Abstract

Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. F. Stebbings and et al., “Studies of xenon atoms in high Rydberg states,” Phys. Rev. A12, 1453–1458 (1975); S. Liberman and J. Pinard, “Experimental studies of high-lying Rydberg states in atomic rubidium,” Phys. Rev. A20, 507–518 (1979).
  2. J. J. Wynne and J. A. Armstrong, “Systematic behavior in alkaline earth spectra: A multichannel quantum defect analysis,” IBM J. Res. Dev. 23, 490–503 (1979).
    [Crossref]
  3. G. I. Bekov and et al., “Multistep laser spectroscopy of high-lying triplet states of ytterbium atoms,” Opt. Spectros. USSR 48, 435–439 (1980).
  4. P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
    [Crossref]
  5. L. N. Ivanov and V. S. Letokhov, “Selective ionization of atoms by light and electric field,” Quantum Electron. USSR 2, 585–590 (1975); R. V. Ambartzumjan and et al., “Dye-laser-excitation of high-lying states of sodium atoms and autoionization by electric field,” JETP Lett. 21, 595–598 (1975).
  6. U. Fano, “Quantum defect theory of 1 uncoupling in H2 as an example of channel-interaction treatment,” Phys. Rev. A 2, 353–365 (1970).
    [Crossref]
  7. K. T. Lu, “Spectroscopy and collision theory. The Xe absorption spectrum,” Phys. Rev. A 4, 579–596 (1971).
    [Crossref]
  8. K. T. Lu, “Quantum-defect analysis of the effects of np2terms on the singlet terms of alkaline earths and of their isoelectronics sequences,” J. Opt. Soc. Am. 64, 706–711 (1974).
    [Crossref]
  9. E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).
  10. C. M. Lee, “Spectroscopy and collision theory III. Atomic eigenchannel calculation by a Hartree–Fock–Roothaan method,” Phys. Rev. A 10, 584–600 (1974).
    [Crossref]
  11. W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels. The Rare-Earth Elements (National Bureau of Standards, Washington, D.C., 1978).
  12. L. N. Ivanov and L. I. Podobedova, “Formally exact perturbation theory with a model potential as a zeroth approximation I. Transition energies in Fe ions including effects of inner-shell electrons,” J. Phys. B. 10, 1001–1013 (1977).
    [Crossref]

1981 (1)

E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).

1980 (2)

G. I. Bekov and et al., “Multistep laser spectroscopy of high-lying triplet states of ytterbium atoms,” Opt. Spectros. USSR 48, 435–439 (1980).

P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
[Crossref]

1979 (1)

J. J. Wynne and J. A. Armstrong, “Systematic behavior in alkaline earth spectra: A multichannel quantum defect analysis,” IBM J. Res. Dev. 23, 490–503 (1979).
[Crossref]

1977 (1)

L. N. Ivanov and L. I. Podobedova, “Formally exact perturbation theory with a model potential as a zeroth approximation I. Transition energies in Fe ions including effects of inner-shell electrons,” J. Phys. B. 10, 1001–1013 (1977).
[Crossref]

1975 (2)

R. F. Stebbings and et al., “Studies of xenon atoms in high Rydberg states,” Phys. Rev. A12, 1453–1458 (1975); S. Liberman and J. Pinard, “Experimental studies of high-lying Rydberg states in atomic rubidium,” Phys. Rev. A20, 507–518 (1979).

L. N. Ivanov and V. S. Letokhov, “Selective ionization of atoms by light and electric field,” Quantum Electron. USSR 2, 585–590 (1975); R. V. Ambartzumjan and et al., “Dye-laser-excitation of high-lying states of sodium atoms and autoionization by electric field,” JETP Lett. 21, 595–598 (1975).

1974 (2)

K. T. Lu, “Quantum-defect analysis of the effects of np2terms on the singlet terms of alkaline earths and of their isoelectronics sequences,” J. Opt. Soc. Am. 64, 706–711 (1974).
[Crossref]

C. M. Lee, “Spectroscopy and collision theory III. Atomic eigenchannel calculation by a Hartree–Fock–Roothaan method,” Phys. Rev. A 10, 584–600 (1974).
[Crossref]

1971 (1)

K. T. Lu, “Spectroscopy and collision theory. The Xe absorption spectrum,” Phys. Rev. A 4, 579–596 (1971).
[Crossref]

1970 (1)

U. Fano, “Quantum defect theory of 1 uncoupling in H2 as an example of channel-interaction treatment,” Phys. Rev. A 2, 353–365 (1970).
[Crossref]

Armstrong, J. A.

J. J. Wynne and J. A. Armstrong, “Systematic behavior in alkaline earth spectra: A multichannel quantum defect analysis,” IBM J. Res. Dev. 23, 490–503 (1979).
[Crossref]

Bekov, G. I.

