Abstract

We present experimental and theoretical investigations of the He spectral series 2S1nQ1 (n=3÷9, Q=S,P,D,,n1) and 2P1nQ1 (n=3÷9, Q=S,P,D,,n1) in electric fields up to 1635kV/cm. Apart from the allowed transitions with |ΔL|=1, the transitions with |ΔL|=0,2,3,—without field strictly forbidden—were observed. Several He patterns become similar to hydrogen patterns, which means they are nearly symmetric and show in higher fields nearly linear Stark shifts. The applied fields are high enough that patterns belonging to neighboring principal quantum numbers (for n>6) begin to overlap, which leads to interesting level-anticrossing effects. The experimental results are compared with numerical calculations, taking into account mixing between states of different principal quantum numbers and between singlet and triplet states. The agreement between experimental and theoretical results is quite good.

© 2012 Optical Society of America

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  1. U. Yoshida, On the Regularity in the Stark Effect on the Spectral Lines of Hydrogen and Helium (Kyoto, 1920).
  2. J. S. Foster, “Stark patterns observed in helium,” Proc. R. Soc. A 114, 47–66 (1927).
    [CrossRef]
  3. J. S. Foster, “Application of quantum mechanics to the Stark effect in helium,” Proc. R. Soc. A 117, 137–163 (1927).
    [CrossRef]
  4. Y. Ishida, “Notes on helium spectrum in the presence of the electric field,” Sci. Papers I. P. C. R. 14, 49 (1930).
  5. S. Sueoka, “On the Stark effect of helium in strong electric field (I),” J. Phys. Soc. Jpn. 5, 244–248 (1950).
    [CrossRef]
  6. S. Sueoka and M. Sato, “On the Stark effect of helium in strong electric field (II),” J. Phys. Soc. Jpn. 6, 444–451 (1951).
    [CrossRef]
  7. E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
    [CrossRef]
  8. N. Ryde, Atoms and Molecules in Electric Fields (Almqvist and Wiksell International, 1976).
  9. R. Eßl, “Über den Starkeffekt des Heliums bei hohen Feldstärken,” Ph D. thesis (Technical University of Graz, 1974).
  10. P. Berglez, “Über den Starkeffekt des Heliums im sichtbaren Spektralbereich,” Diploma thesis (Technical University of Graz, 1976).
  11. R. Gebauer and R. Eßl, “Über den Stark-effekt der tripletthauptserie des heliums bei hohen Feldstärken,” Acta Phys. Austriaca 47, 199–227 (1977).
  12. L. Windholz, “Stark effect of Ar-lines,” Phys. Scr. 21, 67–74 (1980).
    [CrossRef]
  13. H. Jäger and L. Windholz, “Stark effect of Ne I-lines (I),” Phys. Scr. 29, 344–350 (1984).
    [CrossRef]
  14. H. Jäger, and L. Windholz, “Untersuchungen des Starkeffektes bei Hhohen Feldstärken,” Contrib. Plasma Phys. 31, 143–165 (1991).
    [CrossRef]
  15. L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
    [CrossRef]
  16. L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
    [CrossRef]
  17. L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).
  18. L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
    [CrossRef]
  19. D. R. Cok and S. R. Lundeen, “Magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 19, 1830–1840 (1979).
    [CrossRef]
  20. D. R. Cok and S. R. Lundeen, “Erratum: magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 24, 3283–3284 (1981).
    [CrossRef]
  21. W. C. Martin, “Improved He4 I 1snl ionization energy, energy levels, and Lamb shifts for 1sns and 1snp terms,” Phys. Rev. A 36, 3575–3589 (1987).
    [CrossRef]
  22. D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
    [CrossRef]
  23. D. Kaiser, “Laserspektroskopie der 1s3d-Anticrossings Des Helium-Spektrums I’m elektrischen Feld,” Ph D. thesis (Technischen Universitat Berlin, 1993).
  24. Y. Ralchenko, A. E. Kramida, and J. Reader and NIST ASD Team, NIST Atomic Spectra Database (ver. 4.1.0), http://physics.nist.gov/asd3 , National Institute of Standards and Technology (2011).
  25. E. S. Chang, “Fine structure of the Rydberg levels in helium derived from experiment and theory,” Phys. Rev. A 35, 2777–2790 (1987).
    [CrossRef]
  26. A. Kono and S. Hattori, “Accurate oscillator strengths for neutral helium,” Phys. Rev. A 29, 2981–2988 (1984).
    [CrossRef]
  27. H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, 1957).

