Abstract

We present a high-resolution analysis of the six electronic states that share the same dissociation limit with the second excited electronic state B in molecular iodine. These six states are coupled to the B state via hyperfine interactions. The four hyperfine parameters, CB, δB, dB, and eqQB, are calculated with the available potential energy curves and wave functions constructed from the separated-atom basis set. We obtain a maximum separation of the respective contributions from all six electronic states and compare each individual contribution with high-precision spectroscopic data, providing an independent verification of the relevant electronic structure.

© 2005 Optical Society of America

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    [Crossref]
  2. B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
    [Crossref]
  3. H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
    [Crossref]
  4. J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
    [Crossref]
  5. F.-L. Hong, J. Ye, L.-S. Ma, S. Picard, C. J. Bordé, and J. L. Hall, "Rotation dependence of electric quadrupole hyperfine interaction in the ground state of molecular iodine by high-resolution laser spectroscopy," J. Opt. Soc. Am. B 18, 379-387 (2001).
    [Crossref]
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    [Crossref]
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    [Crossref]
  8. C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
    [Crossref]
  9. C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
    [Crossref]
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    [Crossref]
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    [Crossref]
  14. F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
    [Crossref]
  15. W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
    [Crossref]
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    [Crossref]
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    [Crossref]
  20. J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
    [Crossref]
  21. F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
    [Crossref]
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    [Crossref]
  23. J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
    [Crossref]
  24. J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
    [Crossref]
  25. A. Morinaga, "Hyperfine structure and hyperfine coupling constant of molecular iodine," Jpn. J. Appl. Phys., Part 1 23, 774-775 (1984).
    [Crossref]
  26. W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  30. W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
    [Crossref]
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    [Crossref]
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    [Crossref]
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2004 (2)

H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
[Crossref]

L. Chen, W.-Y. Cheng, and J. Ye, "Hyperfine interactions and perturbation effects in the B0u+(Piu3) state of I2127," J. Opt. Soc. Am. B 21, 820-832 (2004).
[Crossref]

2003 (1)

L. Chen and J. Ye, "Extensive, high-resolution measurement of hyperfine interactions: precise investigations of molecular potentials and wave functions," Chem. Phys. Lett. 381, 777-783 (2003).
[Crossref]

2002 (1)

B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
[Crossref]

2001 (1)

2000 (2)

F. L. Hong and J. Ishikawa, "Hyperfine structures of the R(122) 35-0 and P(84) 33-0 transitions of I2127 near 532 nm," Opt. Commun. 183, 101-108 (2000).
[Crossref]

W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
[Crossref]

1999 (2)

T. J. Quinn, "Practical realization of the definition of the metre (1997)," Metrologia 36, 211-244 (1999).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

1998 (1)

W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
[Crossref]

1997 (2)

W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
[Crossref]

H. R. Simonsen, "Iodine-stabilized extended cavity diode laser at lambda=633 nm," IEEE Trans. Instrum. Meas. 46, 141-144 (1997).
[Crossref]

1996 (1)

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

1993 (2)

A. Razet, J. Gagniere, and P. Juncar, "Hyperfine structure analysis of the 33P (6-3) line of I2127 at 633 nm using a continuous-wave tunable dye laser," Metrologia 30, 61-65 (1993).
[Crossref]

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

1989 (1)

1988 (1)

P. Gill and J. A. Clancy, "A microprocessor-controlled iodine-stabilized ion laser," J. Phys. E 21, 213-218 (1988).
[Crossref]

1987 (1)

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

1986 (2)

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

1985 (1)

S. Gerstenkorn, P. Luc, and C. Amiot, "Analysis of the long range potential of iodine in the BPi0u+3 state," J. Phys. (France) 46, 355-364 (1985).
[Crossref]

1984 (3)

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

A. Morinaga, "Hyperfine structure and hyperfine coupling constant of molecular iodine," Jpn. J. Appl. Phys., Part 1 23, 774-775 (1984).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

1983 (1)

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

1982 (1)

M. Saute and M. Aubert-Frécon, "Calculated long-range potential-energy curves for the 23 molecular states of I2," J. Chem. Phys. 77, 5639-5646 (1982).
[Crossref]