G. I. Bekov and et al., “Multistep laser spectroscopy of high-lying triplet states of ytterbium atoms,” Opt. Spectros. USSR 48, 435–439 (1980).

Camus, P.

P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
[Crossref]

Debarre, A.

P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
[Crossref]

Fano, U.

U. Fano, “Quantum defect theory of 1 uncoupling in H2 as an example of channel-interaction treatment,” Phys. Rev. A 2, 353–365 (1970).
[Crossref]

Hagan, L.

W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels. The Rare-Earth Elements (National Bureau of Standards, Washington, D.C., 1978).

Ivanov, L. N.

E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).

L. N. Ivanov and L. I. Podobedova, “Formally exact perturbation theory with a model potential as a zeroth approximation I. Transition energies in Fe ions including effects of inner-shell electrons,” J. Phys. B. 10, 1001–1013 (1977).
[Crossref]

L. N. Ivanov and V. S. Letokhov, “Selective ionization of atoms by light and electric field,” Quantum Electron. USSR 2, 585–590 (1975); R. V. Ambartzumjan and et al., “Dye-laser-excitation of high-lying states of sodium atoms and autoionization by electric field,” JETP Lett. 21, 595–598 (1975).

Ivanova, E. P.

E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).

Lee, C. M.

C. M. Lee, “Spectroscopy and collision theory III. Atomic eigenchannel calculation by a Hartree–Fock–Roothaan method,” Phys. Rev. A 10, 584–600 (1974).
[Crossref]

Letokhov, V. S.

L. N. Ivanov and V. S. Letokhov, “Selective ionization of atoms by light and electric field,” Quantum Electron. USSR 2, 585–590 (1975); R. V. Ambartzumjan and et al., “Dye-laser-excitation of high-lying states of sodium atoms and autoionization by electric field,” JETP Lett. 21, 595–598 (1975).

Lu, K. T.

Martin, W. C.

W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels. The Rare-Earth Elements (National Bureau of Standards, Washington, D.C., 1978).

Morillon, C.

P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
[Crossref]

Podobedova, L. I.

L. N. Ivanov and L. I. Podobedova, “Formally exact perturbation theory with a model potential as a zeroth approximation I. Transition energies in Fe ions including effects of inner-shell electrons,” J. Phys. B. 10, 1001–1013 (1977).
[Crossref]

Stebbings, R. F.

R. F. Stebbings and et al., “Studies of xenon atoms in high Rydberg states,” Phys. Rev. A12, 1453–1458 (1975); S. Liberman and J. Pinard, “Experimental studies of high-lying Rydberg states in atomic rubidium,” Phys. Rev. A20, 507–518 (1979).

Vidolova-Angelova, E. P.

E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).

Wynne, J. J.

J. J. Wynne and J. A. Armstrong, “Systematic behavior in alkaline earth spectra: A multichannel quantum defect analysis,” IBM J. Res. Dev. 23, 490–503 (1979).
[Crossref]

Zalubas, R.

W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels. The Rare-Earth Elements (National Bureau of Standards, Washington, D.C., 1978).

IBM J. Res. Dev. (1)

J. J. Wynne and J. A. Armstrong, “Systematic behavior in alkaline earth spectra: A multichannel quantum defect analysis,” IBM J. Res. Dev. 23, 490–503 (1979).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. B (1)

P. Camus, A. Debarre, and C. Morillon, “Highly excited levels of neutral ytterbium I. Two-photon and two-step spectroscopy of even spectra,” J. Phys. B 13, 1073–1987 (1980).
[Crossref]

J. Phys. B. (1)

L. N. Ivanov and L. I. Podobedova, “Formally exact perturbation theory with a model potential as a zeroth approximation I. Transition energies in Fe ions including effects of inner-shell electrons,” J. Phys. B. 10, 1001–1013 (1977).
[Crossref]

Opt. Spectros. USSR (1)

G. I. Bekov and et al., “Multistep laser spectroscopy of high-lying triplet states of ytterbium atoms,” Opt. Spectros. USSR 48, 435–439 (1980).

Opt. Spectrosc. USSR (1)

E. P. Vidolova-Angelova, E. P. Ivanova, and L. N. Ivanov, “Energies and autoionization widths of low-lying resonances of ytterbium atoms,” Opt. Spectrosc. USSR 50, 243–250 (1981).

Phys. Rev. (1)

R. F. Stebbings and et al., “Studies of xenon atoms in high Rydberg states,” Phys. Rev. A12, 1453–1458 (1975); S. Liberman and J. Pinard, “Experimental studies of high-lying Rydberg states in atomic rubidium,” Phys. Rev. A20, 507–518 (1979).