2008 (1)

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

2006 (1)

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

2005 (1)

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

1996 (1)

L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
[CrossRef]

1993 (1)

D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
[CrossRef]

1991 (1)

H. Jäger, and L. Windholz, “Untersuchungen des Starkeffektes bei Hhohen Feldstärken,” Contrib. Plasma Phys. 31, 143–165 (1991).
[CrossRef]

1988 (1)

E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
[CrossRef]

1987 (2)

E. S. Chang, “Fine structure of the Rydberg levels in helium derived from experiment and theory,” Phys. Rev. A 35, 2777–2790 (1987).
[CrossRef]

W. C. Martin, “Improved He4 I 1snl ionization energy, energy levels, and Lamb shifts for 1sns and 1snp terms,” Phys. Rev. A 36, 3575–3589 (1987).
[CrossRef]

1984 (2)

A. Kono and S. Hattori, “Accurate oscillator strengths for neutral helium,” Phys. Rev. A 29, 2981–2988 (1984).
[CrossRef]

H. Jäger and L. Windholz, “Stark effect of Ne I-lines (I),” Phys. Scr. 29, 344–350 (1984).
[CrossRef]

1981 (1)

D. R. Cok and S. R. Lundeen, “Erratum: magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 24, 3283–3284 (1981).
[CrossRef]

1980 (1)

L. Windholz, “Stark effect of Ar-lines,” Phys. Scr. 21, 67–74 (1980).
[CrossRef]

1979 (1)

D. R. Cok and S. R. Lundeen, “Magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 19, 1830–1840 (1979).
[CrossRef]

1977 (1)

R. Gebauer and R. Eßl, “Über den Stark-effekt der tripletthauptserie des heliums bei hohen Feldstärken,” Acta Phys. Austriaca 47, 199–227 (1977).

1951 (1)

S. Sueoka and M. Sato, “On the Stark effect of helium in strong electric field (II),” J. Phys. Soc. Jpn. 6, 444–451 (1951).
[CrossRef]

1950 (1)

S. Sueoka, “On the Stark effect of helium in strong electric field (I),” J. Phys. Soc. Jpn. 5, 244–248 (1950).
[CrossRef]

1930 (1)

Y. Ishida, “Notes on helium spectrum in the presence of the electric field,” Sci. Papers I. P. C. R. 14, 49 (1930).

1927 (2)

J. S. Foster, “Stark patterns observed in helium,” Proc. R. Soc. A 114, 47–66 (1927).
[CrossRef]

J. S. Foster, “Application of quantum mechanics to the Stark effect in helium,” Proc. R. Soc. A 117, 137–163 (1927).
[CrossRef]

Berglez, P.

P. Berglez, “Über den Starkeffekt des Heliums im sichtbaren Spektralbereich,” Diploma thesis (Technical University of Graz, 1976).

Bethe, H.

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, 1957).

Chang, E. S.

E. S. Chang, “Fine structure of the Rydberg levels in helium derived from experiment and theory,” Phys. Rev. A 35, 2777–2790 (1987).
[CrossRef]

Cok, D. R.

D. R. Cok and S. R. Lundeen, “Erratum: magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 24, 3283–3284 (1981).
[CrossRef]

D. R. Cok and S. R. Lundeen, “Magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 19, 1830–1840 (1979).
[CrossRef]

Den Hartog, E. A.

E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
[CrossRef]

Doughty, D. A.

E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
[CrossRef]

Drozdowski, R.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

Eßl, R.

R. Gebauer and R. Eßl, “Über den Stark-effekt der tripletthauptserie des heliums bei hohen Feldstärken,” Acta Phys. Austriaca 47, 199–227 (1977).

R. Eßl, “Über den Starkeffekt des Heliums bei hohen Feldstärken,” Ph D. thesis (Technical University of Graz, 1974).

Foster, J. S.

J. S. Foster, “Stark patterns observed in helium,” Proc. R. Soc. A 114, 47–66 (1927).
[CrossRef]

J. S. Foster, “Application of quantum mechanics to the Stark effect in helium,” Proc. R. Soc. A 117, 137–163 (1927).
[CrossRef]

Gebauer, R.

