent levels in some instances. The 4fN parent levels of the 4fN6s configurations of the singly ionized atoms are present only in the doubly ionized atom.
  8. B. R. Judd, Phys. Rev. 125, 613 (1962).
    [CrossRef]
  9. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), Vol. II, pp. 122 ff.
  10. H. N. Russell and C. E. Moore, J. Res. Natl. Bur. Std. 55, 299 (1955).
    [CrossRef]
  11. H. N. Russell and A. S. King, Astrophys. J. 90, 155 (1939).
    [CrossRef]
  12. W. F. Meggers and B. F. Scribner, J. Res. Natl. Bur. Std. 19, 651 (1937).
    [CrossRef]
  13. C. E. Moore, Natl. Bur. Std. (U. S.) Circ. 467, Vol.  III (1958).
  14. J. Blaise and R. Vetter, Compt. Rend. 256, 630 (1963).
  15. W. Albertson, Phys. Rev. 52, 644 (1937).
    [CrossRef]
  16. J. Reader and J. Sugar, Phys. Rev. 137, B784 (1965).
    [CrossRef]
  17. H. N. Russell and W. F. Meggers, J. Res. Natl. Bur. Std. 9, 625 (1932).
    [CrossRef]
  18. M. Wilson and W. R. S. Garton, private communication (1965).
  19. K. Murakawa, J. Phys. Soc. Japan 20, 1733 (1965).
    [CrossRef]
  20. C. E. Moore, Appl. Opt. 2, 665 (1963). The fact that the ionization energy of Yb i given in this reference is due to Russell was communicated to us by C. E. Moore.
    [CrossRef]
  21. G. Smith and B. G. Wybourne, J. Opt. Soc. Am. 55, 121 (1965).
    [CrossRef]
  22. W. F. Meggers, private communication (1965).
  23. Y. Bordarier, R. Vetter, and J. Blaise, J. Phys. Radium 24, 1107 (1963).

1965 (5)

J. Reader and J. Sugar, Phys. Rev. 137, B784 (1965).
[CrossRef]

K. Murakawa, J. Phys. Soc. Japan 20, 1733 (1965).
[CrossRef]

G. Risberg, Arkiv. Fysik 28, 381 (1965).

G. Smith and B. G. Wybourne, J. Opt. Soc. Am. 55, 121 (1965).
[CrossRef]

J. Sugar and J. Reader, J. Opt. Soc. Am. 55, 1286 (1965).
[CrossRef]

1964 (2)

I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
[CrossRef]

P. F. A. Klinkenberg, Z. Physik 180, 174 (1964).
[CrossRef]

1963 (4)

1962 (1)

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

1958 (1)

C. E. Moore, Natl. Bur. Std. (U. S.) Circ. 467, Vol.  III (1958).

1955 (1)

H. N. Russell and C. E. Moore, J. Res. Natl. Bur. Std. 55, 299 (1955).
[CrossRef]

1950 (1)

1939 (1)

H. N. Russell and A. S. King, Astrophys. J. 90, 155 (1939).
[CrossRef]

1937 (2)

W. F. Meggers and B. F. Scribner, J. Res. Natl. Bur. Std. 19, 651 (1937).
[CrossRef]

W. Albertson, Phys. Rev. 52, 644 (1937).
[CrossRef]

1932 (1)

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

Albertson, W.

W. Albertson, Phys. Rev. 52, 644 (1937).
[CrossRef]

Bender, I.

I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
[CrossRef]

Blaise, J.

Y. Bordarier, R. Vetter, and J. Blaise, J. Phys. Radium 24, 1107 (1963).

J. Blaise and R. Vetter, Compt. Rend. 256, 630 (1963).

Bordarier, Y.

Y. Bordarier, R. Vetter, and J. Blaise, J. Phys. Radium 24, 1107 (1963).

Garton, W. R. S.

M. Wilson and W. R. S. Garton, private communication (1965).

Judd, B. R.

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

King, A. S.

H. N. Russell and A. S. King, Astrophys. J. 90, 155 (1939).
[CrossRef]

Klinkenberg, P. F. A.

