3.1. Atomic Structure and Electron Scattering Data
We have used the following nine configurations in our calculation: 1s
22s
22p
6: 3s
2, 3s3p, 3p
2, 3s3d, 3p3d, 3s4s, 3s4p, 3s4d, and 3s5s, which give rise to 38 levels, which are listed in
Table 1 with their energies in cm
−1. These values have been compared with the observed ones taken from the tables of the National Institute of Standards and Technology database: NIST [
22] which are originally from Saloman [
23]. We compare also with the energies computed using the multiconfiguration Hartree–Fock method (MCHF) [
24] and with those obtained using the AUTOSTRUCTURE code [
25]. The averaged disagreement between these three results is less than 1%. We detect an inversion between the two levels 10/13 and 25/26 regarding those of NIST and MCHF. This inversion does not affect the calculations since the agreement is still acceptable (about 5%).
We present also in
Table 2 radiative decay rates
, weighted oscillator strengths
, and line strengths
S for some Ar VII lines up to the level 14 (3s3d
). Our
values have been compared with those obtained from the AUTOSTRUCTURE code [
25], and with those from the SUPERSTRUCTURE code [
26] using five configurations (1s
22s
22p
6: 3s
2, 3s3p, 3p
2, 3s3d, and 3s4s). The averaged difference is about 20% with the results of [
25] and about 24% with those of Christensen et al. [
26]. Some transitions present a high difference, especially those for which
are relatively small (about 10
6 s
−1 and below). The
values have been compared only with Christensen et al. [
26] and the difference is about 24 %. The
values are calculated in [
26], but we took them from the database CHIANTI version 8.0 [
27].
With the code JAJOM, fine structure collision strengths are calculated for low partial waves
l of the incoming electron up to 29. For large partial waves
l, this method becomes cumbersome and inaccurate, but their contributions to collision strengths cannot be neglected. For
, two different procedures have been used: for dipole transitions, the contribution has been calculated using the JAJOM-CBe code (Dubau, unpublished results) based upon the Coulomb–Bethe formulation of Burgess and Sheorey [
28] and adapted to JAJOM approximation. For non-dipole transitions, the contribution has been estimated by the SERIE-GEOM code assuming a geometric series behavior for high partial wave collision strengths [
29,
30].
We present our collision strengths from the lowest five levels to the first 14 levels in
Table 3 at electron energy values 7.779, 13.674, and 23.336 Ry. We compared them with the 5-configurations collision strengths of Christensen et al. [
26]. Some important discrepancies exist for transitions involving levels arising from the 3p
3 configuration (levels 7, 8, and 9). Except for these transitions, the agreement (averaged over the three energies and all the other transitions) is about 20%. The agreement between our results and those of [
26] is the worse for the electron energy 7.779 Ry. This energy is close to the excitation energy of the last calculated level (here the energy 6.80 Ry of the level 38). In this situation, the contribution of elastic collisions (which are mostly due to close/strong collisions) is important. We remark also that the agreement is better for transitions from higher levels: for example,
is about 39% for transitions from the level
1, and it is about 15% for transitions from the levels
. We note that, in [
26], calculations have been carried out for partial waves
. This may be the origin of the above disagreement for some transitions (we have taken into account partial waves up to 50 in the present work). The difference in the configurations number may also affect the collision strength values.
3.2. Line Broadening Results
Two methods for line broadening calculations have been used in our work. The first is the quantum mechanical approach (
Q), and the second is the semiclassical perturbation method
. To evaluate the line broadening through the second method, we need atomic parameters such as energy levels and oscillator strengths. In our SCP calculations (
), we have taken atomic data of the code SST [
14]. We compare our results (
Q and
) to the SCP calculations (
) performed in [
12], where atomic data have been taken from the method of Bates and Damgaard [
13]. This method has been used many times with different ions, and it has been shown that the corresponding results (using the Bates and Damgaard or the SST data) are in good agreement with experimental and other theoretical results [
31,
32,
33]. Many of these SCP results have been stored in the database STARK-B [
34].
We have performed quantum (
Q) and semiclassical perturbation (
) Stark broadening for 12 lines of Ar VII for electron temperature range (
K and at electron density
cm
−3. We present our results in
Table 4 for transitions between singlets, in
Table 5 for the resonance line 3s
2 −3s3p
, and in
Table 6 for transitions between triplets. A comparison was made between our quantum and our semiclassical perturbation results
in
Table 4 and
Table 5. We also included the semiclassical results
[
12] in
Table 6 in our comparison.
Table 4 and
Table 6 show that the quantum line widths are always higher than the two semiclassical ones (
and
). We also found that, except for the resonance line, the ratio
increases and decreases with temperature. The decreasing part starts in general at
K. For the resonance line 3s
2 −3s3p
, the ratio
increases with
T. As per
Table 5, this ratio has the same behavior as that of the other lines (increasing and after decreasing) but starts to decrease for higher temperatures (
K).
Table 6 shows that, in all studied cases, the
widths are closer to the quantum results than the
ones. The disagreement between
and
results is due to the difference in the source of the used atomic data.
To understand the difference between SCP and quantum calculations, we present also, in
Table 4 and
Table 6, the contributions of elastic
and strong
collisions to the
line broadening. Firstly, we remark that, for
K and except the resonance line, the ratios
and
decrease with the temperature. Secondly, we see that, for each line, as the elastic and strong collisions contributions decrease, the two results (Q and SCP) become close to each other. For electron temperature
K, we can detect in some cases an opposite behavior between
and
on the one hand and the ratio
on the other hand. This may be due to the contributions of resonances that are dominant at low temperatures. These contributions are taken into account differently in the quantum and the semiclassical perturbative methods.
Figure 1 shows the behavior of the ratios
and
with the electron temperature for the 3s3d
− 3s4p
, 3s3p
−3s4d
, 3s4p
−3s4d
, and 3s3p
−3s4s
transitions. In fact, the Ar VII perturbing levels
and
are so far from the initial (
i) and final (
f) levels of the considered transition (
and
are high) and, due to this fact, for collisions by electrons, the close collisions are important. Furthermore, with the used temperature values, the ratio
is high and consequently, the inelastic cross sections are small compared to the elastic ones that become dominant (mostly due to the close collisions). The perturbative treatment in the semiclassical approach does not correctly estimate this contribution. In that situation, it is necessary to perform more sophisticated calculations such as the quantum ones. We have shown in Elabidi et al. [
11], through extensive comparisons between quantum and semiclassical Stark broadening of Ar XV lines, that the disagreement between the two results increases with the increase in strong collision contributions.
Figure 2 displays the Stark widths as a function of the electron temperature at a constant electron density for two selected lines between singlets : 3s
2 −3s4p
and 3s4p
−3s5s
and two lines between triplets: 3s3p
−3s4d
, and 3s3d
3s4p
.
The obtained Stark broadening parameters will be useful for the investigation and modeling of the plasma of stellar atmospheres. They will be also important for the investigation of laser-produced and inertial fusion plasmas.