R. Gebauer and R. Eßl, “Über den Stark-effekt der tripletthauptserie des heliums bei hohen Feldstärken,” Acta Phys. Austriaca 47, 199–227 (1977).

Hattori, S.

A. Kono and S. Hattori, “Accurate oscillator strengths for neutral helium,” Phys. Rev. A 29, 2981–2988 (1984).
[CrossRef]

Heldt, J.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

Ishida, Y.

Y. Ishida, “Notes on helium spectrum in the presence of the electric field,” Sci. Papers I. P. C. R. 14, 49 (1930).

Jäger, H.

H. Jäger, and L. Windholz, “Untersuchungen des Starkeffektes bei Hhohen Feldstärken,” Contrib. Plasma Phys. 31, 143–165 (1991).
[CrossRef]

H. Jäger and L. Windholz, “Stark effect of Ne I-lines (I),” Phys. Scr. 29, 344–350 (1984).
[CrossRef]

Kaiser, D.

D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
[CrossRef]

D. Kaiser, “Laserspektroskopie der 1s3d-Anticrossings Des Helium-Spektrums I’m elektrischen Feld,” Ph D. thesis (Technischen Universitat Berlin, 1993).

Kono, A.

A. Kono and S. Hattori, “Accurate oscillator strengths for neutral helium,” Phys. Rev. A 29, 2981–2988 (1984).
[CrossRef]

Kwela, J.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

Lawler, J. E.

E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
[CrossRef]

Liu, Y. Q.

D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
[CrossRef]

Lundeen, S. R.

D. R. Cok and S. R. Lundeen, “Erratum: magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 24, 3283–3284 (1981).
[CrossRef]

D. R. Cok and S. R. Lundeen, “Magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 19, 1830–1840 (1979).
[CrossRef]

Martin, W. C.

W. C. Martin, “Improved He4 I 1snl ionization energy, energy levels, and Lamb shifts for 1sns and 1snp terms,” Phys. Rev. A 36, 3575–3589 (1987).
[CrossRef]

Neger, T.

L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
[CrossRef]

Ryde, N.

N. Ryde, Atoms and Molecules in Electric Fields (Almqvist and Wiksell International, 1976).

Salpeter, E.

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, 1957).

Sato, M.

S. Sueoka and M. Sato, “On the Stark effect of helium in strong electric field (II),” J. Phys. Soc. Jpn. 6, 444–451 (1951).
[CrossRef]

Schuh, B.

L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
[CrossRef]

Sueoka, S.

S. Sueoka and M. Sato, “On the Stark effect of helium in strong electric field (II),” J. Phys. Soc. Jpn. 6, 444–451 (1951).
[CrossRef]

S. Sueoka, “On the Stark effect of helium in strong electric field (I),” J. Phys. Soc. Jpn. 5, 244–248 (1950).
[CrossRef]

von Oppen, G.

D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
[CrossRef]

Wasowicz, T. J.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

Windholz, L.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
[CrossRef]

H. Jäger, and L. Windholz, “Untersuchungen des Starkeffektes bei Hhohen Feldstärken,” Contrib. Plasma Phys. 31, 143–165 (1991).
[CrossRef]

H. Jäger and L. Windholz, “Stark effect of Ne I-lines (I),” Phys. Scr. 29, 344–350 (1984).
[CrossRef]

L. Windholz, “Stark effect of Ar-lines,” Phys. Scr. 21, 67–74 (1980).
[CrossRef]

Winklhofer, E.

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

Yoshida, U.

U. Yoshida, On the Regularity in the Stark Effect on the Spectral Lines of Hydrogen and Helium (Kyoto, 1920).

Acta Phys. Austriaca (1)

R. Gebauer and R. Eßl, “Über den Stark-effekt der tripletthauptserie des heliums bei hohen Feldstärken,” Acta Phys. Austriaca 47, 199–227 (1977).

