To properly resolve the complex autoionizing resonances in the collision
cross sections for each transition, we have utilized a very fine mesh of
incident impact energies (
0.0002 Ryd in the vicinity of the threshold
regions). The detailed resonances located below the highest-lying target
state threshold included in the present calculation
(2s22p23s
S
) are true structures,
whereas those found at energies above this level (8.96 Ryd) are
pseudo-resonances arising due to our inclusion of pseudo-orbitals in the
wavefunction representation (Burke et al. 1981). For increasing
temperatures this high impact energy region becomes much more important,
hence it is necessary to average over the pseudo-resonances to prevent
distortion of the results when the thermal averaging is performed.
Figure 1: Collision strength as a function of incident
electron energy in Rydbergs, and the effective collision strength
as a function of log temperature in Kelvin, for the
2s22p
S
-
2s22p
P
a) and b) and
2s22pS -
2s2p
P
c) and d)
fine-structure transitions
In Table 5 the effective collision strengths for all 253 possible independent transitions in MgVI are presented for a wide range of electron temperatures (log T(K) = 5.0 - log T(K) = 6.1). The index values assigned to the fine-structure levels in Table 3 (click here) are utilized again here to denote a particular transition. It is very difficult to gauge the behavior of the effective collision strengths from such a large table. Hence, in order to illustrate the physical effects more clearly, we have chosen four particular transitions all involving the 2s22p3 ground state configuration of MgVI.
S -
2s22pP (Figs. 1 (click here)a and b):
an example of a spin forbidden transition from the ground state
where the low-energy collision strength is strongly enhanced by
resonances.
S -
2s2pP (Figs. 1 (click here)c and d):
an example of an allowed transition from the ground state where
contributions from the higher-partial waves L>12 become more
important as the temperature increases.
D -
2s2p
D (Figs. 2 (click here)a and b):
an example of an allowed transition out of a metastable state
where the collision strength in the low-energy region is
sensitive to configuration-interaction, channel coupling
and resonance effects.
P -
2p
P (Figs. 2 (click here)c and d):
an example of a forbidden transition where resonance effects
in the collision cross section do not significantly effect
the corresponding effective collision strength.
S -
2s22pP fine-structure forbidden
transition. The low-energy collision strength is dominated by a mass of
resonance structure which results in a slightly enhanced effective
collision strength in the low temperature region. Such enhancements due
to resonances converging to the target state thresholds is a common
characteristic for forbidden transitions and has been consistently found
by Ramsbottom et al. (1994, 1995, 1996a,
1997) when investigating
electron-impact excitation of NIV, NeVII, SII and
ArIV respectively. It is difficult to gauge by how much the
resonances have enhanced the effective collision strength due to the
lack of other theoretical data available for comparison. Also common
for forbidden transitions of this kind is the decrease in the effective
collision strength as the temperature increases.
In Figs. 1 (click here)c and d we present the collision strength and the
corresponding effective collision strength for the dipole-allowed
2s22pS - 2s2pP
fine-structure transition. The most noticeable feature is the absence of
resonance structure in the collision cross section across the entire range
of electron-impact energies. This leads to an almost constant effective
collision strength in the low
temperature region. Contributions from the
high-partial waves L>12, however, become more and more important as the
temperature increases, resulting in a larger effective collision
strength at the high temperatures. This behavior is common for
dipole-allowed transitions of this kind. In contrast the collision strength
plotted in Fig. 2 (click here)a for the allowed 2s22pD -
2s2pD fine-structure transition has an abundance of
resonance structure in the low-energy region superimposed on an almost
constant background cross section. The corresponding effective collision
strength for this transition, plotted in Fig. 2 (click here)b, is as expected
significantly enhanced in the low temperature region by the presence of
these autoionizing resonances converging to the target state thresholds.
The characteristic rise of the effective collision strength for this
allowed transition is again evident in the high temperature region.
Figure 2: Collision strength as a function of incident
electron energy in Rydbergs, and the effective collision strength
as a function of log temperature in Kelvin, for the
2s22pD -
2s2pD a) and b) and
2s22pP -
2pP c) and d)
fine-structure transitions
Finally in Figs. 2 (click here)c and d we present the results for the remaining
forbidden transition considered, the 2s22pP -
2pP. The absence of autoionizing resonances
in the collision strength and the almost constant background cross section
leads to a uniform
effective collision strength across the entire
temperature range considered. At the higher temperatures, however, the
effective collision strength does seem to be decreasing which is
characteristic for a forbidden transition. Evidently there is a need for
a further sophisticated theoretical calculation to verify the results
presented here in the absence of a meaningful comparison.
The MgVI emission lines in the solar spectrum should be routinely detected by both the Coronal Diagnostic Spectrometer (CDS) and Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instruments on the Solar and Heliosphere Observatory, which cover the wavelength regions 150 - 800 Å and 500 - 1600 Å, respectively (Harrison et al. 1995; Wilhelm et al. 1995). In the near future we therefore intend to compare CDS/SUMER observations with MgVI theoretical line strengths generated using our atomic data, to investigate the usefulness of the lines as diagnostics.