Abstract

The x-ray spectra in the range 5–8 Å emitted from laser-produced plasmas of Hf, Ta, W, and Re were observed. Lines belonging to the 3d10 − 3d9 4f and 3d10 − 3d9 4p transitions, as well as the 3p63d10 − 3p53d10 4s and 3p63d10 − 3p53d10 4d transitions in the Ni-like isoelectronic sequence, were identified. In addition, the interpretation of some previously measured lines of the same sequence were revised.

© 1980 Optical Society of America

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References

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  1. B. Edlen, “Spectra of Highly Ionized Atoms,” Physica 13, 545–554 (1947).
    [Crossref]
  2. B. Edlen, “Atomic Spectra,” Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1964), Vol. XXVII, pp. 80–220.
  3. E. Alexander, M. Even-Zohar, B. S. Fraenkel, and S. Goldsmith, “Classification of transitions in the euv spectra of Y ix–xiii, Zn x–xiv, Nb xi–xv, and Mo xii–xvi,” J. Opt. Soc. Am. 61, 508–514 (1971).
    [Crossref]
  4. M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).
  5. P. G. Burkhaller, U. Feldman, and R. D. Cowan, “Transition in highly ionized Sn spectra from a laser produced plasma,” J. Opt. Soc. Am. 64, 1058–1062 (1974).
    [Crossref]
  6. P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
    [Crossref]
  7. P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
    [Crossref]
  8. M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
    [Crossref]
  9. E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].
  10. U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).
  11. M. Klapisch, J. L. Schwob, B. S. Fraenkel, and J. Oreg, “The 1s-3p Kβ-like x-ray spectrum of highly ionized ions,” J. Opt. Soc. Am. 67, 148–155 (1977).
    [Crossref]
  12. I. P. Grant, “A Program to Calculate Angular Momentum Coefficients in Relativistic Atomic Structure (revised),” Comput. Phys. Commun. 11, 397–405 (1976).
    [Crossref]
  13. K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
    [Crossref]
  14. A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
    [Crossref]

1979 (1)

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

1978 (2)

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

1977 (2)

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

P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
[Crossref]

1976 (2)

I. P. Grant, “A Program to Calculate Angular Momentum Coefficients in Relativistic Atomic Structure (revised),” Comput. Phys. Commun. 11, 397–405 (1976).
[Crossref]

K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
[Crossref]

1974 (4)

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

P. G. Burkhaller, U. Feldman, and R. D. Cowan, “Transition in highly ionized Sn spectra from a laser produced plasma,” J. Opt. Soc. Am. 64, 1058–1062 (1974).
[Crossref]

P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
[Crossref]

1971 (1)

1947 (1)

B. Edlen, “Spectra of Highly Ionized Atoms,” Physica 13, 545–554 (1947).
[Crossref]

Aglitzkii, E. V.

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Alexander, E.

Bar-Shalom, A.

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

Boiko, V. A.

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Breton, C.

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

Burkhaller, P. G.

Burkhalter, P. G.

P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
[Crossref]

P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
[Crossref]

Cowan, R. D.

P. G. Burkhaller, U. Feldman, and R. D. Cowan, “Transition in highly ionized Sn spectra from a laser produced plasma,” J. Opt. Soc. Am. 64, 1058–1062 (1974).
[Crossref]

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

De Michelis, C.

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

Doschek, G. A.

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

Dozier, C. M.

P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
[Crossref]

Edlen, B.

B. Edlen, “Spectra of Highly Ionized Atoms,” Physica 13, 545–554 (1947).
[Crossref]

B. Edlen, “Atomic Spectra,” Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1964), Vol. XXVII, pp. 80–220.

Egert, S.

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

Eidman, K.

K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
[Crossref]

Even-Zohar, M.

Faenov, A. Ya.

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Feldman, U.

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

P. G. Burkhaller, U. Feldman, and R. D. Cowan, “Transition in highly ionized Sn spectra from a laser produced plasma,” J. Opt. Soc. Am. 64, 1058–1062 (1974).
[Crossref]

Finkenthal, M.

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

Fraenkel, B. S.

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

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

E. Alexander, M. Even-Zohar, B. S. Fraenkel, and S. Goldsmith, “Classification of transitions in the euv spectra of Y ix–xiii, Zn x–xiv, Nb xi–xv, and Mo xii–xvi,” J. Opt. Soc. Am. 61, 508–514 (1971).
[Crossref]

Goldsmith, S.