Contrib. Plasma Phys. (1)

H. Jäger, and L. Windholz, “Untersuchungen des Starkeffektes bei Hhohen Feldstärken,” Contrib. Plasma Phys. 31, 143–165 (1991).
[CrossRef]

J. Phys. B (1)

D. Kaiser, Y. Q. Liu, and G. von Oppen, “Electric-field singlet-triplet anticrossings of He I,” J. Phys. B 26, 363–380 (1993).
[CrossRef]

J. Phys. Soc. Jpn. (2)

S. Sueoka, “On the Stark effect of helium in strong electric field (I),” J. Phys. Soc. Jpn. 5, 244–248 (1950).
[CrossRef]

S. Sueoka and M. Sato, “On the Stark effect of helium in strong electric field (II),” J. Phys. Soc. Jpn. 6, 444–451 (1951).
[CrossRef]

Opt. Appl. (1)

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Stark effect in He I in extremely high electric field,” Opt. Appl. 36, 569–574 (2006).

Phys. Rev. A (6)

D. R. Cok and S. R. Lundeen, “Magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 19, 1830–1840 (1979).
[CrossRef]

D. R. Cok and S. R. Lundeen, “Erratum: magnetic and electric fine structure in helium Rydberg states,” Phys. Rev. A 24, 3283–3284 (1981).
[CrossRef]

W. C. Martin, “Improved He4 I 1snl ionization energy, energy levels, and Lamb shifts for 1sns and 1snp terms,” Phys. Rev. A 36, 3575–3589 (1987).
[CrossRef]

E. A. Den Hartog, D. A. Doughty, and J. E. Lawler, “Laser optogalvanic and fluorescence studies of the cathode region of a glow discharge,” Phys. Rev. A 38, 2471–2491 (1988).
[CrossRef]

E. S. Chang, “Fine structure of the Rydberg levels in helium derived from experiment and theory,” Phys. Rev. A 35, 2777–2790 (1987).
[CrossRef]

A. Kono and S. Hattori, “Accurate oscillator strengths for neutral helium,” Phys. Rev. A 29, 2981–2988 (1984).
[CrossRef]

Phys. Scr. (4)

L. Windholz, “Stark effect of Ar-lines,” Phys. Scr. 21, 67–74 (1980).
[CrossRef]

H. Jäger and L. Windholz, “Stark effect of Ne I-lines (I),” Phys. Scr. 29, 344–350 (1984).
[CrossRef]

L. Windholz, E. Winklhofer, R. Drozdowski, J. Kwela, T. J. Wasowicz, and J. Heldt, “Stark effect of atomic Helium second triplet series in electric fields up to 1600  kV/cm,” Phys. Scr. 78, 065303 (2008).
[CrossRef]

L. Windholz, B. Schuh, and T. Neger, “Experimental investigation of the Stark effect of the level groups 7p, 6p’ and 6d of neutral xenon,” Phys. Scr. 54, 85–90 (1996).
[CrossRef]

Proc. R. Soc. A (2)

J. S. Foster, “Stark patterns observed in helium,” Proc. R. Soc. A 114, 47–66 (1927).
[CrossRef]

J. S. Foster, “Application of quantum mechanics to the Stark effect in helium,” Proc. R. Soc. A 117, 137–163 (1927).
[CrossRef]

Proc. SPIE (1)

L. Windholz, R. Drozdowski, T. J. Wasowicz, and J. Kwela, “Anticrossing effects in Stark spectra of helium,” Proc. SPIE 5849, 24–28 (2005).
[CrossRef]

Sci. Papers I. P. C. R. (1)

Y. Ishida, “Notes on helium spectrum in the presence of the electric field,” Sci. Papers I. P. C. R. 14, 49 (1930).

Other (7)

N. Ryde, Atoms and Molecules in Electric Fields (Almqvist and Wiksell International, 1976).

R. Eßl, “Über den Starkeffekt des Heliums bei hohen Feldstärken,” Ph D. thesis (Technical University of Graz, 1974).

P. Berglez, “Über den Starkeffekt des Heliums im sichtbaren Spektralbereich,” Diploma thesis (Technical University of Graz, 1976).

D. Kaiser, “Laserspektroskopie der 1s3d-Anticrossings Des Helium-Spektrums I’m elektrischen Feld,” Ph D. thesis (Technischen Universitat Berlin, 1993).

Y. Ralchenko, A. E. Kramida, and J. Reader and NIST ASD Team, NIST Atomic Spectra Database (ver. 4.1.0), http://physics.nist.gov/asd3 , National Institute of Standards and Technology (2011).

H. Bethe and E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, 1957).

U. Yoshida, On the Regularity in the Stark Effect on the Spectral Lines of Hydrogen and Helium (Kyoto, 1920).

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Figures (28)

Fig. 1.
Fig. 1.