1981 (2)

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

1980 (1)

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

1979 (1)

J. Vigué, M. Broyer, and J. C. Lehmann, "Ab initio calculation of hyperfine and magnetic parameters in the I2B state," Phys. Rev. Lett. 42, 883-887 (1979).
[Crossref]

1978 (1)

M. Broyer, J. Vigué, and J. C. Lehmann, "Effective hyperfine hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine," J. Phys. (France) 39, 591-609 (1978).
[Crossref]

1952 (1)

N. F. Ramsey and E. M. Purcell, "Interactions between nuclear spins in molecules," Phys. Rev. 85, 143L-144L (1952).
[Crossref]

Amiot, C.

S. Gerstenkorn, P. Luc, and C. Amiot, "Analysis of the long range potential of iodine in the BPi0u+3 state," J. Phys. (France) 46, 355-364 (1985).
[Crossref]

Aubert-Frécon, M.

M. Saute and M. Aubert-Frécon, "Calculated long-range potential-energy curves for the 23 molecular states of I2," J. Chem. Phys. 77, 5639-5646 (1982).
[Crossref]

Bacis, R.

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

Barney, W. S.

W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
[Crossref]

Barwood, G. P.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

Bertinetto, F.

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

Bodermann, B.

H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
[Crossref]

B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
[Crossref]

Bordé, C. J.

F.-L. Hong, J. Ye, L.-S. Ma, S. Picard, C. J. Bordé, and J. L. Hall, "Rotation dependence of electric quadrupole hyperfine interaction in the ground state of molecular iodine by high-resolution laser spectroscopy," J. Opt. Soc. Am. B 18, 379-387 (2001).
[Crossref]

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

Broyer, M.

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

J. Vigué, M. Broyer, and J. C. Lehmann, "Ab initio calculation of hyperfine and magnetic parameters in the I2B state," Phys. Rev. Lett. 42, 883-887 (1979).
[Crossref]

M. Broyer, J. Vigué, and J. C. Lehmann, "Effective hyperfine hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine," J. Phys. (France) 39, 591-609 (1978).
[Crossref]

Camy, G.

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

Chen, L.

L. Chen, W.-Y. Cheng, and J. Ye, "Hyperfine interactions and perturbation effects in the B0u+(Piu3) state of I2127," J. Opt. Soc. Am. B 21, 820-832 (2004).
[Crossref]

L. Chen and J. Ye, "Extensive, high-resolution measurement of hyperfine interactions: precise investigations of molecular potentials and wave functions," Chem. Phys. Lett. 381, 777-783 (2003).
[Crossref]

Cheng, W.-Y.

L. Chen, W.-Y. Cheng, and J. Ye, "Hyperfine interactions and perturbation effects in the B0u+(Piu3) state of I2127," J. Opt. Soc. Am. B 21, 820-832 (2004).
[Crossref]

W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
[Crossref]

Churassy, S.

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

Clancy, J. A.

P. Gill and J. A. Clancy, "A microprocessor-controlled iodine-stabilized ion laser," J. Phys. E 21, 213-218 (1988).
[Crossref]

Cordiale, P.

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

de Jong, W. A.

W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
[Crossref]

Decomps, B.

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

Descoubes, J.-P.

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

Donovan, R. J.

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

Edwards, C. S.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

Field, R. W.

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

Fontana, S.

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

Gagniere, J.

A. Razet, J. Gagniere, and P. Juncar, "Hyperfine structure analysis of the 33P (6-3) line of I2127 at 633 nm using a continuous-wave tunable dye laser," Metrologia 30, 61-65 (1993).
[Crossref]

Gerstenkorn, S.

S. Gerstenkorn, P. Luc, and C. Amiot, "Analysis of the long range potential of iodine in the BPi0u+3 state," J. Phys. (France) 46, 355-364 (1985).
[Crossref]

Gill, P.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

P. Gill and J. A. Clancy, "A microprocessor-controlled iodine-stabilized ion laser," J. Phys. E 21, 213-218 (1988).
[Crossref]

Hall, J. L.

Hartmann, F.

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

Hong, F. L.

