Abstract

Line shapes in high-resolution triple-resonance ionization spectroscopy have been calculated and compared with experimental measurements on the 4s 2 1 S 0→ 4s4p 1 P 1 → 4s4d 1 D 2 → 4snf 1 F 3→ Ca+ system of calcium. Calculations based on the density matrix formalism integrated the fundamental equations over experimental atomic angular and velocity distributions and laser intensity profiles. The measurements reveal and confirm all predicted structures arising from the complex coupling of four atomic states with three laser fields and the Doppler distribution of the atomic ensemble. Effects of different laser beam geometries on the line shapes have been investigated. The agreement between calculated and experimental spectra is generally good over a dynamic range of 10 orders of magnitude. Thus these calculations can accurately predict optical isotopic selectivity in multistep resonance ionization, with a value of S opt ∼ 1010 expected for detection of the ultratrace isotope 41Ca.

© 2000 Optical Society of America

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  1. D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
    [CrossRef]
  2. H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
    [CrossRef]
  3. M. G. Payne, L. Deng, N. Thonnard, “Applications of resonance ionization mass spectrometry,” Rev. Sci. Instrum. 65, 2433–2459 (1994).
    [CrossRef]
  4. K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
    [CrossRef]
  5. B. A. Bushaw, “High-resolution laser-induced ionization spectroscopy,” Prog. Analyt. Spectrosc. 12, 247–276 (1989).
  6. B. A. Bushaw, “Attogram measurement of rare isotopes by cw resonance ionization mass spectrometry,” in Proceedings of the Sixth International Symposium on Resonance Ionization Spectroscopy and its Applications 1992, C. M. Miller, J. E. Parks, eds. (Institute of Physics, London, 1992), Vol. 128, pp. 31–36.
  7. L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
    [CrossRef]
  8. B. A. Bushaw, B. D. Cannon, “Diode laser based resonance ionization mass spectrometric measurement of strontium-90,” Spectrochim. Acta Part B 52, 1839–1854 (1997).
    [CrossRef]
  9. P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.
  10. K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).
  11. B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.
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  14. S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
    [CrossRef]
  15. W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
    [CrossRef]
  16. G. M. Raisbeck, F. Yiou, “Possible use of 41Ca for radioactive dating,” Nature (London) 277, 42–44 (1979).
    [CrossRef]
  17. K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).
  18. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992).
  19. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
    [CrossRef]
  20. R. M. Whitley, C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
    [CrossRef]
  21. M. S. Feld, A. Javan, “Laser-induced line-narrowing effects in coupled Doppler-broadened transitions,” Phys. Rev. 177, 540–562 (1969).
    [CrossRef]
  22. T. Hänsch, P. Toschek, “Theory of a three-level gas laser amplifier,” Z. Phys. 236, 213–244 (1970).
    [CrossRef]
  23. R. Salomaa, S. Stenholm, “Two-photon spectroscopy: effects of a resonant intermediate state,” J. Phys. B 8, 1795–1805 (1975).
    [CrossRef]
  24. R. P. Lucht, R. Trebino, L. A. Rahn, “Resonant multiwave-mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
    [CrossRef] [PubMed]
  25. T. A. Reichardt, R. P. Lucht, “Theoretical calculation of lineshapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
    [CrossRef]
  26. P. Lambropoulos, A. Lyras, “Theory of resonant ionization by broad-band radiation in the determination of isotopic abundances,” Phys. Rev. A 40, 2199–2202 (1989).
    [CrossRef] [PubMed]
  27. O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
    [CrossRef]
  28. B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
    [CrossRef]
  29. P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
    [CrossRef]
  30. W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
    [CrossRef]
  31. B. A. Bushaw, B. D. Cannon, G. K. Gerke, T. J. Whitaker, “Laser-enhanced electron-impact ionization spectroscopy,” Opt. Lett. 11, 422–424 (1986).
    [CrossRef] [PubMed]
  32. S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
    [CrossRef]
  33. W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
    [CrossRef]
  34. J. Mitroy, “Energy levels and oscillator strengths for neutral calcium,” J. Phys. B 26, 3703–3718 (1993).
    [CrossRef]
  35. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).
  36. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990).

