The Rmatrix computer packages utilized in the present computations
have been described in detail by Berrington et al. (1987). The twelve target
eigenstates which are included in the wavefunction representation of the
MgVI parent ion are
2s^{2}2pS, ^{2}D, ^{2}P;
2s2pP, ^{2}D, ^{2}S,
^{2}P;
2pP;
2s^{2}2p^{2}3sP, ^{2}P, ^{2}D and
^{2}S. These target eigenstates are represented by
configurationinteraction type waveexpansions constructed from seven
orthogonal oneelectron basis orbitals, consisting of four "spectroscopic"
(1s, 2s, 2p, 3s) and three "pseudo" type orbitals (,
, ), the latter being included to allow
explicitly for additional correlation effects. The radial part of each
of these orbitals may be expanded in the form:
Since the Rmatrix program requires all the target states to be
represented in terms of a singleorbital basis, our choice of orbital
parameters (, , ) were as follows.
The 1s, 2s and 2p orbital parameters were taken directly from the analysis
of Clementi & Roetti (1974). The parameters for the 3s spectroscopic
orbital were obtained by optimizing on the energy of the
2s^{2}2p^{2}3sP state using the
configurationinteraction computer package CIV3 as described by Hibbert
(1975). The configurations 2s2p^{4}, 2s^{2}2p^{2}3s and
2s2p^{3}[^{3}P] were included in this
optimization procedure. The parameters for the
pseudoorbital were similarly obtained by optimizing on the energy of the
2pP state using the configurations 2s^{2}2p^{3},
2p^{5} and 2p^{4}[^{3}P], while those for the
pseudoorbital were found by optimizing on the
2s2pP level with configurations 2s2p^{4},
2s^{2}2p^{2}[^{3}P] and
2s2p^{3}[^{3}P]. Finally the parameters for the only
n=4 pseudoorbital, , were obtained by optimizing
on the energy of the 2s2pD
state with configurations 2s2p^{4}, 2p^{4}3s, 2p and
2s2p^{3}[^{1}D].
The parameters adopted for all seven orbitals are presented in Table 1 (click here).
Table 2 (click here) displays the configurations, formed from this set of basis
orbitals, which are retained in the wavefunction expansion for both even
and odd parity target states.
2s^{2}2p^{3}  2s^{2}2p^{2} [3s, , ] 
2s^{2}2p  2s^{2}2p3s 
2s^{2}2p [3s^{2}, , , ]  2s2p^{4} 
2s2p^{3} [3s, , ]  2s2p 
2s^{2}2p3s [, ]  2s2p^{2} [3s^{2}, , , ] 
2s2p^{2}3s  2s2p^{2}3s [, ] 
2s2p3s [, , ]  2s2p3s 
2s2p3s^{2} [, ]  2s2p 
2p  2p^{4} [3s, , ] 
2p^{5}  2p^{3}3s 
2p^{3}3s^{2}  2p^{2}3s^{2} [, ] 
2p^{3}3s [, ]  2p^{2}3s [, , ] 
2p^{3} [, , ]  
2p^{2}3s  
2p3s^{2} [, , ]  

The twelve target eigenstates included in the present calculation correspond to 23 finestructure levels, each of which is assigned an index number in Table 3 (click here). Also shown in this table are the evaluated target state energies in atomic units relative to the 2s^{2}2pS ground state of MgVI. An examination of these energies can give a reasonable measure of the accuracy of the ion representation utilized in the present calculation. On comparing with the most recent experimental values of Kaufman & Martin (1991) we see that most of the theoretical thresholds differ by less than 1 from the experimental values, the greatest disparity occuring for the 2s^{2}2pS  2s^{2}2pD separation with a difference of less than 6%. Excellent agreement is also evident between the present thresholds and those obtained by the International Opacity Project (Burke & Lennon, unpublished). Following the normal Rmatrix procedures the present calculation has been carried out with the energies shifted to their experimental values. Also shown in Table 3 (click here) are the total number of configurations retained to describe each state.
A further indication of the reliability of the present wavefunction representation can be found by examining the close conformity between the length and velocity oscillator strength values for transitions between the target states. In Table 4 (click here) we present oscillator strengths, obtained using the configurationinteraction computer code CIV3 (Hibbert 1975), for optically allowed transitions among the lowest twelve LS states of MgVI, in both the length and velocity formulations. Transitions for which the oscillator strength is less than 10^{5} are not included. Excellent agreement is evident between the present length and velocity values with differences better than 9. There is at present a severe lack of other available oscillator strengths for MgVI. Hence, our comparison is limited to those obtained by the Opacity Project. Good agreement is, however, evident between their length values and the length values obtained by the present calculation. This would suggest that the present length values can be assigned an accuracy by using the difference between the present results and those from the Opacity Project. With a few exceptions, this would suggest an accuracy of better than 5. We note that the results of Bhatia & Mason (1980) for the 2s^{2}2p^{3}  2s2p^{4} transitions are always larger than both the present data and the Opacity Project values by typically 30%.