Phys. Rev. A (3)

U. Fano, “Quantum defect theory of 1 uncoupling in H2 as an example of channel-interaction treatment,” Phys. Rev. A 2, 353–365 (1970).
[Crossref]

K. T. Lu, “Spectroscopy and collision theory. The Xe absorption spectrum,” Phys. Rev. A 4, 579–596 (1971).
[Crossref]

C. M. Lee, “Spectroscopy and collision theory III. Atomic eigenchannel calculation by a Hartree–Fock–Roothaan method,” Phys. Rev. A 10, 584–600 (1974).
[Crossref]

Quantum Electron. USSR (1)

L. N. Ivanov and V. S. Letokhov, “Selective ionization of atoms by light and electric field,” Quantum Electron. USSR 2, 585–590 (1975); R. V. Ambartzumjan and et al., “Dye-laser-excitation of high-lying states of sodium atoms and autoionization by electric field,” JETP Lett. 21, 595–598 (1975).

Other (1)

W. C. Martin, R. Zalubas, and L. Hagan, Atomic Energy Levels. The Rare-Earth Elements (National Bureau of Standards, Washington, D.C., 1978).

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 (5)

Fig. 1
Fig. 1

One-electron and two-electron diagrams allowed for in the calculations.

Fig. 2
Fig. 2

Ladder diagrams effectively allowed for in the calculations.

Fig. 3
Fig. 3

Changes in the quantum defect δ in the series under study (calculation).

Fig. 4
Fig. 4

Theoretical (solid lines) and experimental (dotted lines)3 dependencies of the quantum defect δ of the 6snp3,1P° series on level energy.

Fig. 5
Fig. 5

Arrangement of the levels of the singlet (S) and triplet (T) series of the Yb atom at large values of the principal quantum number n.

Tables (3)

Tables Icon

Table 1 Energies of 6sns 1,3S Rydberg States of Yb Counted from Ground-State 6s2 1S0 (in cm−1)

Tables Icon

Table 2 Energies of 6snp 1,3P° Rydberg States of Yb Counted from the Ground-State 6s2 1S0 (in cm−1)

Tables Icon

Table 3 Comparison of Theoretical (Ecalc) and Experimental (Eexp) Energies of Yb Rydberg States (in cm−1)

Equations (9)

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

V ( r / β ) = - 1 r Z { 1 - 2 [ e - 2 r ( 1 + r ) ] - 8 [ 1 - e - 0.8 r ( 1 + 0.6 r + 0.16 r 2 + 0.032 r 3 ) ] - ( N - 10 ) ( 1 - 1 1 + β r + β 2 r 2 + γ r 3 ) } ,
[ h ( r / β ) - i exp ( 7 s 1 / 2 ) ] φ 7 s 1 / 2 ( r / β ) = 0 ,
- i V e l ( r i ) + i > j 1 r i j
Δ n l j ~ ( 1 n 1 - 1 n ) 1 n 4             with n ,
Δ V e l = d r ( r / 6 s ) r - r ,
Δ v ( r 1 , r 2 ) ~ 1 r 1 2 r 2 2             with r 1 , r 2 .
Δ ( 6 s 1 / 2 n l j ) ~ 1 n 4             with n
6 s 1 / 2 n s 1 / 2 [ J = 0 ] with 6 p 1 / 2 2 [ J = 0 ] , 6 p 3 / 2 2 [ J = 0 ] , 6 s 1 / 2 n s 1 / 2 [ J = 1 ] with 6 p 1 / 2 6 p 3 / 2 [ J = 1 ] , 6 s 1 / 2 n p 1 / 2 [ J = 0 ] with 6 p 3 / 2 5 d 3 / 2 [ J = 0 ] , 6 s 1 / 2 n p 1 / 2 [ J = 1 ] with 6 p 3 / 2 5 d 3 / 2 [ J = 1 ] , 6 p 3 / 2 5 d 5 / 2 [ J = 1 ] , 6 s 1 / 2 n p 3 / 2 [ J = 1 ] with 6 p 1 / 2 5 d 3 / 2 [ 1 ] , 6 p 3 / 2 5 d 3 / 2 [ 1 ] , 6 p 3 / 2 5 d 5 / 2 [ 1 ] , 6 s 1 / 2 n p 3 / 2 [ J = 2 ] with 6 p 1 / 2 5 d 3 / 2 [ 2 ] , 6 p 1 / 2 5 d 5 / 2 [ 2 ] , 6 p 3 / 2 5 d 3 / 2 [ 2 ] , 6 p 3 / 2 5 d 5 / 2 [ 2 ] .
M = - 1 2 n 2 + A n 3 + B n 4 .