2000 (1)

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

1999 (2)

B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

1998 (4)

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
[CrossRef]

T. A. Reichardt, R. P. Lucht, “Theoretical calculation of lineshapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

1997 (3)

S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

B. A. Bushaw, B. D. Cannon, “Diode laser based resonance ionization mass spectrometric measurement of strontium-90,” Spectrochim. Acta Part B 52, 1839–1854 (1997).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

1996 (1)

O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
[CrossRef]

1994 (2)

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

M. G. Payne, L. Deng, N. Thonnard, “Applications of resonance ionization mass spectrometry,” Rev. Sci. Instrum. 65, 2433–2459 (1994).
[CrossRef]

1993 (3)

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
[CrossRef]

J. Mitroy, “Energy levels and oscillator strengths for neutral calcium,” J. Phys. B 26, 3703–3718 (1993).
[CrossRef]

1992 (2)

R. P. Lucht, R. Trebino, L. A. Rahn, “Resonant multiwave-mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

1991 (1)

M. Paul, I. Ahmad, W. Kutschera, “Half-life of 41Ca,” Z. Phys. A 340, 249–254 (1991).
[CrossRef]

1990 (1)

D. Fink, J. Klein, R. Middleton, “41Ca: past, present and future,” Nucl. Instrum. Methods Phys. Res. B 52, 572–582 (1990).
[CrossRef]

1989 (2)

B. A. Bushaw, “High-resolution laser-induced ionization spectroscopy,” Prog. Analyt. Spectrosc. 12, 247–276 (1989).

P. Lambropoulos, A. Lyras, “Theory of resonant ionization by broad-band radiation in the determination of isotopic abundances,” Phys. Rev. A 40, 2199–2202 (1989).
[CrossRef] [PubMed]

1986 (1)

1980 (1)

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

1979 (1)

G. M. Raisbeck, F. Yiou, “Possible use of 41Ca for radioactive dating,” Nature (London) 277, 42–44 (1979).
[CrossRef]

1976 (1)

R. M. Whitley, C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

1975 (1)

R. Salomaa, S. Stenholm, “Two-photon spectroscopy: effects of a resonant intermediate state,” J. Phys. B 8, 1795–1805 (1975).
[CrossRef]

1970 (1)

T. Hänsch, P. Toschek, “Theory of a three-level gas laser amplifier,” Z. Phys. 236, 213–244 (1970).
[CrossRef]

1969 (1)

M. S. Feld, A. Javan, “Laser-induced line-narrowing effects in coupled Doppler-broadened transitions,” Phys. Rev. 177, 540–562 (1969).
[CrossRef]

Ahmad, I.

M. Paul, I. Ahmad, W. Kutschera, “Half-life of 41Ca,” Z. Phys. A 340, 249–254 (1991).
[CrossRef]

Arakawa, E. T.

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

Beekman, D. W.

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

Bhowmick, G. K.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

Blaum, K.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

Blum, K.

K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
[CrossRef]

Bushaw, B. A.

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
[CrossRef]

B. A. Bushaw, B. D. Cannon, “Diode laser based resonance ionization mass spectrometric measurement of strontium-90,” Spectrochim. Acta Part B 52, 1839–1854 (1997).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

B. A. Bushaw, “High-resolution laser-induced ionization spectroscopy,” Prog. Analyt. Spectrosc. 12, 247–276 (1989).

B. A. Bushaw, B. D. Cannon, G. K. Gerke, T. J. Whitaker, “Laser-enhanced electron-impact ionization spectroscopy,” Opt. Lett. 11, 422–424 (1986).
[CrossRef] [PubMed]

B. A. Bushaw, “Attogram measurement of rare isotopes by cw resonance ionization mass spectrometry,” in Proceedings of the Sixth International Symposium on Resonance Ionization Spectroscopy and its Applications 1992, C. M. Miller, J. E. Parks, eds. (Institute of Physics, London, 1992), Vol. 128, pp. 31–36.

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

Callcott, T. A.

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

Cannon, B. D.