P. F. A. Klinkenberg, Z. Physik 180, 174 (1964).
[CrossRef]

Martin, W. C.

Meggers, W. F.

W. F. Meggers and B. F. Scribner, J. Res. Natl. Bur. Std. 19, 651 (1937).
[CrossRef]

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

W. F. Meggers, private communication (1965).

Moore, C. E.

C. E. Moore, Appl. Opt. 2, 665 (1963). The fact that the ionization energy of Yb i given in this reference is due to Russell was communicated to us by C. E. Moore.
[CrossRef]

C. E. Moore, Natl. Bur. Std. (U. S.) Circ. 467, Vol.  III (1958).

H. N. Russell and C. E. Moore, J. Res. Natl. Bur. Std. 55, 299 (1955).
[CrossRef]

Murakawa, K.

K. Murakawa, J. Phys. Soc. Japan 20, 1733 (1965).
[CrossRef]

Penselin, S.

I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
[CrossRef]

Reader, J.

J. Sugar and J. Reader, J. Opt. Soc. Am. 55, 1286 (1965).
[CrossRef]

J. Reader and J. Sugar, Phys. Rev. 137, B784 (1965).
[CrossRef]

Risberg, G.

G. Risberg, Arkiv. Fysik 28, 381 (1965).

Russell, H. N.

H. N. Russell and C. E. Moore, J. Res. Natl. Bur. Std. 55, 299 (1955).
[CrossRef]

H. N. Russell, J. Opt. Soc. Am. 40, 550 (1950).
[CrossRef]

H. N. Russell and A. S. King, Astrophys. J. 90, 155 (1939).
[CrossRef]

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

Schlüpman, K.

I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
[CrossRef]

Scribner, B. F.

W. F. Meggers and B. F. Scribner, J. Res. Natl. Bur. Std. 19, 651 (1937).
[CrossRef]

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), Vol. II, pp. 122 ff.

Smith, G.

Sugar, J.

J. Reader and J. Sugar, Phys. Rev. 137, B784 (1965).
[CrossRef]

J. Sugar and J. Reader, J. Opt. Soc. Am. 55, 1286 (1965).
[CrossRef]

Vetter, R.

Y. Bordarier, R. Vetter, and J. Blaise, J. Phys. Radium 24, 1107 (1963).

J. Blaise and R. Vetter, Compt. Rend. 256, 630 (1963).

Wilson, M.

M. Wilson and W. R. S. Garton, private communication (1965).

Wybourne, B. G.

Appl. Opt. (1)

Arkiv. Fysik (1)

G. Risberg, Arkiv. Fysik 28, 381 (1965).

Astrophys. J. (1)

H. N. Russell and A. S. King, Astrophys. J. 90, 155 (1939).
[CrossRef]

Compt. Rend. (1)

J. Blaise and R. Vetter, Compt. Rend. 256, 630 (1963).

J. Opt. Soc. Am. (4)

J. Phys. Radium (1)

Y. Bordarier, R. Vetter, and J. Blaise, J. Phys. Radium 24, 1107 (1963).

J. Phys. Soc. Japan (1)

K. Murakawa, J. Phys. Soc. Japan 20, 1733 (1965).
[CrossRef]

J. Res. Natl. Bur. Std. (3)

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

W. F. Meggers and B. F. Scribner, J. Res. Natl. Bur. Std. 19, 651 (1937).
[CrossRef]

H. N. Russell and C. E. Moore, J. Res. Natl. Bur. Std. 55, 299 (1955).
[CrossRef]

Natl. Bur. Std. (U. S.) Circ. 467 (1)

C. E. Moore, Natl. Bur. Std. (U. S.) Circ. 467, Vol.  III (1958).

Phys. Rev. (3)

W. Albertson, Phys. Rev. 52, 644 (1937).
[CrossRef]

J. Reader and J. Sugar, Phys. Rev. 137, B784 (1965).
[CrossRef]

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

Z. Physik (2)

I. Bender, S. Penselin, and K. Schlüpman, Z. Physik 179, 4 (1964).
[CrossRef]

P. F. A. Klinkenberg, Z. Physik 180, 174 (1964).
[CrossRef]

Other (4)

W. F. Meggers, private communication (1965).

M. Wilson and W. R. S. Garton, private communication (1965).

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), Vol. II, pp. 122 ff.

