Abstract

The magnetic-dipole hyperfine-structure (hfs) constants for 15 levels of the 5p26p configuration of Te ii were recently observed. To carry out the theoretical analysis of these experimental data, the intermediate coupling coefficients for all 21 levels belonging to 5p26p were calculated. The theoretical gJ factors show good agreement with the experimental values known from Zeeman-effect data. The hyperfine-structure analysis was performed by the effective-operator formalism. On the basis of the experimentally determined A hfs constants the values of the effective radial parameters aksk1 have been obtained in two versions: in version 1 we have taken into consideration all 15 known A values; in version 2 the A constant for the 1115/2 level was eliminated. The following values for the hfs parameters aksk1 in these two versions were obtained: a5p01=-107.7 and −108.8 mK, a5p12=-170.3 and −151.9 mK, a5p10=1.1 and 1.9 mK, a6p01=-21.8 and −10.9 mK, a6p12=-6.2 and −29.5 mK, a6p12=1.5 and −6.7 mK, respectively.

© 1982 Optical Society of America

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  1. M. B. Handrup and J. E. Mack, “On the spectrum of ionized tellurium,” Physica 30, 1245–1275 (1964).
    [Crossref]
  2. J. S. Ross and K. Murakawa, “Hyperfine structure and isotope shift in the spectrum of tellurium,” Phys. Rev. 85, 559–563 (1952).
    [Crossref]
  3. K. Werel and L. Augustiniak, “Hyperfine structure analysis of some tellurium ii lines,” Phys. Scr. 23, 856–858 (1981).
    [Crossref]
  4. P. G. H. Sandars and J. E. Beck, “Relativistic effects in many electron hyperfine structure,” Proc. R. Soc. London Sect. A 289, 97–107 (1965).
    [Crossref]
  5. A. Rosén, “Analysis of the hyperfine structure of the ground state multiplet of the samarium atom,” J. Phys. B 2, 1257–1260 (1969).
    [Crossref]
  6. W. J. Childs, “Hyperfine structure of many atomic levels of Tb159 and the Tb159 nuclear electric quadrupole moment,” Phys. Rev. A 2, 316–336 (1970).
    [Crossref]
  7. W. J. Childs and L. S. Goodman, “Hyperfine and Zeeman studies of low lying atomic levels of La139 and the nuclear electric quadrupole moment,” Phys. Rev. A 3, 25–45 (1971).
    [Crossref]
  8. J. Dembczyński and M. Frackoviak, “Hyperfine structure in intermediate coupling of the first excited electron configuration 6p27s of  83209Bi (I= 9/2),” Acta Phys. Pol. 48, 139–155 (1975).
  9. J. Dembczyński, “Determination of the quadrupole moment of  51151Sb (I= 5/2) nucleus from hyperfine structure analysis,” Acta Phys. Pol. 49, 541–554 (1976).
  10. B. Arcimowicz and J. Dembczyński, “Relativistic effects in the hyperfine structure of the second spectrum of the Bi ii ion,” Acta Phys. Pol. 56, 661–671 (1979).
  11. S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
    [Crossref]
  12. K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
    [Crossref]
  13. C. E. Moore, Atomic Energy Levels (U.S. Government Printing Office, Washington, D.C., 1958).
  14. L. Armstrong, Theory of the Hyperfine Structure of Free Atoms (Wiley, Interscience, New York, 1971).
  15. H. Kopfermann, Kernmomente (Frankfurt am Main, Germany, 1956).
  16. S. S. Dharmatti and H. E. Weaver, “On the magnetic moment of Te123,125 and Si29*,” Phys. Rev. 84, 843–844 (1951).
    [Crossref]

1981 (1)

K. Werel and L. Augustiniak, “Hyperfine structure analysis of some tellurium ii lines,” Phys. Scr. 23, 856–858 (1981).
[Crossref]

1980 (1)

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

1979 (1)

B. Arcimowicz and J. Dembczyński, “Relativistic effects in the hyperfine structure of the second spectrum of the Bi ii ion,” Acta Phys. Pol. 56, 661–671 (1979).