B. A. Bushaw, B. D. Cannon, “Diode laser based resonance ionization mass spectrometric measurement of strontium-90,” Spectrochim. Acta Part B 52, 1839–1854 (1997).
[CrossRef]

B. A. Bushaw, B. D. Cannon, G. K. Gerke, T. J. Whitaker, “Laser-enhanced electron-impact ionization spectroscopy,” Opt. Lett. 11, 422–424 (1986).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992).

Deng, L.

M. G. Payne, L. Deng, N. Thonnard, “Applications of resonance ionization mass spectrometry,” Rev. Sci. Instrum. 65, 2433–2459 (1994).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992).

Feld, M. S.

M. S. Feld, A. Javan, “Laser-induced line-narrowing effects in coupled Doppler-broadened transitions,” Phys. Rev. 177, 540–562 (1969).
[CrossRef]

Fink, D.

D. Fink, J. Klein, R. Middleton, “41Ca: past, present and future,” Nucl. Instrum. Methods Phys. Res. B 52, 572–582 (1990).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).

Freeman, S. P. H. T.

S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

Geppert, P.

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

Gerke, G. K.

Grüning, C.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992).

Hänsch, T.

T. Hänsch, P. Toschek, “Theory of a three-level gas laser amplifier,” Z. Phys. 236, 213–244 (1970).
[CrossRef]

Herrmann, G.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Hohmann, R.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Horn, R.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

Huber, G.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

Hurst, G. S.

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

Jaffe, S. M.

S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
[CrossRef]

Javan, A.

M. S. Feld, A. Javan, “Laser-induced line-narrowing effects in coupled Doppler-broadened transitions,” Phys. Rev. 177, 540–562 (1969).
[CrossRef]

Jones, O. R.

O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
[CrossRef]

Juston, F.

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

Kato, K.

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

King, J. C.

S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

Klein, J.

D. Fink, J. Klein, R. Middleton, “41Ca: past, present and future,” Nucl. Instrum. Methods Phys. Res. B 52, 572–582 (1990).
[CrossRef]

Kluge, H.-J.

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Korschinek, G.

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

Kramer, S. D.

D. W. Beekman, T. A. Callcott, S. D. Kramer, E. T. Arakawa, G. S. Hurst, “Resonance ionization source for mass spectroscopy,” Int. J. Mass Spectrom. Ion Phys. 34, 89–97 (1980).
[CrossRef]

Kratz, J. V.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

Kunz, P.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

Kunze, S.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Kutschera, W.

M. Paul, I. Ahmad, W. Kutschera, “Half-life of 41Ca,” Z. Phys. A 340, 249–254 (1991).
[CrossRef]

Lambropoulos, P.

P. Lambropoulos, A. Lyras, “Theory of resonant ionization by broad-band radiation in the determination of isotopic abundances,” Phys. Rev. A 40, 2199–2202 (1989).
[CrossRef] [PubMed]

Lantzsch, J.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Lucht, R. P.

T. A. Reichardt, R. P. Lucht, “Theoretical calculation of lineshapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

R. P. Lucht, R. Trebino, L. A. Rahn, “Resonant multiwave-mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Lyras, A.

P. Lambropoulos, A. Lyras, “Theory of resonant ionization by broad-band radiation in the determination of isotopic abundances,” Phys. Rev. A 40, 2199–2202 (1989).
[CrossRef] [PubMed]

Middleton, R.

D. Fink, J. Klein, R. Middleton, “41Ca: past, present and future,” Nucl. Instrum. Methods Phys. Res. B 52, 572–582 (1990).
[CrossRef]

Mitroy, J.

J. Mitroy, “Energy levels and oscillator strengths for neutral calcium,” J. Phys. B 26, 3703–3718 (1993).
[CrossRef]

Monz, L.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Morinaga, H.

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

Müller, P.

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

Nolte, E.

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

Nörtershäuser, W.

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

Nunnemann, M.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

Orozco, L. A.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Otten, E. W.

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

Otten, E.-W.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Passler, G.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Paul, M.

M. Paul, I. Ahmad, W. Kutschera, “Half-life of 41Ca,” Z. Phys. A 340, 249–254 (1991).
[CrossRef]

Payne, M. G.