F. L. Hong and J. Ishikawa, "Hyperfine structures of the R(122) 35-0 and P(84) 33-0 transitions of I2127 near 532 nm," Opt. Commun. 183, 101-108 (2000).
[Crossref]

Hong, F.-L.

Ishikawa, J.

F. L. Hong and J. Ishikawa, "Hyperfine structures of the R(122) 35-0 and P(84) 33-0 transitions of I2127 near 532 nm," Opt. Commun. 183, 101-108 (2000).
[Crossref]

Ito, N.

Janda, K. C.

W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
[Crossref]

Jewsbury, P. J.

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

Juncar, P.

A. Razet, J. Gagniere, and P. Juncar, "Hyperfine structure analysis of the 33P (6-3) line of I2127 at 633 nm using a continuous-wave tunable dye laser," Metrologia 30, 61-65 (1993).
[Crossref]

Knöckel, H.

H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
[Crossref]

B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
[Crossref]

Koffend, J. B.

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

Kraemer, G. T.

R. J. Le Roy and G. T. Kraemer, "BCONT 2.0. Computer program for calculating absorption coefficients, emission intensities or (golden rule) predissociation rates," University of Waterloo Chemical Physics Research Rep. CP-650 (University of Waterloo, Waterloo, Ontario, Canada, 2001). The source code and manual for this program may be obtained from the internet site http://leroy.uwaterloo.ca.

Lawley, K. P.

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

Le Roy, R. J.

R. J. Le Roy, "LEVEL 7.5: a computer program for solving the radial Schrödinger equation for bound and quasibound levels," University of Waterloo Chemical Physics Research Rep. CP-655 (University of Waterloo, Waterloo, Ontario, Canada, 2002). The source code and manual for this program may be obtained from the Computer Programs link on the Internet site http://leroy.uwaterloo.ca.

R. J. Le Roy and G. T. Kraemer, "BCONT 2.0. Computer program for calculating absorption coefficients, emission intensities or (golden rule) predissociation rates," University of Waterloo Chemical Physics Research Rep. CP-650 (University of Waterloo, Waterloo, Ontario, Canada, 2001). The source code and manual for this program may be obtained from the internet site http://leroy.uwaterloo.ca.

Lehmann, J. C.

J. Vigué, M. Broyer, and J. C. Lehmann, "Ab initio calculation of hyperfine and magnetic parameters in the I2B state," Phys. Rev. Lett. 42, 883-887 (1979).
[Crossref]

M. Broyer, J. Vigué, and J. C. Lehmann, "Effective hyperfine hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine," J. Phys. (France) 39, 591-609 (1978).
[Crossref]

Lin, T.

W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
[Crossref]

Llorente, F. Rodriguez

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

Luc, P.

S. Gerstenkorn, P. Luc, and C. Amiot, "Analysis of the long range potential of iodine in the BPi0u+3 state," J. Phys. (France) 46, 355-364 (1985).
[Crossref]

Ma, L.-S.

Martin, F.

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

Morinaga, A.

A. Morinaga, K. Sugiyama, and N. Ito, "Hyperfine structure of low-lying vibrational levels in the B-electronic state of molecular iodine," J. Opt. Soc. Am. B 6, 1656-1659 (1989).
[Crossref]

A. Morinaga, "Hyperfine structure and hyperfine coupling constant of molecular iodine," Jpn. J. Appl. Phys., Part 1 23, 774-775 (1984).
[Crossref]

Nieuwpoort, W. C.

W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
[Crossref]

Picard, S.

Picotto, G. B.

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

Pique, J. P.

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

Purcell, E. M.

N. F. Ramsey and E. M. Purcell, "Interactions between nuclear spins in molecules," Phys. Rev. 85, 143L-144L (1952).
[Crossref]

Quinn, T. J.

T. J. Quinn, "Practical realization of the definition of the metre (1997)," Metrologia 36, 211-244 (1999).
[Crossref]

Ramsey, N. F.

N. F. Ramsey and E. M. Purcell, "Interactions between nuclear spins in molecules," Phys. Rev. 85, 143L-144L (1952).
[Crossref]

Razet, A.