1978 (1)

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

1976 (1)

J. Dembczyński, “Determination of the quadrupole moment of  51151Sb (I= 5/2) nucleus from hyperfine structure analysis,” Acta Phys. Pol. 49, 541–554 (1976).

1975 (1)

J. Dembczyński and M. Frackoviak, “Hyperfine structure in intermediate coupling of the first excited electron configuration 6p27s of  83209Bi (I= 9/2),” Acta Phys. Pol. 48, 139–155 (1975).

1971 (1)

W. J. Childs and L. S. Goodman, “Hyperfine and Zeeman studies of low lying atomic levels of La139 and the nuclear electric quadrupole moment,” Phys. Rev. A 3, 25–45 (1971).
[Crossref]

1970 (1)

W. J. Childs, “Hyperfine structure of many atomic levels of Tb159 and the Tb159 nuclear electric quadrupole moment,” Phys. Rev. A 2, 316–336 (1970).
[Crossref]

1969 (1)

A. Rosén, “Analysis of the hyperfine structure of the ground state multiplet of the samarium atom,” J. Phys. B 2, 1257–1260 (1969).
[Crossref]

1965 (1)

P. G. H. Sandars and J. E. Beck, “Relativistic effects in many electron hyperfine structure,” Proc. R. Soc. London Sect. A 289, 97–107 (1965).
[Crossref]

1964 (1)

M. B. Handrup and J. E. Mack, “On the spectrum of ionized tellurium,” Physica 30, 1245–1275 (1964).
[Crossref]

1952 (1)

J. S. Ross and K. Murakawa, “Hyperfine structure and isotope shift in the spectrum of tellurium,” Phys. Rev. 85, 559–563 (1952).
[Crossref]

1951 (1)

S. S. Dharmatti and H. E. Weaver, “On the magnetic moment of Te123,125 and Si29*,” Phys. Rev. 84, 843–844 (1951).
[Crossref]

Arcimowicz, B.

B. Arcimowicz and J. Dembczyński, “Relativistic effects in the hyperfine structure of the second spectrum of the Bi ii ion,” Acta Phys. Pol. 56, 661–671 (1979).

Armstrong, L.

L. Armstrong, Theory of the Hyperfine Structure of Free Atoms (Wiley, Interscience, New York, 1971).

Augustiniak, L.

K. Werel and L. Augustiniak, “Hyperfine structure analysis of some tellurium ii lines,” Phys. Scr. 23, 856–858 (1981).
[Crossref]

Beck, J. E.

P. G. H. Sandars and J. E. Beck, “Relativistic effects in many electron hyperfine structure,” Proc. R. Soc. London Sect. A 289, 97–107 (1965).
[Crossref]

Bürger, K. H.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

Büttgenbach, S.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

Childs, W. J.

W. J. Childs and L. S. Goodman, “Hyperfine and Zeeman studies of low lying atomic levels of La139 and the nuclear electric quadrupole moment,” Phys. Rev. A 3, 25–45 (1971).
[Crossref]

W. J. Childs, “Hyperfine structure of many atomic levels of Tb159 and the Tb159 nuclear electric quadrupole moment,” Phys. Rev. A 2, 316–336 (1970).
[Crossref]

Dembczynski, J.

B. Arcimowicz and J. Dembczyński, “Relativistic effects in the hyperfine structure of the second spectrum of the Bi ii ion,” Acta Phys. Pol. 56, 661–671 (1979).

J. Dembczyński, “Determination of the quadrupole moment of  51151Sb (I= 5/2) nucleus from hyperfine structure analysis,” Acta Phys. Pol. 49, 541–554 (1976).

J. Dembczyński and M. Frackoviak, “Hyperfine structure in intermediate coupling of the first excited electron configuration 6p27s of  83209Bi (I= 9/2),” Acta Phys. Pol. 48, 139–155 (1975).

Dharmatti, S. S.

S. S. Dharmatti and H. E. Weaver, “On the magnetic moment of Te123,125 and Si29*,” Phys. Rev. 84, 843–844 (1951).
[Crossref]

Dicke, R.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

Frackoviak, M.

