The energy levels have been taken from Martin (1973). For
the *g*-levels which are missing, we have calculated the energies by using an
asymptotic expression of the quantum defect and the polarisation potential
(Deutsch 1969).

Calculations of oscillator strengths which enter the expressions of the
semi-classical cross-sections and the *A* parameters have been obtained with
the Bates & Damgaard approximation. Owing to the high levels involved, this
approximation is sufficient. Moreover these transitions and the corresponding
high levels are not included in the recent and sophisticated data of TOPbase
(Cunto et al. 1993). Thus for the calculations of the oscillator strengths
we have updated a code given by Dimitrijevic who used the tables by
Oertel & Shomo (1968) and the Van Regemorter et al. (1979) formula adapted
for high levels. For the transitions between the very high levels
*nf*-*n*'*g* (*n*, *n*' > 7), we have used the Coulomb approximation, the
corresponding quantum defects being negligible.

*C _{1}* is the impact validity criterion.

gives the ratio of the contribution of inelastic collisions versus elastic ones for the width.

*C _{3}* is the criterion for the "one state'' approximation validity criterion.

*C _{4}* is the ratio of the contribution of strong collisions to the total
impact width and thus gives a validity criterion for the perturbation theory
approximation.

*C _{5}* is the criterion for the isolated line approximation, defined by
(Dimitrijevic & Sahal Bréchot 1984; Baranger 1958b).

,

where *W* is the total width,

,

is the width due to electron
collisions, that due proton collisions and that due to collisions with He^{+}. We neglect collisions with He^{++}
in this criterion and we assume that protons and He^{+} ions are in
proportion of 90% and 10% respectively.

is the energy distance between the upper level and the nearest perturbing level.

Our calculations show that for all studied lines, when the impact
approximation is not valid (*C _{1}*>1), the elastic collisions
are generally dominant (

According to Dimitrijevic & Sahal-Bréchot (1984),
if *C _{5}*< 1, energy levels broadened by collisions do not overlap.
Then the line is isolated. If

In addition, we have checked the validity condition of the
perturbation theory. The validity criterion is given by *C _{4}*, which
represents the relative contribution of strong collisions to the total
impact width. It is well satisfied (

Finally, it can be noticed that the ionic shifts of 8651 Å and 8736 Å
lines present some deviations from linearity at 10^{13} cm^{-3} due
to the Debye cut-off.

Considering the validity conditions discussed above, our data can then be used for astrophysical purposes as follows:

1. If the impact approximation criterion () is satisfied, the resulting profiles are lorentzian, and the total widths and shifts are given by:

,

.

2. If the impact approximation criterion is satisfied for electronic collisions and not satisfied for the collisions with ions, then the quasistatic approximation can be used:

2a. If *C _{2}*> 1, the quasistatic interaction is dipolar. This case is not
treated in this paper.

2b. If the quasistatic interaction is quadratic (*C _{2}*< 1), which is
the predominant case, the resulting widths and shifts are given by:

,

.

However, it must be noticed that an intermediate region between the impact and quasistatic approximations is expected for collisions with ions, for which neither of the two limiting approximations is valid. For such conditions the static model employed can only give an estimate for the line shape.

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