A. Razet, J. Gagniere, and P. Juncar, "Hyperfine structure analysis of the 33P (6-3) line of I2127 at 633 nm using a continuous-wave tunable dye laser," Metrologia 30, 61-65 (1993).
[Crossref]

Ridley, T.

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

Rowley, W. R. C.

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

Saute, M.

M. Saute and M. Aubert-Frécon, "Calculated long-range potential-energy curves for the 23 molecular states of I2," J. Chem. Phys. 77, 5639-5646 (1982).
[Crossref]

Shy, J. T.

W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
[Crossref]

Simonsen, H. R.

H. R. Simonsen, "Iodine-stabilized extended cavity diode laser at lambda=633 nm," IEEE Trans. Instrum. Meas. 46, 141-144 (1997).
[Crossref]

Sugiyama, K.

Tiemann, E.

H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
[Crossref]

B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
[Crossref]

Vergès, J.

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

Vigué, J.

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

J. Vigué, M. Broyer, and J. C. Lehmann, "Ab initio calculation of hyperfine and magnetic parameters in the I2B state," Phys. Rev. Lett. 42, 883-887 (1979).
[Crossref]

M. Broyer, J. Vigué, and J. C. Lehmann, "Effective hyperfine hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine," J. Phys. (France) 39, 591-609 (1978).
[Crossref]

Visscher, L.

W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
[Crossref]

Western, C. M.

W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
[Crossref]

Ye, J.

Chem. Phys. Lett. (1)

L. Chen and J. Ye, "Extensive, high-resolution measurement of hyperfine interactions: precise investigations of molecular potentials and wave functions," Chem. Phys. Lett. 381, 777-783 (2003).
[Crossref]

Eur. Phys. J. D (2)

B. Bodermann, H. Knöckel, and E. Tiemann, "Widely usable interpolation formulae for hyperfine splittings in the I2127 spectrum," Eur. Phys. J. D 19, 31-44 (2002).
[Crossref]

H. Knöckel, B. Bodermann, and E. Tiemann, "High precision description of the rovibronic structure of the I2B-X spectrum," Eur. Phys. J. D 28, 199-209 (2004).
[Crossref]

IEEE Trans. Instrum. Meas. (2)

H. R. Simonsen, "Iodine-stabilized extended cavity diode laser at lambda=633 nm," IEEE Trans. Instrum. Meas. 46, 141-144 (1997).
[Crossref]

F. Bertinetto, P. Cordiale, S. Fontana, and G. B. Picotto, "Helium-neon lasers stabilized to iodine at 605-nm," IEEE Trans. Instrum. Meas. 36, 609-612 (1987).
[Crossref]

J. Chem. Phys. (6)

R. Bacis, M. Broyer, S. Churassy, J. Vergès, and J. Vigué, "eQq measurements in the X, 1g, 0g+ and B state of I2: a test of the electronic molecular eigenfunctions," J. Chem. Phys. 73, 2641-2650 (1980).
[Crossref]

J. P. Pique, R. Bacis, M. Broyer, S. Churassy, and J. B. Koffend, "Calculation of the magnetic hyperfine interaction in the E and X states of iodine with the separated-atom theory," J. Chem. Phys. 80, 1390-1393 (1984).
[Crossref]

F. Martin, S. Churassy, R. Bacis, R. W. Field, and J. Vergès, "Long range behavior of the gerade states near the P3/22+P3/22 iodine dissociation limit by laser-induced-fluorescence Fourier-transform spectroscopy," J. Chem. Phys. 79, 3725-3737 (1983).
[Crossref]

W. S. Barney, C. M. Western, and K. C. Janda, "Measurement of the electronic wave function: separated atom wave function analysis of the R-dependent hyperfine constants of the iodine monochloride A state," J. Chem. Phys. 113, 7211-7223 (2000).
[Crossref]

W. A. de Jong, L. Visscher, and W. C. Nieuwpoort, "Relativistic and correlated calculations on the ground, excited, and ionized states of iodine," J. Chem. Phys. 107, 9046-9058 (1997).
[Crossref]

M. Saute and M. Aubert-Frécon, "Calculated long-range potential-energy curves for the 23 molecular states of I2," J. Chem. Phys. 77, 5639-5646 (1982).
[Crossref]