J. Dembczyński and M. Frackoviak, “Hyperfine structure in intermediate coupling of the first excited electron configuration 6p27s of  83209Bi (I= 9/2),” Acta Phys. Pol. 48, 139–155 (1975).

Gebauer, H.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

Goodman, L. S.

W. J. Childs and L. S. Goodman, “Hyperfine and Zeeman studies of low lying atomic levels of La139 and the nuclear electric quadrupole moment,” Phys. Rev. A 3, 25–45 (1971).
[Crossref]

Handrup, M. B.

M. B. Handrup and J. E. Mack, “On the spectrum of ionized tellurium,” Physica 30, 1245–1275 (1964).
[Crossref]

Kopfermann, H.

H. Kopfermann, Kernmomente (Frankfurt am Main, Germany, 1956).

Kuhnen, R.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

Mack, J. E.

M. B. Handrup and J. E. Mack, “On the spectrum of ionized tellurium,” Physica 30, 1245–1275 (1964).
[Crossref]

Moore, C. E.

C. E. Moore, Atomic Energy Levels (U.S. Government Printing Office, Washington, D.C., 1958).

Murakawa, K.

J. S. Ross and K. Murakawa, “Hyperfine structure and isotope shift in the spectrum of tellurium,” Phys. Rev. 85, 559–563 (1952).
[Crossref]

Rosén, A.

A. Rosén, “Analysis of the hyperfine structure of the ground state multiplet of the samarium atom,” J. Phys. B 2, 1257–1260 (1969).
[Crossref]

Ross, J. S.

J. S. Ross and K. Murakawa, “Hyperfine structure and isotope shift in the spectrum of tellurium,” Phys. Rev. 85, 559–563 (1952).
[Crossref]

Sandars, P. G. H.

P. G. H. Sandars and J. E. Beck, “Relativistic effects in many electron hyperfine structure,” Proc. R. Soc. London Sect. A 289, 97–107 (1965).
[Crossref]

Träber, F.

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

Weaver, H. E.

S. S. Dharmatti and H. E. Weaver, “On the magnetic moment of Te123,125 and Si29*,” Phys. Rev. 84, 843–844 (1951).
[Crossref]

Werel, K.

K. Werel and L. Augustiniak, “Hyperfine structure analysis of some tellurium ii lines,” Phys. Scr. 23, 856–858 (1981).
[Crossref]

Acta Phys. Pol. (3)

J. Dembczyński and M. Frackoviak, “Hyperfine structure in intermediate coupling of the first excited electron configuration 6p27s of  83209Bi (I= 9/2),” Acta Phys. Pol. 48, 139–155 (1975).

J. Dembczyński, “Determination of the quadrupole moment of  51151Sb (I= 5/2) nucleus from hyperfine structure analysis,” Acta Phys. Pol. 49, 541–554 (1976).

B. Arcimowicz and J. Dembczyński, “Relativistic effects in the hyperfine structure of the second spectrum of the Bi ii ion,” Acta Phys. Pol. 56, 661–671 (1979).

J. Phys. B (1)

A. Rosén, “Analysis of the hyperfine structure of the ground state multiplet of the samarium atom,” J. Phys. B 2, 1257–1260 (1969).
[Crossref]

Phys. Rev. (2)

J. S. Ross and K. Murakawa, “Hyperfine structure and isotope shift in the spectrum of tellurium,” Phys. Rev. 85, 559–563 (1952).
[Crossref]

S. S. Dharmatti and H. E. Weaver, “On the magnetic moment of Te123,125 and Si29*,” Phys. Rev. 84, 843–844 (1951).
[Crossref]

Phys. Rev. A (2)

W. J. Childs, “Hyperfine structure of many atomic levels of Tb159 and the Tb159 nuclear electric quadrupole moment,” Phys. Rev. A 2, 316–336 (1970).
[Crossref]

W. J. Childs and L. S. Goodman, “Hyperfine and Zeeman studies of low lying atomic levels of La139 and the nuclear electric quadrupole moment,” Phys. Rev. A 3, 25–45 (1971).
[Crossref]

Phys. Scr. (1)