The canal ray discharge running between the shaped field electrodes acts as a light source and is imaged stigmatically to the entrance slit of a spectrograph. Depending on the needed field strength range, the central spacing varied between 1 mm and 0.07 mm. The right part shows the field strength along the path of the canal ray.

Fig. 2.
Fig. 2.

The observed shift (black dots) of the line 1 s 2 p P 1 1 s 6 d D 1 compared with calculated positions of lines 2 P 1 6 Q 1 ( Q = S , P , D , ) obtained for (a) experimental and (b) theoretical ionization energy of the level 6 P 1 . The calculations have been performed using the basis set of levels with n = 1 ÷ 8 .

Fig. 3.
Fig. 3.

The measured shift (black dots) of the line 1 s 2 p P 1 1 s 6 d D 1 on the background of theoretical curves obtained with different basis sets: (a)  n = 1 ÷ 8 , (b)  n = 1 ÷ 11 , (c)  n = 1 ÷ 12 , (d)  n = 1 ÷ 16 .

Fig. 4.
Fig. 4.

Observed lines 2 S 1 3 Q 1 , Q = S , P , D . The wavelength is increasing from right to left; thus the wavenumber increases from left to right as in the graphs with measured and calculated shifts. The continuous spectral intensity in regions of high field strength comes from sparks between the field electrodes. White horizontal stripes mark lines with the same field strength value. The wavelengths of forbidden transitions (without field) are given in parentheses.

Fig. 5.
Fig. 5.

Observed lines 2 P 1 3 Q 1 , Q = S , P , D . The line 7281.35 Å is not shown in this spectrum. The splitting of the hydrogen line H α was used to determine the field strength. The sensitivity of the photo plate decreases fast for wavelengths larger than 6800 Å.

Fig. 6.
Fig. 6.

Shifts and splittings of the lines 2 S 1 3 Q 1 , Q = S , P , D .

Fig. 7.
Fig. 7.

Shifts and splittings of the lines 2 P 1 3 Q 1 , Q = S , P , D .

Fig. 8.
Fig. 8.

Observed lines 2 S 1 4 Q 1 , Q = S , P , D , F . In order to have better confidence of the observed shifts, they are reproduced with two values of the highest field strength, 1325 kV / cm (left side) and 724 kV / cm (right side).

Fig. 9.
Fig. 9.

Observed lines 2 P 1 4 Q 1 , Q = S , P , D , F .

Fig. 10.
Fig. 10.

Shifts and splittings of the lines 2 S 1 4 Q 1 , Q = S , P , D , F .

Fig. 11.
Fig. 11.

Shifts and splittings of the lines 2 P 1 4 Q 1 , Q = S , P , D , F .

Fig. 12.
Fig. 12.

Observed lines 2 S 1 5 Q 1 , Q = S , P , D , F , G .

Fig. 13.
Fig. 13.

Observed lines 2 P 1 5 Q 1 , Q = S , P , D , F , G .

Fig. 14.
Fig. 14.

Shifts and splittings of the lines 2 S 1 5 Q 1 , Q = S , P , D , F , G .

Fig. 15.
Fig. 15.

Shifts and splittings of the lines 2 P 1 5 Q 1 , Q = S , P , D , F , G .

Fig. 16.
Fig. 16.

Observed lines 2 S 1 6 Q 1 , Q = S , P , , H .

Fig. 17.
Fig. 17.

Observed lines 2 P 1 6 Q 1 , Q = S , P , , H .

Fig. 18.
Fig. 18.

Shifts and splittings of the lines 2 S 1 6 Q 1 , Q = S , P , , H .

Fig. 19.
Fig. 19.

Shifts and splittings of the lines 2 P 1 6 Q 1 , Q = S , P , , H .

Fig. 20.
Fig. 20.

Observed lines 2 S 1 7 Q 1 , Q = S , P , , I .

Fig. 21.
Fig. 21.

Observed lines 2 P 1 7 Q 1 , Q = S , P , , I .

Fig. 22.
Fig. 22.

Shifts and splittings of the lines 2 S 1 7 Q 1 , Q = S , P , , I .

Fig. 23.
Fig. 23.

Shifts and splittings of the 2 P 1 7 Q 1 , Q = S , P , , I lines. In the central region, spectral components are overlapped by intensive other lines and the shift could not be measured (see Fig. 21).