J. Mol. Spectrosc. (1)

P. J. Jewsbury, T. Ridley, K. P. Lawley, and R. J. Donovan, "Parity mixing in the valence states of I2 probed by optical-optical double-resonance excitation of ion-pair states--characterization of a new ion-pair state, H1u(P13), and a valence state, c1g," J. Mol. Spectrosc. 157, 33-49 (1993).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. (France) (5)

C. J. Bordé, G. Camy, B. Decomps, and J.-P. Descoubes, "High precision saturation spectroscopy of I2127 with argon lasers at 5145 Å and 5017 Å--main resonances," J. Phys. (France) 42, 1393-1411 (1981).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. II. Experiments on I2," J. Phys. (France) 47, 1917-1929 (1986).
[Crossref]

M. Broyer, J. Vigué, and J. C. Lehmann, "Effective hyperfine hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine," J. Phys. (France) 39, 591-609 (1978).
[Crossref]

S. Gerstenkorn, P. Luc, and C. Amiot, "Analysis of the long range potential of iodine in the BPi0u+3 state," J. Phys. (France) 46, 355-364 (1985).
[Crossref]

J. P. Pique, F. Hartmann, S. Churassy, and R. Bacis, "Hyperfine interactions in homonuclear diatomic molecules and u-g perturbations. I. Theory," J. Phys. (France) 47, 1909-1916 (1986).
[Crossref]

J. Phys. E (1)

P. Gill and J. A. Clancy, "A microprocessor-controlled iodine-stabilized ion laser," J. Phys. E 21, 213-218 (1988).
[Crossref]

Jpn. J. Appl. Phys., Part 1 (1)

A. Morinaga, "Hyperfine structure and hyperfine coupling constant of molecular iodine," Jpn. J. Appl. Phys., Part 1 23, 774-775 (1984).
[Crossref]

Metrologia (3)

C. S. Edwards, G. P. Barwood, P. Gill, and W. R. C. Rowley, "A 633 nm iodine-stabilized diode-laser frequency standard," Metrologia 36, 41-45 (1999).
[Crossref]

A. Razet, J. Gagniere, and P. Juncar, "Hyperfine structure analysis of the 33P (6-3) line of I2127 at 633 nm using a continuous-wave tunable dye laser," Metrologia 30, 61-65 (1993).
[Crossref]

T. J. Quinn, "Practical realization of the definition of the metre (1997)," Metrologia 36, 211-244 (1999).
[Crossref]

Opt. Commun. (4)

F. L. Hong and J. Ishikawa, "Hyperfine structures of the R(122) 35-0 and P(84) 33-0 transitions of I2127 near 532 nm," Opt. Commun. 183, 101-108 (2000).
[Crossref]

C. S. Edwards, G. P. Barwood, P. Gill, F. Rodriguez Llorente, and W. R. C. Rowley, "Frequency-stabilised diode lasers in the visible region using Doppler-free iodine spectra," Opt. Commun. 132, 94-100 (1996).
[Crossref]

W.-Y. Cheng, J. T. Shy, and T. Lin, "A compact iodine-stabilized HeNe laser and crossover resonances at 543 nm," Opt. Commun. 156, 170-177 (1998).
[Crossref]

J. P. Pique, F. Hartmann, R. Bacis, and S. Churassy, "Hyperfine structure of higher rovibrational levels in the iodine B state studied by Ar+ laser induced fluorescence," Opt. Commun. 36, 354-358 (1981).
[Crossref]

Phys. Rev. (1)

N. F. Ramsey and E. M. Purcell, "Interactions between nuclear spins in molecules," Phys. Rev. 85, 143L-144L (1952).
[Crossref]

Phys. Rev. Lett. (2)

J. P. Pique, F. Hartmann, R. Bacis, S. Churassy, and J. B. Koffend, "Hyperfine-induced ungerade-gerade symmetry breaking in a homonuclear diatomic molecule near a dissociation limit: I2127 at the P3/22-P1/22 limit," Phys. Rev. Lett. 52, 267-270 (1984).
[Crossref]

J. Vigué, M. Broyer, and J. C. Lehmann, "Ab initio calculation of hyperfine and magnetic parameters in the I2B state," Phys. Rev. Lett. 42, 883-887 (1979).
[Crossref]

Other (2)

R. J. Le Roy, "LEVEL 7.5: a computer program for solving the radial Schrödinger equation for bound and quasibound levels," University of Waterloo Chemical Physics Research Rep. CP-655 (University of Waterloo, Waterloo, Ontario, Canada, 2002). The source code and manual for this program may be obtained from the Computer Programs link on the Internet site http://leroy.uwaterloo.ca.

