Abstract

Transitions from the doubly excited 2s22p53l4l′ and 2s2p63l4l′ levels of Na-like Kr25+ were observed in spectra from plasmas produced in laser-irradiated gas-puff targets. These transitions produce satellites to n = 3–2 and n = 4–2 Ne-like Kr26+ resonance lines. High-resolution x-ray spectra were measured with a relative uncertainty of ±0.001 Å by means of a spherical crystal spectrograph. A simple kinetics model was successfully used to model the experimental spectra, to assist the line identification, and to demonstrate the potential of these lines for diagnosing the plasma conditions. In addition, contributions of these lines to x-ray spectra should be taken into account in the analysis of n = 4–2 Ne-like linewidth diagnostics proposed for electron density measurements in compressed inertial confinement fusion plasmas.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).
  2. W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
    [Crossref] [PubMed]
  3. R. C. Elton, X-ray Lasers (Academic, New York, 1990), and references therein.
  4. B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
    [Crossref]
  5. C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
    [Crossref]
  6. C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
    [Crossref] [PubMed]
  7. J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).
  8. J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
    [Crossref]
  9. B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
    [Crossref]
  10. S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).
  11. S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
    [Crossref]
  12. S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
    [Crossref]
  13. J. Nilsen, “Dielectronic satellite spectra for neon-like ions,” At. Data Nucl. Data Tables 41, 131–177 (1989).
    [Crossref]
  14. H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
    [Crossref]
  15. B. L. Henke, F. G. Fujiwara, M. A. Tester, C. H. Dittmore, and M. A. Palmer, “Low-energy x-ray response of photographic films. II. Experimental characterization,” J. Opt. Soc. Am. B 1, 828–849 (1984).
    [Crossref]
  16. M. Klapisch, J. L. Schwob, B. S. Fraenkel, and J. Oreg, “The 1s–3p Kβ-like x-ray spectrum of highly ionized iron,” J. Opt. Soc. Am. 67, 148–155 (1977).
    [Crossref]
  17. J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
    [Crossref] [PubMed]
  18. R. Mewe, “Interpolation formulae for the electron impact excitation of ions in the H-, He-, Li-, and Ne-sequences,” Astron. Astrophys. 20, 215–221 (1972).
  19. I. Yu. Skobelev and S. Ya. Khakhalin, “Relaxation characteristics of Ne-like ions,” in Methods of Investigation of High Temperature Plasma. Optical Characteristics, I. Yu. Skobelev and A. Ya. Faenov, eds. (VNIIFTRI, Moscow Region, 1989), pp. 69–79 (in Russian).
  20. H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
    [Crossref]
  21. S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
    [Crossref] [PubMed]

1994 (6)

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

1993 (3)

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
[Crossref] [PubMed]

1991 (1)

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

1990 (2)

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

1989 (1)

J. Nilsen, “Dielectronic satellite spectra for neon-like ions,” At. Data Nucl. Data Tables 41, 131–177 (1989).
[Crossref]

1987 (1)

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

1984 (1)

1979 (1)

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

1977 (1)

1972 (1)

R. Mewe, “Interpolation formulae for the electron impact excitation of ions in the H-, He-, Li-, and Ne-sequences,” Astron. Astrophys. 20, 215–221 (1972).

Bailey, J.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Bar-Shalom, A.

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

Bartnik, A.

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

Beiersdorfer, P.

S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
[Crossref] [PubMed]

Bell, P.

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

Boiko, V. A.

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

Bryunetkin, B. A.

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

Calisti, A.

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Chen, M. H.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Cowan, R. D.

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

Dittmore, C. H.

Dyakin, V. M.

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

Elliott, S.

S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
[Crossref] [PubMed]

Elton, R. C.

R. C. Elton, X-ray Lasers (Academic, New York, 1990), and references therein.

Ermatov, Sh. A.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

Faenov, A. Ya.

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

Fiedorowicz, H.

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

Fortner, R.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Fraenkel, B. S.

Fujiwara, F. G.

Goldstein, W. H.

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Gordon, H.

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

Hammel, B. A.

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Henke, B. L.

Hobby, M. G.

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

Kania, D. R.

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

Keane, C. J.

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

Khabibulaev, B. K.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

Khakhalin, S. Ya.

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

I. Yu. Skobelev and S. Ya. Khakhalin, “Relaxation characteristics of Ne-like ions,” in Methods of Investigation of High Temperature Plasma. Optical Characteristics, I. Yu. Skobelev and A. Ya. Faenov, eds. (VNIIFTRI, Moscow Region, 1989), pp. 69–79 (in Russian).

Khelfaoui, F.

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Klapisch, M.

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

M. Klapisch, J. L. Schwob, B. S. Fraenkel, and J. Oreg, “The 1s–3p Kβ-like x-ray spectrum of highly ionized iron,” J. Opt. Soc. Am. 67, 148–155 (1977).
[Crossref]

Lee, R. W.

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Lewis, C. L. S.

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

Mewe, R.