K. Werel and L. Augustiniak, “Hyperfine structure analysis of some tellurium ii lines,” Phys. Scr. 23, 856–858 (1981).
[Crossref]

Physica (1)

M. B. Handrup and J. E. Mack, “On the spectrum of ionized tellurium,” Physica 30, 1245–1275 (1964).
[Crossref]

Proc. R. Soc. London Sect. A (1)

P. G. H. Sandars and J. E. Beck, “Relativistic effects in many electron hyperfine structure,” Proc. R. Soc. London Sect. A 289, 97–107 (1965).
[Crossref]

Z. Phys. A (2)

S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine structure of seven atomic levels of 91Zn and the 91Zn nuclear electric quadrupole moment,” Z. Phys. A 286, 125–131 (1978).
[Crossref]

K. H. Bürger, S. Büttgenbach, R. Dicke, H. Gebauer, R. Kuhnen, and F. Träber, “Hyperfine and Zeeman studies of low lying atomic levels of 181Ta and the nuclear electric quadrupole moment,” Z. Phys. A 298, 159–165 (1980).
[Crossref]

Other (3)

C. E. Moore, Atomic Energy Levels (U.S. Government Printing Office, Washington, D.C., 1958).

L. Armstrong, Theory of the Hyperfine Structure of Free Atoms (Wiley, Interscience, New York, 1971).

H. Kopfermann, Kernmomente (Frankfurt am Main, Germany, 1956).

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Figures (1)

Fig. 1
Fig. 1

Intensity distribution of the λ 629.4-nm ( 81 3 / 2 - 97 1 / 2 ) transition. Open circles, experimental profile linear in intensity; solid line, theoretical profile; dashed lines, theoretical profiles of single hfs components.

Tables (7)

Tables Icon

Table 1 Hyperfine-Structure Splittings and A Constants for the Energy Levels of the 5s25p26p Configuration of Te ii

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Table 2 Radial Parameters for 5p26p Configuration of Te ii

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Table 3 Observed and Calculated Energy Levels and g Factors of the 5p26p Configuration in Te ii

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Table 4 Eigenvectors αττ of the 5p26p Configuration in Te ii

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Table 5 Nonvanishing Matrix Elements Diagonal in J for Magnetic-Dipole hfs Interaction in the 5p26p Configuration of Te ii

Tables Icon

Table 6 Experimental and Theoretical (Calculated in Casimir Approximation) aksk1 Values for the 5p26p Configuration of Te ii (in mK)

Tables Icon

Table 7 Experimental and Calculated A hfs Constants for the Energy Levels of 5p26p Configuration of Te ii (in mK)

Equations (5)