The theory describing the expansion of the MgVI ion plus electron system has been discussed in detail by Burke & Robb (1975). The Rmatrix boundary was set at 5.6 a.u., twenty continuum orbitals were included for each channel angular momentum and the electronimpact energy range of interest lies between 0 and 50 Rydbergs. All incident partial waves with total angular momentum , for both even and odd parities, and singlet, triplet and quintet multiplicities, were included in the wavefunction expansion. These seventyeight partial waves were found to be sufficient to ensure convergence of the collision strengths for the optically forbidden transitions. Contributions from the partial waves with total angular momentum L>12 become much more important for the dipole allowed transitions and need to be taken into account. It has been conclusively shown by Ramsbottom et al. (1994, 1995, 1996a, 1997), when investigating electronimpact excitation of NIV, NeVII, SII and ArIV respectively, that it is possible to estimate quite accurately these additional contributions for allowed transitions by assuming the partial collision strengths form a geometric series with a geometric scaling factor equal to the ratio of two adjacent terms. Contributions from the high partial waves L>12 can be as much as 1520% for some of the slowest converging transitions.
The Rmatrix computer packages produce collision strengths for
transitions between LS states only. However, for many astrophysical
and plasma applications it is often the collision strengths among
the finestructure levels which are required. Transforming to a
jjcoupling scheme can easily be achieved by utilizing the program
developed by Saraph (1978). Finally a thermally averaged effective
collision strength () may be derived from the collision
strength () by
where is the electron temperature in K, the energy of the final electron and k is Boltzmann's constant.
Index  J Level  Mg VI  Present  Expt.  Opacity  BAM  No. 
State  LS Energy  Project  Configs.  
1  3/2  2s^{2}2pS  0.0000  0.0000  0.0000  0.0000  31 
2  3/2  2s^{2}2pD  0.2668  0.2523  0.2592  0.2652  70 
3  5/2  
4  1/2  2s^{2}2pP  0.3971  0.3827  0.3915  0.3762  86 
5  3/2  
6  1/2  2s2pP  1.1259  1.1341  1.1219  1.1283  70 
7  3/2  
8  5/2  
9  3/2  2s2pD  1.5657  1.5572  1.5560  1.6029  97 
10  5/2  
11  1/2  2s2pS  1.8455  1.8308  1.8372  1.8680  47 
12  1/2  2s2pP  1.9601  1.9403  1.9495  2.0214  85 
13  3/2  
14  1/2  2pP  2.9704  2.9741  2.9650  86  
15  3/2  
16  1/2  2s^{2}2p^{2}3sP  4.0865  4.0802  4.0985  70  
17  3/2  
18  5/2  
19  1/2  2s^{2}2p^{2}3sP  4.1527  4.1448  4.1648  85  
20  3/2  
21  3/2  2s^{2}2p^{2}3sD  4.2984  4.2776  4.3031  97  
22  5/2  
23  1/2  2s^{2}2p^{2}3sS  4.5254  4.4808  4.5164  47  

  f_{L}  f_{V}  f_{L}  f_{V}  
2s^{2}2pS    2s2pP  0.1967  0.2158  0.2008  0.2168  0.261 
2s^{2}2pS    2s^{2}2p^{2}3sP  0.0985  0.0996  0.1255  0.1285  
2s^{2}2pD    2s2pD  0.1168  0.1264  0.1180  0.1280  0.155 
2s^{2}2pD    2s2pP  0.1679  0.1802  0.1680  0.1840  0.202 
2s^{2}2pD    2s^{2}2p^{2}3sP  0.0442  0.0458  0.0465  0.0466  
2s^{2}2pD    2s^{2}2p^{2}3sD  0.0481  0.0490  0.0582  0.0591  
2s^{2}2pP    2s2pD  0.0348  0.0368  0.0347  0.0375  0.046 
2s^{2}2pP    2s2pS  0.0708  0.0777  0.0718  0.0775  0.092 
2s^{2}2pP    2s2pP  0.0913  0.0987  0.0893  0.0975  0.113 
2s^{2}2pP    2s^{2}2p^{2}3sP  0.0705  0.0741  0.0635  0.0655  
2s^{2}2pP    2s^{2}2p^{2}3sD  0.0371  0.0382  0.0365  0.0378  
2s^{2}2pP    2s^{2}2p^{2}3sS  0.0168  0.0169  0.0248  0.0247  
2s2pD    2pP  0.1012  0.1073  0.1020  0.1120  
2s2pS    2pP  0.0380  0.0419  0.0373  0.0415  
2s2pP    2pP  0.2025  0.2181  0.2067  0.2250  
  