R. Mewe, “Interpolation formulae for the electron impact excitation of ions in the H-, He-, Li-, and Ne-sequences,” Astron. Astrophys. 20, 215–221 (1972).

Nilsen, J.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
[Crossref] [PubMed]

J. Nilsen, “Dielectronic satellite spectra for neon-like ions,” At. Data Nucl. Data Tables 41, 131–177 (1989).
[Crossref]

Oreg, J.

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

M. Klapisch, J. L. Schwob, B. S. Fraenkel, and J. Oreg, “The 1s–3p Kβ-like x-ray spectrum of highly ionized iron,” J. Opt. Soc. Am. 67, 148–155 (1977).
[Crossref]

Osterheld, A.

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

Osterheld, A. L.

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Palmer, M. A.

Parys, P.

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

Patron, Z.

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

Peacock, N. J.

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

Phillips, T.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Pikuz, S. A.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

Schwob, J. L.

Skobelev, I. Yu.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

I. Yu. Skobelev and S. Ya. Khakhalin, “Relaxation characteristics of Ne-like ions,” in Methods of Investigation of High Temperature Plasma. Optical Characteristics, I. Yu. Skobelev and A. Ya. Faenov, eds. (VNIIFTRI, Moscow Region, 1989), pp. 69–79 (in Russian).

Skobolev, I. Yu.

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

Stamm, R.

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Stewart, R. E.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Suter, L. J.

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Talin, B.

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Tester, M. A.

Vinogradov, A. V.

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

Walling, R. S.

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Ya Khakhalin, S.

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

Appl. Phys. Lett. (1)

H. Fiedorowicz, A. Bartnik, Z. Patron, and P. Parys, “X-ray emission from laser-irradiated gas puff targets,” Appl. Phys. Lett. 62, 2778–2780 (1993).
[Crossref]

Astron. Astrophys. (1)

R. Mewe, “Interpolation formulae for the electron impact excitation of ions in the H-, He-, Li-, and Ne-sequences,” Astron. Astrophys. 20, 215–221 (1972).

At. Data Nucl. Data Tables (1)

J. Nilsen, “Dielectronic satellite spectra for neon-like ions,” At. Data Nucl. Data Tables 41, 131–177 (1989).
[Crossref]

Izmer. Tech. (1)

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “High-precision measurements and identification of emission spectra of laser-produced plasma, caused by transitions from doubly excited levels of Na-like ions of Se,” Izmer. Tech. 5, 3–15 (1994).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

H. Gordon, M. G. Hobby, N. J. Peacock, and R. D. Cowan, “Classification of x-ray spectra of 2–3 transitions in the Ne-like and Na-like isoelectronic sequences of the elements from krypton to molybdenum,” J. Phys. B 12, 881–891 (1979).
[Crossref]

JETP Lett. (1)

S. Ya. Khakhalin, B. A. Bryunetkin, I. Yu. Skobolev, A. Ya. Faenov, J. Nilsen, A. Osterheld, and S. A. Pikuz, “Dielectron satellites of Ne-like ions in high-temperature plasma,” JETP Lett. 78, 633–644 (1994).

Phys. Rev. A (2)

J. Oreg, W. H. Goldstein, M. Klapisch, and A. Bar-Shalom, “Autoionization and radiationless electron capture in complex spectra,” Phys. Rev. A 44, 1750–1758 (1991).
[Crossref] [PubMed]

S. Elliott, P. Beiersdorfer, and J. Nilsen, “Measurements of line overlaps for resonant photopumping of transitions in neon-like ions by nickel-like ions,” Phys. Rev. A 47, 1403–1406 (1993).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

C. J. Keane, B. A. Hammel, A. L. Osterheld, and D. R. Kania, “Density and temperature sensitive features in high temperature plasma L-shell xenon emission spectra,” Phys. Rev. Lett. 72, 3029–3032 (1994).
[Crossref] [PubMed]

W. H. Goldstein, R. S. Walling, J. Bailey, M. H. Chen, R. Fortner, M. Klapisch, T. Phillips, and R. E. Stewart, “Independent determinations of temperature and ionization balance in a laser-produced plasma by use of L-shell x-ray spectra,” Phys. Rev. Lett. 58, 2300–2303 (1987).
[Crossref] [PubMed]

Phys. Scr. (2)

S. Ya. Khakhalin, A. Ya. Faenov, I. Yu. Skobelev, S. A. Pikuz, J. Nilsen, and A. Osterheld, “The observation of the Ne-like ion resonance line satellites for Cr xv–Ni xix in CO2-laser produced plasma,” Phys. Scr. 50, 102–105 (1994).
[Crossref]

S. Ya. Khakhalin, V. M. Dyakin, A. Ya. Faenov, H. Fiedorowicz, A. Bartnik, P. Parys, J. Nilsen, and A. Osterheld, “The dielectronic satellites to the 2s–3p Ne-like krypton resonance lines,” Phys. Scr. 50, 106–109 (1994).
[Crossref]