It should be noted that this terminology is a departure from that used in Ref. 1. In that paper these unperturbed centers of gravity were referred to as parent levels in some instances. The 4fN parent levels of the 4fN6s configurations of the singly ionized atoms are present only in the doubly ionized atom.

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Figures (3)

F. 1
F. 1

Schematic representation of the 4f136sns levels of Tm i. The relative separations of the centers of gravity of the configurations and the core levels are approximately to scale. The splittings in the states labeled by J′ and J are somewhat exaggerated. The states based on the 2F5/2 core level have not been indicated.

F. 2
F. 2

Energy difference ΔT between the centers of gravity of the 4fN6s7s and 4fN6s8s configurations of the neutral rare earths.

F. 3
F. 3

Energy difference ΔT between the centers of gravity of the 4fN6s2 and 4fN6s7s configurations of the neutral rare earths.

Tables (3)

Tables Icon

Table I Values of the electrostatic parameters used for determination of the positions of the unperturbed centers of gravity.

Tables Icon

Table II Ionization energies of the neutral rare earths obtained by series calculations, and quantities involved in their determination. Values for La i and Gd i derived by other authors are given for completeness. The quantities appropriate to the special case of Ce i are given in the text. The parentheses enclosing the result for Tb i are used to indicate the questionable nature of this result as discussed in the text.

Tables Icon

Table III Comparison of present results with those obtained by surface ionization.

Equations (7)

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UCG [ 6 s 7 s ] = E [ 6 s 7 s ³ S 1 ] + 1 2 G 0 ( 6 s 7 s ) = 26 575 cm 1 UCG [ 6 s 8 s ] = E [ 6 s 8 s ³ S 1 ] + 1 2 G 0 ( 6 s 8 s ) = 34 000 cm 1 .
UCG [ 4 f 7 ( S 7 / 2 ) 6 s 7 s ] = E [ 4 f 7 ( S ) 6 s 7 s 10 S 9 / 2 ] + 1 2 G 0 ( 6 s 7 s ) + 7 2 G 3 ( 4 f 6 s ) + 7 2 G 3 ( 4 f 7 s ) = 30 002 cm 1 UCG [ 4 f 7 ( S 7 / 2 ) 6 s 8 s ] = E [ 4 f 7 ( S ) 6 s 8 s 10 S 9 / 2 ] + 1 2 G 0 ( 6 s 8 s ) + 7 2 G 3 ( 4 f 6 s ) + 7 2 G 3 ( 4 f 8 s ) = 38 061 cm 1 .
UCG [ 6 s 7 s ] = E [ 6 s 7 s ³ S 1 ] + 1 2 G 0 ( 6 s 7 s ) = 33 110 cm 1 UCG [ 6 s 8 s ] = E [ 6 s 8 s ³ S 1 ] + 1 2 G 0 ( 6 s 8 s ) = 41 710 cm 1 .
Δ T = R / [ n a ( 4 f N 6 s 7 s ) ] 2 R / [ n a ( 4 f N 6 s 7 s ) + Δ n a ] 2
T = R / n a 2 .
UCG [ 4 f 13 ( ² F 7 / 2 ) 6 s 7 s ] = E [ 4 f 13 ( ² F 7 / 2 ) 6 s 7 s 4 F 9 / 2 ] + 1 2 G 0 ( 6 s 7 s ) + 1 2 G 3 ( 4 f 6 s ) + 1 2 G 3 ( 4 f 7 s ) = 32 750 cm 1 .
UCG [ 4 f 6 ( F 6 ) 6 s 7 s ] = E [ 4 f 6 ( F 6 ) 6 s 7 s F 7 ] + 1 2 G 0 ( 6 s 7 s ) + 3 G 3 ( 4 f 6 s ) + 3 G 3 ( 4 f 7 s ) = 33 688 cm 1 .