Grant, I. P.

I. P. Grant, “A Program to Calculate Angular Momentum Coefficients in Relativistic Atomic Structure (revised),” Comput. Phys. Commun. 11, 397–405 (1976).
[Crossref]

Key, M. H.

K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
[Crossref]

Klapisch, M.

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

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

Loebenstein, H. M.

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

Mattioli, M.

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

Nagel, D. J.

P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
[Crossref]

P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
[Crossref]

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

Oreg, J.

Pikuz, S. A.

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Schwob, J. L.

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

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

Sigel, R.

K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
[Crossref]

Whitlock, R. R.

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
[Crossref]

Zakharov, S. M.

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Zigler, A.

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

Zmora, H.

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

Astrophys. J. (1)

U. Feldman, G. A. Doschek, D. J. Nagel, R. D. Cowan, and R. R. Whitlock, “Satellite line spectra from laser produced plasma,” Astrophys. J. 187, 192–213 (1974).

Comput. Phys. Commun. (1)

I. P. Grant, “A Program to Calculate Angular Momentum Coefficients in Relativistic Atomic Structure (revised),” Comput. Phys. Commun. 11, 397–405 (1976).
[Crossref]

J. Appl. Phys. (2)

K. Eidman, M. H. Key, and R. Sigel, “X-ray emission from laser-irradiated plane solid targets,” J. Appl. Phys. 47, 2402–2414 (1976).
[Crossref]

A. Zigler, H. Zmora, H. M. Loebenstein, and J. L. Schwob, “Investigation of the transient ionizing regime of laser-produced plasma,” J. Appl. Phys. 50, 165–167 (1979).
[Crossref]

J. Opt. Soc. Am. (3)

Kvant. Elektron. (Moscow) (1)

E. V. Aglitzkii, V. A. Boiko, S. M. Zakharov, S. A. Pikuz, and A. Ya. Faenov, “Observation in laser plasmas and identification of dielectron satellites of spectral lines of hydrogen- and helium-like ions of elements in the Na-V range.,” Kvant. Elektron. (Moscow) 1, 908–936 (1974) [Sov. J. Quantum Electron. 4, 500–513 (1974)].

Phys. Lett. (1)

M. Klapisch, A. Bar-Shalom, J. L. Schwob, B. S. Fraenkel, C. Breton, C. De Michelis, M. Finkenthal, and M. Mattioli, “Identification of magnetic quadrupole lines of highly ionized Ni, Cr, Fe in the TFR 600 Tokamak plasma,” Phys. Lett. 69A, 34–36 (1978).

Phys. Rev. A (2)

P. G. Burkhalter, D. J. Nagel, and R. R. Whitlock, “Laser-produced rare-earth x-ray spectra,” Phys. Rev. A 9, 2331–2339 (1974).
[Crossref]

P. G. Burkhalter, C. M. Dozier, and D. J. Nagel, “X-ray spectra from exploded wire plasmas,” Phys. Rev. A 15, 700–717 (1977).
[Crossref]

Phys. Rev. Lett. (1)

M. Klapisch, J. L. Schwob, M. Finkenthal, B. S. Fraenkel, S. Egert, A. Bar-Shalom, C. Breton, C. De Michelis, and M. Mattioli, “Identification of forbidden lines in the soft x-ray spectrum of the TFR Tokamak,” Phys. Rev. Lett. 41, 403–406 (1978).
[Crossref]

Physica (1)

B. Edlen, “Spectra of Highly Ionized Atoms,” Physica 13, 545–554 (1947).
[Crossref]

Other (1)

B. Edlen, “Atomic Spectra,” Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1964), Vol. XXVII, pp. 80–220.

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Figures (2)

FIG. 1
FIG. 1

X-ray spectrum of Hf. All indicated transitions are to the 3p63d10 ground state of Hf xlv.

FIG. 2
FIG. 2

Plot of ΔE/Z vs Z for the observed and classified transitions in the Ni-like isoelectronic sequence for Z = 62 through Z = 75. All transitions are to the 3p63d10 ground state. ○: present work, experimental;·●: present work, theoretical; △: Ref. (6), experimental.

Tables (2)

Tables Icon

TABLE I Experimental and calculated results for Ni-like Hf, Ta, W, and Re.

Tables Icon

TABLE II Experimental (Ref. 6) and calculated results for Sm, Gd, and Dy.