Quantum Electron. (2)

J. Nilsen, S. A. Pikuz, I. Yu. Skobelev, A. Ya. Faenov, S. Ya Khakhalin, B. K. Khabibulaev, and Sh. A. Ermatov, “L-spectra of zinc ions observed in the wavelength range 0.65–1.18 nm in a plasma heated by Nd laser radiation,” Quantum Electron. 23, 1010–1025 (1993).
[Crossref]

B. A. Bryunetkin, V. M. Dyakin, J. Nilsen, I. Yu. Skobelev, A. Ya. Faenov, and S. Ya. Khakhalin, “Use of a laser plasma in determination of resonance defect of the Lyα1,2lines of Mg xii and the 2s–3p lines of Ge xxiii, Quantum Electron. 24, 133–137 (1994).
[Crossref]

Rev. Sci. Instrum. (2)

B. A. Hammel, P. Bell, C. J. Keane, R. W. Lee, and C. L. S. Lewis, “High-Z x-ray spectroscopy of laser-imploded capsules,” Rev. Sci. Instrum. 61, 2774–2776 (1990).
[Crossref]

C. J. Keane, R. W. Lee, B. A. Hammel, A. L. Osterheld, L. J. Suter, A. Calisti, F. Khelfaoui, R. Stamm, and B. Talin, “Line broadening of Ne-like xenon as a diagnostic for high density implosion experiments,” Rev. Sci. Instrum. 61, 2780–2782 (1990).
[Crossref]

Other (3)

R. C. Elton, X-ray Lasers (Academic, New York, 1990), and references therein.

V. A. Boiko, A. V. Vinogradov, S. A. Pikuz, I. Yu. Skobelev, and A. Ya. Faenov, X-Ray Spectroscopy of Laser-Produced Plasmas (Radioteknika, Moscow, 1980), Vol. 27 (in Russian).

I. Yu. Skobelev and S. Ya. Khakhalin, “Relaxation characteristics of Ne-like ions,” in Methods of Investigation of High Temperature Plasma. Optical Characteristics, I. Yu. Skobelev and A. Ya. Faenov, eds. (VNIIFTRI, Moscow Region, 1989), pp. 69–79 (in Russian).

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

Densitometer traces of krypton x-ray spectra in the regions of (a) the 2p–4d and the 2p–4s Ne-like resonance lines and (b) the 2s–3p Ne-like resonance lines. The Ne-like transitions 4d3/2–2p1/2 (4C), 4d5/2–2p3/2 (4D), 4s1/2–2p1/2 (4F), 4s1/2–2p3/2 (4 G), 3p3/2–2s1/2 (3A), and 3p1/2–2s1/2 (3B) are indicated.

Fig. 2
Fig. 2

Calculated spectra of dielectronic 3l4l′ Na-like satellites to the Ne-like krypton resonance lines 3A (2s2p63p1P1–2p6 1S0) and 3B (2s2p63p3P1–2p6 1S0). The positions of the Ne-like resonance lines are indicated by vertical lines. The dashed curve spectrum is obtained with the assumption that only the dielectronic capture contributes to the 3l4l′-level populations. The solid curve denotes the satellite spectrum when only the inner-shell electron collisional excitation is taken into account. The spectra were produced with model parameters Δλ/λ = 4.5 × 10−4 and Te = 300 eV, and the relative normalization of the two curves is arbitrary.

Fig. 3
Fig. 3

Comparison between observed (solid curve) and calculated (dashed curve) spectra in the region of the (3p–2s) Ne-like resonance lines 3A and 3B. The calculated spectra were produced with Δλ/λ = 3 × 10−4, Te = 300 eV, and ion abundance ratio N(Na)/N(Ne) = 9, adjusted for best fit between observed and synthetic spectra. The letters a–q denote 3l3l′ satellites (see Ref. 12).

Fig. 4
Fig. 4

Comparison between observed (solid curve) and calculated (dashed curve) spectra in the region of (n = 4–2) Ne-like resonance lines. The model parameters were the same as in Fig. 3.

Fig. 5
Fig. 5

Comparison between observed (upper solid curve) and calculated (lower solid and dotted curves) satellite shapes in the region (5.355–5.385) Å. The model spectra are obtained with different values of Δλ/λ = 4.5 × 10−4 (dotted lower curve) and 3 × 10−4 (solid lower curve).

Tables (1)

Tables Icon

Table 1 Experimental Wavelengths and Theoretical Atomic Parameters of Satellites to the Kr xxvii Resonance Lines 4C, 4D, 4F, 4E, 3A, 3B

Equations (3)

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

I d s = N e ( N g Ne - like R g d A d s r Γ d + s N s Na - like Q s d A d s r Γ d ) ,
I d s DC = N e N g Ne - like 1 2 g g ( 2 π 2 m k T e ) 3 / 2 × exp [ - ( E d / k T e ) ] F 2 ( d s ) ,
F 2 ( d s ) = g d A d g a A d s r Γ d .

Metrics