Fig. 24.
Fig. 24.

Observed lines 2 S 1 8 Q 1 , Q = S , P , , K .

Fig. 25.
Fig. 25.

Observed lines 2 P 1 8 Q 1 , Q = S , P , , K .

Fig. 26.
Fig. 26.

Shifts and splittings of the lines 2 S 1 8 Q 1 , Q = S , P , , K .

Fig. 27.
Fig. 27.

Shifts and splittings of the lines 2 P 1 8 Q 1 , Q = S , P , , K . In the region above 25450 cm 1 , spectral components are overlapped by intensive other lines and the shift could not be measured (see Fig. 25).

Fig. 28.
Fig. 28.

Shifts and splittings of the lines n = 9 , 2 S 1 9 S 1 .

Tables (15)

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Table 1. Terms of He for n = 9 , 10 (in cm 1 ), according to [24]

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Table 2. Values for Terms of He I for n = 11 16 (in cm 1 ) Used in Our Calculations, according to [21,24]

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Table 3. Results for 2 S 1 3 Q 1 ( Q = S , P , D )a

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Table 4. Results for 2 P 1 3 Q 1 ( Q = S , P , D )

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Table 5. Results for 2 S 1 4 Q 1 ( Q = S , P , D , F )

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Table 6. Results for 2 P 1 4 Q 1 ( Q = S , P , D , F )

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Table 7. Results for 2 S 1 5 Q 1 ( Q = S , P , D , F , G )

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Table 8. Results for 2 P 1 5 Q 1 ( Q = S , P , D , F , G )

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Table 9. Results for 2 S 1 6 Q 1 ( Q = S , P , , H )

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Table 10. Results for 2 P 1 6 Q 1 ( Q = S , P , , H )

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Table 11. Results for 2 S 1 7 Q 1 ( Q = S , P , , I )

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Table 12. Results for 2 P 1 7 Q 1 ( Q = S , P , , I )

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Table 13. Results for 2 S 1 8 Q 1 ( Q = S , P , , K )

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Table 14. Results for 2 P 1 8 Q 1 ( Q = S , P , , K )

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Table 15. Results for 2 S 1 9 Q 1 ( Q = S , P ; other lines could not be investigated)

Equations (17)

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H = H 0 + H mp + H spin + H rel ,
n ( L 0 ) L M | H | n ( L 0 ) L M = E n L 0 ,
n ( L 1 ) L 1 M | H | n ( L 1 ) L 1 M = E n L 1 ( L + 1 ) h s o + 2 L + 2 2 L 1 h s s ,
n ( L 1 ) L M | H | n ( L 1 ) L M = E n L 1 h s o 2 h s s ,
n ( L 1 ) L + 1 M | H | n ( L 1 ) L + 1 M = E n L 1 + L h s o + 2 L 2 L + 3 h s s ,
n ( L 1 ) L M | H | n ( L 0 ) L M = n ( L 0 ) L M | H | n ( L 1 ) L M = L ( L + 1 ) h off .
h off = 3 h s o ,
h s o = h off / 3 = h S S = h .
H = H + H e l ,
H e l = d⃗ · E⃗ = e z E z .
n L S J M | e z E z | n L S J M = e E z S S M M × M L , M S C M L M S M L S J C M L M S M L S J C M L 0 M L L 1 L ( 2 L + 1 ) 1 2 n L r n L ,
| n L + 1 S r n L S | 2 = 3 ( 2 L + 1 ) 2 | E n L + 1 S I o n E n L S I o n | | f n L S n L + 1 S | ,
n L 1 r n L = L R n l n l 1 ,
n L + 1 r n L = L + 1 R n l n l + 1 ,
R n l n l ± 1 = 0 R n l R n l ± 1 r 3 d r .
R n l n l 1 = R n l 1 n l = 3 2 n n 2 l 2 ,
R n l n l 1 = ( 1 ) n l 4 ( 2 l 1 ) ! ( n + l ) ! ( n + l 1 ) ! ( n l 1 ) ! ( n l ) ! ( 4 n n ) l + 1 ( n n ) n + n 2 l 2 ( n + n ) n + n × { F ( n r , n r , 2 l , 4 n n ( n n ) 2 ) ( n n n + n ) 2 F ( n r 2 , n r , 2 l , 4 n n ( n n ) 2 ) } ,

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