R. J. Le Roy and G. T. Kraemer, "BCONT 2.0. Computer program for calculating absorption coefficients, emission intensities or (golden rule) predissociation rates," University of Waterloo Chemical Physics Research Rep. CP-650 (University of Waterloo, Waterloo, Ontario, Canada, 2001). The source code and manual for this program may be obtained from the internet site http://leroy.uwaterloo.ca.

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Figures (11)

Fig. 1
Fig. 1

PECs for ten electronic states converging to the P 3 2 2 + P 1 2 2 dissociation limit over the range 2.5 Å < R < 6.5 Å . These PECs are adopted from the relativistic calculations by de Jong et al.[30] except for the B state, for which an empirical PEC[29] is used.

Fig. 2
Fig. 2

Long-range PECs for the ten electronic states, adopted from Ref. [32]. Dashed line, the P 3 2 2 + P 1 2 2 dissociation limit. Note that 1 u and 1 g refer to the C : 1 u ( Σ u + 3 ) and 1 g ( Σ g 3 ) states, respectively.

Fig. 3
Fig. 3

Combining the short- and long-range potentials. Solid curves, the short-range ( R < 7 Å ) PECs from the ab initio calculation[30]; dashed curves, the ab initio long-range PECs from Ref. [32]. To make a smooth connection between two segments of the PEC, each short-range ( R < 7 Å ) PEC has been shifted vertically to match the corresponding long-range one. The unchanged B-state empirical PEC[29] and ab initio long-range PEC are also included.

Fig. 4
Fig. 4

B-state rovibrational structure. Thick solid curves are the empirical B-state rotationless potential.[29] Vibrational levels υ = 57 68 are indicated as short-dashed lines. The rotational levels at several vibrational levels are also drawn as short bars. The curve of long dashes is the effective potential (a sum of the rotationless and centrifugal potentials) associated with a rotational level ( υ = 60 , J = 83 ) . The probability distributions of the molecular vibration for levels ( υ = 60 , J = 0 ) and ( υ = 60 , J = 83 ) are plotted as thin solid curves for comparison of the internuclear separations populated by the two levels.

Fig. 5
Fig. 5

Two 1 u PECs used in the calculation of C B . Also plotted is the B-state empirical potential,[29] which is used for all internuclear separations. C : 1 u and 1 u PECs ( R < 7 Å ) are constructed from theoretical[30] ( R < 7 Å ) and long-range PECs[32] ( R 7 Å ) . The PECs from ab initio calculation are shifted vertically to match the corresponding long-range ones. Dashed lines, the vibrational levels of the C : 1 u state. The 1 u and C : 1 u states are also denoted by 1 u and 1 u , respectively.

Fig. 6
Fig. 6

Second-order calculations of the spin–rotation parameter C B . Filled circles, spectroscopic data from the literature[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; other symbols and lines, calculations. (a) With a mixing parameter α = 0.99 (open circles on solid curve) for two 1 u states, the calculations agree well with the experimental data,[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] whereas changing α to 0.9 (squares on dashed curve) results in a large global deviation from the experimental data. (b) A deliberate reduction of the potential depths of the two 1 u PECs (triangles on solid curve) produces a noticeable discrepancy at R c = 4.2 5.5 Å but does not affect calculations at shorter and longer internuclear separations. (c) At R c < 4 Å , the calculation begins to depart from the experimental data.[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]

Fig. 7
Fig. 7

Rotational dependence of C B around two vibrational levels υ = 47 and 70. Filled circles and solid curves, experimental data[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] and fit, respectively. Open circles, calculation by second-order perturbation theory. Dashed curves, fits to the computed points.

