In (4.6.37)–(4.6.40), b l are dipole moment operators of the considered transitions, m 1
j i, m 2
j i are transition frequencies.
Equations (4.6.37)–(4.6.40) are applicable for a weak interaction. If the transition to the W state is allowed, an admixture of the W
0 state results in extra lines
corresponding to the 2
j i excitation, which borrows the intensity from the 1
j i
transition.
4.6.1.6 Hyperfine Interactions Between Iodine Molecule Valence
States
Among the ten valence states corresponding to the second I 2 (ab) dissociation limit,
the only B0
þ
u state is deeply bound. Interactions between different electronic states
can be observed in the near-dissociation region, where multiple accidental resonances occur. Low-lying rovibrational levels of the B state have a hyperfine
structure, which has been perfectly described in the framework of the second-order
PT. Higher lying rovibrational levels with E > 20,000 cm
−1 energy (see Fig. 4.4)
can interact directly with the rovibrational levels of other electronic states, which
can be described within the first-order PT. Selection rules of the HFI define the
possible coupling between the B state and 9 other ones with X = 0, ± 1 and ± 2
quantum numbers (see Sect. 4.2.3, [7], p. 67 and [50, 53]). Additionally, there is a
superhyperfine structure at low-J rotational levels, also, where the energy gap
between levels is lower than HFI matrix elements, and several rotational levels are
coupled. These effects result in a complicated rovibrational structure of the B state.
Extensive analysis of the B − X transition (more than 10,000 hyperfine lines) was
performed in the range from dissociation limit down to 30 cm
−1 below (v B = 71–
82) [50, 53]. It was shown that the perturbations caused by the DX = 2 selection
rule (MQ interaction) are negligible.
The HF coupling is effective between near-lying rovibrational levels, which have
sufficiently large FCFs. Due to differences in the potential curves of the deeply
bound B and other shallow states, significant overlapping of their vibrational
wavefunctions is localized at the B state outer branch. Calculation of the FCFs
using accurate long-range (R > 7 Å) PECs [54] shows strong B0
þ
u * c1 g and
moderate B0
þ
u * (3)1 u (see Fig. 4.4) mixing that agrees with experiments. The
B * c interaction is the most effective and was found near at v B = 77 and 78 [53]
vibrational states. Analysis of the experimental data showed that the
B * c interaction has MD character essentially.
Using the two-state perturbation model described above, P. Jewsbury et al.
estimated the electronic matrix element for the B,59,J B * c,14,J c coupling of about
0.1 cm
−1 [51], similar that obtained by Pique et al. (0.206 cm
−1 ) [50]. Later, several
additional resonance levels with v B = 57–59, 63, 69, 71, 74, and 76 were found and
used as intermediate states for a population of the c1 u and H1 u IP states [54, 55].
The interaction between the B0
þ
u and (3) 0
À
u (B’) states was also found for some
rovibrational levels [56]. The coupling matrix elements were not estimated.
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4 Photolysis of Free Molecules
j i, m 2
j i are transition frequencies.
Equations (4.6.37)–(4.6.40) are applicable for a weak interaction. If the transition to the W state is allowed, an admixture of the W
0 state results in extra lines
corresponding to the 2
j i excitation, which borrows the intensity from the 1
j i
transition.
4.6.1.6 Hyperfine Interactions Between Iodine Molecule Valence
States
Among the ten valence states corresponding to the second I 2 (ab) dissociation limit,
the only B0
þ
u state is deeply bound. Interactions between different electronic states
can be observed in the near-dissociation region, where multiple accidental resonances occur. Low-lying rovibrational levels of the B state have a hyperfine
structure, which has been perfectly described in the framework of the second-order
PT. Higher lying rovibrational levels with E > 20,000 cm
−1 energy (see Fig. 4.4)
can interact directly with the rovibrational levels of other electronic states, which
can be described within the first-order PT. Selection rules of the HFI define the
possible coupling between the B state and 9 other ones with X = 0, ± 1 and ± 2
quantum numbers (see Sect. 4.2.3, [7], p. 67 and [50, 53]). Additionally, there is a
superhyperfine structure at low-J rotational levels, also, where the energy gap
between levels is lower than HFI matrix elements, and several rotational levels are
coupled. These effects result in a complicated rovibrational structure of the B state.
Extensive analysis of the B − X transition (more than 10,000 hyperfine lines) was
performed in the range from dissociation limit down to 30 cm
−1 below (v B = 71–
82) [50, 53]. It was shown that the perturbations caused by the DX = 2 selection
rule (MQ interaction) are negligible.
The HF coupling is effective between near-lying rovibrational levels, which have
sufficiently large FCFs. Due to differences in the potential curves of the deeply
bound B and other shallow states, significant overlapping of their vibrational
wavefunctions is localized at the B state outer branch. Calculation of the FCFs
using accurate long-range (R > 7 Å) PECs [54] shows strong B0
þ
u * c1 g and
moderate B0
þ
u * (3)1 u (see Fig. 4.4) mixing that agrees with experiments. The
B * c interaction is the most effective and was found near at v B = 77 and 78 [53]
vibrational states. Analysis of the experimental data showed that the
B * c interaction has MD character essentially.
Using the two-state perturbation model described above, P. Jewsbury et al.
estimated the electronic matrix element for the B,59,J B * c,14,J c coupling of about
0.1 cm
−1 [51], similar that obtained by Pique et al. (0.206 cm
−1 ) [50]. Later, several
additional resonance levels with v B = 57–59, 63, 69, 71, 74, and 76 were found and
used as intermediate states for a population of the c1 u and H1 u IP states [54, 55].
The interaction between the B0
þ
u and (3) 0
À
u (B’) states was also found for some
rovibrational levels [56]. The coupling matrix elements were not estimated.
122
4 Photolysis of Free Molecules