M. G. Payne, L. Deng, N. Thonnard, “Applications of resonance ionization mass spectrometry,” Rev. Sci. Instrum. 65, 2433–2459 (1994).
[CrossRef]

Perks, R. M.

O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).

Rahn, L. A.

R. P. Lucht, R. Trebino, L. A. Rahn, “Resonant multiwave-mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Raisbeck, G. M.

G. M. Raisbeck, F. Yiou, “Possible use of 41Ca for radioactive dating,” Nature (London) 277, 42–44 (1979).
[CrossRef]

Reichardt, T. A.

T. A. Reichardt, R. P. Lucht, “Theoretical calculation of lineshapes and saturation effects in polarization spectroscopy,” J. Chem. Phys. 109, 5830–5843 (1998).
[CrossRef]

Rochon, M.

S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
[CrossRef]

Rühm, W.

W. Rühm, K. Kato, G. Korschinek, H. Morinaga, E. Nolte, “36-Cl and 41-Ca depth profiles in a Hiroshima granite stone and the dosimetry system 1986,” Z. Phys. A 341, 235–238 (1992).
[CrossRef]

Salomaa, R.

R. Salomaa, S. Stenholm, “Two-photon spectroscopy: effects of a resonant intermediate state,” J. Phys. B 8, 1795–1805 (1975).
[CrossRef]

Schmitt, A.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

Schwalbach, R.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

Seibert, U.-A.

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

Senne, P.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990).

Simsarian, J. E.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Sprouse, G. D.

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Stenholm, S.

R. Salomaa, S. Stenholm, “Two-photon spectroscopy: effects of a resonant intermediate state,” J. Phys. B 8, 1795–1805 (1975).
[CrossRef]

Stenner, J.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Stratmann, K.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Stroud, C. R.

R. M. Whitley, C. R. Stroud, “Double optical resonance,” Phys. Rev. A 14, 1498–1513 (1976).
[CrossRef]

Telle, H. H.

O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).

Thonnard, N.

M. G. Payne, L. Deng, N. Thonnard, “Applications of resonance ionization mass spectrometry,” Rev. Sci. Instrum. 65, 2433–2459 (1994).
[CrossRef]

Toschek, P.

T. Hänsch, P. Toschek, “Theory of a three-level gas laser amplifier,” Z. Phys. 236, 213–244 (1970).
[CrossRef]

Trautmann, N.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

Trebino, R.

R. P. Lucht, R. Trebino, L. A. Rahn, “Resonant multiwave-mixing spectra of gas-phase sodium: nonperturbative calculations,” Phys. Rev. A 45, 8209–8227 (1992).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).

Vieira, N. E.

S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

Voss-de Haan, P.

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

Waldek, A.

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

Walter, K.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Wendt, K.

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
[CrossRef]

K. Blaum, P. Geppert, P. Müller, W. Nörtershäuser, E. W. Otten, A. Schmitt, N. Trautmann, K. Wendt, B. A. Bushaw, “Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry,” Int. J. Mass Spectrom. Ion Processes 181, 67–87 (1998).

W. Nörtershäuser, N. Trautmann, K. Wendt, B. A. Bushaw, “Isotope shifts and hyperfine structure in the 4s21S0 → 4s4p1P1 → 4s4d1D2 transitions of stable calcium isotopes and calcium-41,” Spectrochim. Acta Part B 53, 709–721 (1998).
[CrossRef]

K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

P. Müller, B. A. Bushaw, K. Blaum, W. Nörtershäuser, A. Schmitt, N. Trautmann, K. Wendt, “Ultratrace determination of the long-lived isotope 41Ca by narrowband cw-RIMS,” in Proceedings of the Ninth International Symposium on Resonance Ionization Spectroscopy and its Applications 1998, J. C. Vickerman, I. Lyon, N. P. Lockyer, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1998), Vol. 454, pp. 73–78.

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S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

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S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
[CrossRef]

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S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
[CrossRef]

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G. M. Raisbeck, F. Yiou, “Possible use of 41Ca for radioactive dating,” Nature (London) 277, 42–44 (1979).
[CrossRef]

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W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

Zimmer, K.