Fig. 8
Fig. 8

Separation of the contributions from the 0 u and 0 g states. (a), The overall contribution of the 0 u and 0 g states to δ B . (b) and (c), Two separated contributions. Filled circles, values deduced from the experimental data[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] on δ B , d B , and eq Q B [see Eqs. (21, 23) and text for details]. Open squares on dashed curves, the calculations; open circles on solid curves, the calculation with the 0 u -long-range PEC replaced by that of the 2 g state (see Fig. 2 for the two long-range PECs). In this calculation, there is no adjustable parameter for the electronic wave functions.

Fig. 9
Fig. 9

Semilogarithmic plot of the second-order calculation of the scalar spin–spin parameter δ B . Filled circles, experimental data[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; open circles, calculations. In the calculation, the mixing parameters for the two 1 u and the two 1 g states are fixed to α = 0.92 and β = 0.84 , respectively. Because the contribution from 1 g ( Π g 1 ) state is extremely sensitive to the corresponding long-range potential, the 1 g ( Π g 1 ) long-range potential is fine tuned (see Fig. 2) to obtain good agreement with the experimental data.[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]

Fig. 10
Fig. 10

Semilogarithmic plot of the second-order calculation of the tensor spin–spin parameter d B . Filled circles, experimental data[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; open circles, calculations. The calculation combines the contributions from all six states [see Eq. (20)] that are determined in the calculation of δ B . The calculation provides a cross-check of the 1 g long-range PEC and the mixing parameters α and β.

Fig. 11
Fig. 11

Second-order calculation of the electric quadrupole parameter eq Q B . Filled circles, experimental data[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; open circles, calculations. The calculation combines the contributions from the same six states used for Figs. 9, 10. The calculation provides a cross-check of the 1 g long-range PEC and the mixing parameters α and β. The relatively large discrepancy is due to the fact that the residual error of δ ( 1 g ) (the contribution of the 1 g states to δ B ) has been amplified by a factor of 10 in the case of eq Q B [see Eq. (19) and expression (22)].

Equations (28)

