T h e o r yT h e o r y

Inner region:

- exchange

- electron-electron correlation

- (N+1)-e- collision complex is similar to a bound state

- multicentre expansion of the target wavefunction

Outer region:

- exchange and correlation are negligible

- single centre expansion of the target wavefunction

The total N+1 wavefunction can be expanded in a close-coupling form:

Ψ(x1…xN+1) = ∑ Φi(x1…xN; rN+1 σN+1) rN+1-1 Fi (rN+1)

where Φ is a set of channel functions, F is the reduced radial wavefunction.

Electron-impact excitation of Be-like Mg

G.Del Zanna1,2, I. Rozum1, N. R. Badnell3

1 Mullard Space Science Laboratory, University College London, UK2 DAMTP, Centre for Mathematical Sciences, University of Cambridge, UK

3 Department of Physics, University of Strathclyde, UK

Support from STFC is acknowledged (GDZ: Advanced Fellowship and APAP network; NRB: APAP network

BackgroundBackground

• We present the first electron-impact excitation of Be-like Mg calculated using the R-matrix theory.• Previous excitation rates for the n=2 complex were obtained by Keenan et al. (1986) by interpolation along the sequence of the rates calculated with the R- matrix in LS-coupling. These have been used in the CHIANTI model, together with n=3 Distorted Wave (DW) data from Sampson et al. (1984). Recently, Bathia and Landi (2007) have done a new DW calculation up to n=4.• The intensity ratios of resonance versus intercombination transitions in the Be-like sequence is a well-known excellent temperature diagnostic.• The ratio between the Be-like Mg 2s 2p 1P1 - 2p2 1D2 (749.55 A) and the intercombination transition 2s2 1So, 2s 2p 3P1 (706.06 A) has provided one of few directed measurements of electron temperatures in the solar corona from SOHO, however discrepancies between theory and observations have been reported.

CalculationCalculation• 98 fine-structure levels, up to n = 4. Excited states generated using 1- and 2- electron excitations. Lowest 10 target states: 2s2 1So, 2s 2p 3Po, 2s 2p 3P1, 2s 2p 3P2, 2s 2p 1P1, 2p2 3Po, 2p2 3P1, 2p2 3P2, 2p2 1D2, 2p2 1So

• R-matrix with ICFT method, similar to Be-like Fe (Chidichimo et al. 2005). 80 (N+1)-electron configurations. In the inner region, exchange effects included up to J=12. Partial waves up to J=40 + top-up procedure for higher partial waves.• Collision strengths calculated for 15195 points in the resonance region (resolution of 0.00128 Ry) and up to 140 Ry outside.

Inner region

outer regione-

Mg

R-matrix boundary

Excitation ratesExcitation rates

• We have compared our collision strengths with those recently calculated by Bhatia & Landi (2007) using the Distorted Wave method and a similar target (boxes). Very good agreement is found in the background values.

Collision strengthsCollision strengths

• We have calculated Maxwellian-averaged collision strengths by extrapolating values toward the high-energy Born limits, calculated with AUTOSTRUCTURE. Each transition from the first 5 levels was visually inspected.

Comparison with a solar observationComparison with a solar observation

ConclusionsConclusions

Our explicit R-matrix calculation shows some significant differences with the interpolated results of Keenan et al. (1986), widely used for astrophysical applications. We have shown that our rates produce good agreement with observations of the solar corona, thus solving a long-standing problem for this ion.

• This plot compares our rates with those obtained by Keenan et al. (1986).• Good agreement is generally found, however some significant differences are present, which affect the populations (via direct excitation and cascading) of some important levels, most notably the 2s 2p 3P0,1,2 . For example, the population of the 2s 2p 3P1 increases by about 50%, due to the increase in the direct excitation from the ground and the cascading from the 2s 2p 3P2 , in turn due to the increased 2s2 1So - 2s 2p 3P2 collision rate.

ReferencesBhatia,A.K., Landi, E., 2007, ADNDT 93,742Chidichimo,M. C., Del Zanna, G.,Mason, H.E., Badnell,N. R., Tully, J.A., Berrington, K.A., 2005, A&A,430,331Feldman, U., Doschek, G. A., Sch¨uhle, U., & Wilhelm, K. 1999, ApJ, 518, 500Keenan, F. P., Berrington, K. A., Burke, P. G., Dufton, P. L., & Kingston, A. E. 1986, Phys. Scr, 34, 216Sampson, D.H., Goett, S.J., Clark, R.E.H, 1984, ADNDT, 30, 125

Emissivity ratio curves of a SOHO/SUMER off-limb spectrum of the quiet solar corona (Feldman et al.1999). The crossing of the intercombination with the 1P1– 1D2 line indicates a temperature of 1.4 MK with the present calculations, in good agreement with the independent measurement of1.35 MK by Feldman et al. (1999). The CHIANTI model indicates a lower temperature of 1 MK.