L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

Eur. J. Phys. D (1)

P. Müller, B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Isotope shifts and hyperfine structure in calcium 4snp1P1 and 4snfF Rydberg states,” Eur. J. Phys. D 12, 33–44 (2000).
[CrossRef]

Fresenius J. Anal. Chem. (2)

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, N. Trautmann, “Resonance ionization spectroscopy for trace analysis and fundamental research,” Fresenius J. Anal. Chem. 350, 323–329 (1994).
[CrossRef]

K. Wendt, K. Blaum, B. A. Bushaw, C. Grüning, R. Horn, G. Huber, J. V. Kratz, P. Kunz, P. Müller, W. Nörtershäuser, M. Nunnemann, G. Passler, A. Schmitt, N. Trautmann, A. Waldek, “Recent developments in and applications of resonance ionization mass spectrometry,” Fresenius J. Anal. Chem. 364, 471–477 (1999).
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[CrossRef]

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[CrossRef]

S. P. H. T. Freeman, J. C. King, N. E. Vieira, L. R. Woodhouse, A. L. Yergey, “Human calcium metabolism including bone resorption measured with 41Ca tracer,” Nucl. Instrum. Methods Phys. Res. B 123, 266–270 (1997).
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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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K. Wendt, G. K. Bhowmick, B. A. Bushaw, G. Herrmann, J. V. Kratz, J. Lantzsch, P. Müller, W. Nörtershäuser, E.-W. Otten, R. Schwalbach, U.-A. Seibert, N. Trautmann, A. Waldek, “Rapid trace analysis of 89,90Sr in environmental samples by collinear laser resonance ionization mass spectrometry,” Radiochim. Acta 79, 183–190 (1997).

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O. R. Jones, R. M. Perks, H. H. Telle, “Isotope specific resonance ionization mass spectrometry using continuous-wave diode and pulsed dye lasers for trace detection and enrichment of elements of environmental and medical importance, exemplified for strontium (Sr). Part I: Theoretical modelling,” Rapid. Commun. Mass Spectrom. 10, 1725–1738 (1996).
[CrossRef]

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S. M. Jaffe, M. Rochon, W. M. Yen, “Increasing the frequency stability of single-frequency lasers,” Rev. Sci. Instrum. 64, 2475–2481 (1993).
[CrossRef]

W. Z. Zhao, J. E. Simsarian, L. A. Orozco, G. D. Sprouse, “A computer-based digital feedback control of frequency drift of multiple lasers,” Rev. Sci. Instrum. 69, 3737–3740 (1998).
[CrossRef]

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L. Monz, R. Hohmann, H.-J. Kluge, S. Kunze, J. Lantzsch, E.-W. Otten, G. Passler, P. Senne, J. Stenner, K. Stratmann, K. Wendt, K. Zimmer, G. Herrmann, N. Trautmann, K. Walter, “Fast, low-level detection of strontium-90 and strontium-89 in environmental samples by collinear resonance ionization spectroscopy,” Spectrochim. Acta Part B 48, 1655–1671 (1993).
[CrossRef]

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[CrossRef]

B. A. Bushaw, W. Nörtershäuser, K. Wendt, “Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry,” Spectrochim. Acta Part B 54, 321–322 (1999).
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B. A. Bushaw, F. Juston, W. Nörtershäuser, N. Trautmann, P. Voss-de Haan, K. Wendt, “Multiple resonance RIMS measurements of calcium isotopes using diode lasers,” in Proceedings of the Eighth International Symposium on Resonance Ionization Spectroscopy and its Applications 1996, N. Winograd, J. E. Parks, eds. (American Institute of Physics, College Park, Md., 1997), Vol. 388, pp. 115–118.

B. A. Bushaw, “Attogram measurement of rare isotopes by cw resonance ionization mass spectrometry,” in Proceedings of the Sixth International Symposium on Resonance Ionization Spectroscopy and its Applications 1992, C. M. Miller, J. E. Parks, eds. (Institute of Physics, London, 1992), Vol. 128, pp. 31–36.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1997).

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990).