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H hf = H hf ( a ) + H hf ( b ) + H hf ( a , b ) ,
H hf = α = a , b k q = k k ( 1 ) q Q q k ( I α ) V q k ( e α ) ,
ψ = Ω υ J I F M F ,
ψ H hf k ( a ) ψ = δ F F δ M F M F ( 1 ) F + Δ I + 2 I a + Δ J + k [ ( 2 J + 1 ) ( 2 J + 1 ) ( 2 I + 1 ) ( 2 I + 1 ) ] 1 2 ( J k J Ω Δ Ω Ω ) { J k J I F I } { k I a I a I a I I } f k ( a , Ω , υ J , Ω , υ J ) ,
f k ( a , Ω , υ J , Ω , υ J ) = ( 1 ) Ω C k ( k I a I a 0 I a I a ) Ω υ J V Δ Ω k ( a ) Ω υ J .
Q I a = e I a , M I a = I a p ( 3 z p 2 r p 2 ) I a , M I a = I a ,
ψ ϵ = ( 1 2 ) ϵ [ Ω , υ J I F M F + ϵ Ω , υ J I F M F ] ,
( 1 2 ) ϵ + ϵ { [ 1 + ϵ ϵ ( 1 ) Δ J ] f k ( a , Ω , υ J , Ω , υ J ) + C ( Ω + ) [ ϵ + ϵ ( 1 ) Δ J ] f k ( a , Ω , υ J , Ω , υ J ) } ,
C ( Ω + ) = ( J k J Ω Ω + Ω ) ( J k J Ω Δ Ω Ω )
( 1 2 ) ϵ [ 1 + ϵ ( 1 ) Δ J ] f k ( a , Ω , υ J , 0 u + , υ J ) .
ψ u , I H hf k ( b ) ψ u , I = ( 1 ) Δ I ψ u , I H hf k ( a ) ψ u , I ,
ψ u , I H hf k ( b ) ψ g , I = ( 1 ) Δ I + 1 ψ u , I H hf k ( a ) ψ g , I ,
V 0 = 2 2 μ R 2 [ J + ( L + S ) + J ( L + + S + ) ] ,
V 0 = 1 u , ϵ = 1 V 0 0 u + = [ 2 J ( J + 1 ) ] 1 2 1 2 [ 1 u ( Ω = 1 ) , υ J 2 2 2 μ R 2 ( L + + S + ) 0 u + υ J + 1 u ( Ω ) , υ J 2 2 2 μ R 2 ( L + S ) 0 u + υ J ] = [ 2 J ( J + 1 ) ] 1 2 2 1 u ( Ω = 1 ) , υ J 2 2 2 μ R 2 ( L + + S + ) 0 u + υ J = [ 2 J ( J + 1 ) ] 1 2 2 f 0 ( 1 u , 0 u + ) .
C B = C D 4 [ I a ( I a + 1 ) ( 2 I a + 1 ) ] 1 2 × 1 u [ υ f 0 ( 1 u , 0 u + ) f 1 ( a , 0 u + , 1 u ) E 0 u + υ J E 1 u υ J + 2 π ( μ 2 2 ) 1 2 E 0 d E 1 u J f 0 ( 1 u , 0 u + ) f 1 ( a , 0 u + , 1 u ) E u ( E 0 0 + υ J E 1 u J ) ] ,
δ B = 2 3 I a ( I a + 1 ) ( 2 I a + 1 ) Ω χ i ( 1 + ϵ ) [ υ f 1 ( a , Ω , 0 u + ) 2 E 0 u + υ J E Ω υ J + 2 π ( μ 2 2 ) 1 2 E 0 d E Ω J f 1 ( a , Ω , 0 u + ) 2 E u ( E 0 u + υ J E Ω J ) ] ,
d B = 1 3 I a ( I a + 1 ) ( 2 I a + 1 ) Ω χ i ( 3 Ω 2 2 ) ( 1 + ϵ ) [ υ f 1 ( a , Ω , 0 u + ) 2 E 0 u + υ J E Ω υ J + 2 π ( μ 2 2 ) 1 2 E 0 d E Ω J f 1 ( a , Ω , 0 u + ) 2 E u ( E 0 u + υ J E Ω J ) ] ,
eq Q B = eq Q 0 4 2 1 u [ υ 4 f 0 ( 1 u , 0 u + ) f 2 ( a , 0 u + , 1 u ) E 0 u + υ J E 1 u υ J + 2 π ( μ 2 2 ) 1 2 E 0 d E 1 u J 4 f 0 ( 1 u , 0 u + ) f 2 ( a , 0 u + , 1 u ) E u ( E 0 u + υ J E 1 u J ) ] + 10 k , k = 1 , 2 Ω ( 1 ) 2 I a + Ω ( 1 + ϵ ) × [ υ 2 f k * ( a , Ω , 0 u + ) f k ( a , Ω , 0 u + ) E 0 u + υ J E Ω υ J + 2 π ( μ 2 2 ) 1 2 × E 0 d E Ω J 2 f k * ( a , Ω , 0 u + ) f k ( a , Ω , 0 u + ) E u ( E 0 u + υ J E Ω J ) ] × ( k k 2 Δ Ω Δ Ω 0 ) { I a 2 I a k I a k } { 2 I a I a 0 I a I a } .
1 u = α 1 u 1 α 2 1 u ,
1 u = α 1 u + 1 α 2 1 u ,
1 g = β 1 g + 1 β 2 1 g ,
1 g = β 1 g 1 β 2 1 g ,
δ B = δ ( 1 u ) + δ ( 1 g ) + δ ( 0 g ) + δ ( 0 u ) .
d B = 1 2 δ ( 1 u ) + 1 2 δ ( 1 g ) δ ( 0 g ) δ ( 0 u ) .
[ δ ( 0 g ) + δ ( 0 u ) ] = 1 3 ( δ B 2 d B ) ,
1 20 [ eq Q B eq Q 0 ] 1 2 δ ( 1 u ) + 1 2 δ ( 1 g ) δ ( 0 g ) + δ ( 0 u ) ,
[ δ ( 1 u ) 2 δ ( 0 u ) ] = d B 1 20 ( eq Q B eq Q 0 ) ,
[ δ ( 1 u ) + 2 δ ( 0 g ) ] = 2 3 δ B 1 3 d B 1 20 ( eq Q B eq Q 0 ) ,

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