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

H hfs ( M 1 ) = i = 1 N [ a i 01 l i - 10 1 / 2 a l 12 ( s × C ( 2 ) ) i ( 1 ) + a l 10 s i ] I + [ a l 01 l N + 1 - 10 1 / 2 a l 12 ( s × C ( 2 ) ) N + 1 ( 1 ) + a l 10 s N + 1 ] I ,
A ( β ) = 2 C τ τ α τ β * α τ β S L J I F H hfs ( M 1 ) S L J I F ,
a l 01 = a n l ( 2 l + 1 ) - 2 [ 2 l ( l + 1 ) F r ( l + ½ , Z e f ) + 2 l ( l + 1 ) F r ( l - ½ , Z e f ) + G r ( l , Z e f ) ] , a l 12 = a n l ( 2 l + 1 ) - 2 [ - 4 l ( l + 1 ) ( 2 l - 1 ) F r ( 1 + ½ , Z e f ) + 4 l ( l + 1 ) ( 2 l + 3 ) F r ( l - ½ , Z e f ) - ( 2 l + 3 ) ( 2 l - 1 ) G r ( l , Z e f ) ] , a l 10 = / a n l l ( l + 1 ) ( 2 l + 1 ) - 2 [ ( l + 1 ) F r ( l + ½ , Z e f ) - l F r ( l - ½ , Z e f ) - G r ( l , Z e f ) ] .
r - 3 n l = ζ p R α 2 a 0 3 Z e f H r ( p , Z e f ) ,
0.34039 a 5 p 01 + 0.28568 a 6 p 01 + 0.14158 a 5 p 12 - 0.05714 a 6 p 12 + 0.23096 a 5 p 10 + 0.14284 a 6 p 10 = - 61 mK ( 103 7 / 2 ) , 0.51664 a 5 p 01 + 0.28568 a 6 p 01 - 0.08444 a 5 p 12 - 0.05713 a 6 p 12 + 0.05471 a 5 p 10 + 0.14284 a 6 p 10 = - 49 mK ( 112 7 / 2 ) , 0.48589 a 5 p 01 + 0.20912 a 6 p 01 + 0.15566 a 5 p 12 + 0.25358 a 6 p 12 + 0.27551 a 5 p 10 + 0.02944 a 6 p 10 = - 85 mK ( 102 5 / 2 ) , 0.41507 a 5 p 01 + 0.30518 a 6 p 01 + 0.16927 a 5 p 12 - 0.05527 a 6 p 12 + 0.22435 a 5 p 10 + 0.05551 a 6 p 10 = - 74 mK ( 105 5 / 2 ) , 0.54994 a 5 p 01 + 0.25927 a 6 p 01 - 0.07679 a 5 p 12 - 0.50307 a 6 p 12 + 0.08016 a 5 p 10 + 0.11059 a 6 p 10 = - 56 mK ( 111 5 / 2 ) , 0.21892 a 5 p 01 + 0.39020 a 6 p 01 - 0.18268 a 5 p 12 - 0.05265 a 6 p 12 + 0.21360 a 5 p 10 + 0.17727 a 6 p 10 = 0 mK ( 100 5 / 2 ) , 0.32995 a 5 p 01 + 0.42775 a 6 p 01 - 0.13996 a 5 p 12 + 0.29357 a 6 p 12 + 0.28404 a 5 p 10 - 0.04175 a 6 p 10 = - 30 mK ( 99 3 / 2 ) , 0.45950 a 5 p 01 + 0.33093 a 6 p 01 + 0.00688 a 5 p 12 + 0.02846 a 6 p 12 + 0.33458 a 5 p 10 - 0.12494 a 6 p 10 = - 54 mK ( 105 3 / 2 ) , 0.59948 a 5 p 01 - 0.33093 a 6 p 01 + 0.22331 a 5 p 12 - 0.11483 a 6 p 12 - 0.44866 a 5 p 10 + 0.28280 a 6 p 12 = - 96 mK ( 103 3 / 2 ) , 0.20799 a 5 p 01 + 0.46683 a 6 p 01 + 0.01858 a 5 p 12 - 0.12732 a 6 p 12 + 0.12472 a 5 p 10 + 0.20045 a 6 p 10 = - 30 mK ( 101 3 / 2 ) , 0.12853 a 5 p 01 + 0.55424 a 6 p 01 - 0.04155 a 5 p 12 - 0.07610 a 6 p 12 + 0.02795 a 5 p 10 + 0.28930 a 6 p 10 = - 10 mK ( 96 3 / 2 ) , - 0.02730 a 5 p 01 + 1.24426 a 6 p 01 + 0.06752 a 5 p 12 + 0.97838 a 6 p 12 + 0.11401 a 5 p 10 - 0.33087 a 6 p 10 = - 50 mK ( 93 1 / 2 ) , 1.25123 a 5 p 01 - 0.11539 a 6 p 01 + 0.73597 a 5 p 12 + 0.33688 a 6 p 12 .03456 a 5 p 10 - 0.17040 a 6 p 10 = - 252 mK ( 106 1 / 2 ) , - 0.32621 a 5 p 01 - 0.00618 a 6 p 01 - 0.27058 a 5 p 12 + 0.02984 a 6 p 12 + 0.55859 a 5 p 10 + 0.77389 a 6 p 10 = 75 mK ( 101 1 / 2 ) , 0.53941 a 5 p 01 + 0.20230 a 6 p 01 - 0.61881 a 5 p 12 - 0.49422 a 6 p 12 + 0.54371 a 5 p 10 - 0.28537 a 6 p 10 = 54 mK ( 97 1 / 2 ) ,