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Figures (5)

Fig. 1
Fig. 1

Excitation schemes for multiple-resonance ionization showing the parameters for DM calculations: (a) generalized N-step ladder scheme and (b) triple-resonance ionization of calcium discussed in this paper. Decay constants used in the calculations are included and are discussed in the text.

Fig. 2
Fig. 2

Calculated triple-resonance line shapes shown as two-dimensional logarithmic contour plots for different laser beam geometries (A)–(D), as discussed in the text. Each column corresponds to one laser, as labeled at the top, fixed on resonance for its respective transition. Axis labels are the detunings of the two scanned lasers, as shown at the bottom, given in megahertz. Calculations were performed for a close-coupled geometry with 0.5% contribution of a 20° Doppler background. Laser parameters were chosen to match experimental conditions (see Fig. 3). Each line shape is normalized to its peak intensity, and the color map was restricted to 6 orders of magnitude with 12 steps. Values below 10-6 are unshaded.

Fig. 3
Fig. 3

Experimentally measured triple-resonance line shapes shown as two-dimensional normalized logarithmic contour plots. Axis labels are as given for Fig. 2. Center laser intensities (mW/cm2) and beam diameters [mm FW(1/e)] for the three laser beams are the following: (a)–(f), I 1 = 48, I 2 = 28, I 3 = 930, w 1 = 0.180, w 2 = 0.220, w 3 = 0.155; (g)–(i), I 1 = 20, I 2 = 14, I 3 = 7000, w 1 = 1.8, w 2 = 1.6, w 3 = 2.4; (j)–(l), I 1 = 51, I 2 = 9, I 3 = 4900, w 1 = 1.1, w 2 = 1.6, w 3 = 2.4.

Fig. 4
Fig. 4

(a) Two-dimensional logarithmic contour plot of the calculated normalized ionization efficiency for 40Ca and 42Ca as a function of second- and third-step detuning whereas the first-step laser is fixed at Δν 1 = 155.5 MHz (resonance of strongest hyperfine component of 41Ca). Frequency scales are given relative to the unperturbed ladder transition frequencies for the predominant isotope 40Ca. The calculation was performed without integration over Doppler distribution. Each color step represents 1 order of magnitude in signal intensity. Strongest 41Ca Rydberg resonances occur along the vertical dashed line. (b) Simplified excitation schemes for explanation of different resonance structures marked in (a).

Fig. 5
Fig. 5

One-dimensional line shapes of 40Ca as a function of third-step laser frequency with first- and second-step laser (Δν 1, Δν 2) fixed at either (0,0) (◇) or (155.5 MHz, 443.4 MHz) (○). The labeling of (A)–(D) refers to the different laser geometries as discussed in the text. For each line shape, the experimental spectra (symbols), the calculation result with 2° atomic beam divergence (dashed curves), and the sum (solid curves) of this spectrum and a 5% contribution from the 20° background are shown. Laser parameters are nearly the same for (A)–(D) with I 1 = 1.3, I 2 = 0.5, I 3 = 35 mW/cm2. The strongest hyperfine component of 41Ca in the transitions to 4snf 1 F 3 Rydberg states with n = 13 to n = 17 occur at the positions indicated in (A).

Equations (8)

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4s2 1S0422.8 nm 4s4p1P1732.8 nm 4s4d1D2860 nm 4snf1F310.6 μmCa+.
Gi=|Ωi|2=Aii-1λ38πhc I1/2,
ddtρjkjk=i m=k+1j Δνm-Γj-γj-Γk-γk-δjN+δkNγIρjk+2Γk+1ρk+1,k+1δjk-iGkρj,k-1-iGk+1*ρj,k+1+iGj*ρj-1,k+iGj+1ρj+1,k,ddt ρjkj<k=ddt ρkj*,
ddt ρkk=2γIρNN;k=N+12γjρjj;k>N+1, j=k-N-1,
Δν2+vp1λ1-1λ2=0,
Δν2=Δν3λ3λ2-λ1λ1λ20.85Δν3,
dkΔνkλk=djΔνjλj,
Δνi+Δνj=dkΔνkλkdiλi+djλj,

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