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T h e o r y Inner region: - exchange - electron-electron correlationPowerPoint Presentation

T h e o r y Inner region: - exchange - electron-electron correlation

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T h e o r y Inner region: - exchange - electron-electron correlation

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T h e o r y Inner region: - exchange - electron-electron correlation

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- Background
- 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 - 2p21D2 (749.55 A) and the
- intercombination transition 2s21So, 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.

e-

outer region

Mg

Inner region

R-matrix boundary

- Calculation
- 98 fine-structure levels, up to n = 4. Excited states generated using 1- and 2-
- electron excitations. Lowest 10 target states: 2s21So, 2s 2p 3Po, 2s 2p 3P1, 2s
- 2p 3P2, 2s 2p 1P1, 2p23Po, 2p23P1, 2p23P2, 2p21D2, 2p21So
- 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.

Electron-impact excitation of Be-like Mg

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

1 Mullard Space Science Laboratory, University College London, UK

2 DAMTP, Centre for Mathematical Sciences, University of Cambridge, UK

3 Department of Physics, University of Strathclyde, UK

T h e o r y

Inner region:

- exchange

- electron-electron correlation

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

- multicentre expansionof 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+1σN+1) rN+1-1 Fi (rN+1)

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

Excitation rates

- 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.

Collision strengths

- 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 2s21So - 2s 2p 3P2 collision rate.

- 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.

Comparison with a solar observation

- Conclusions
- Our explicit R-matrix calculation shows some significant differences with the interpolated results ofKeenan 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.

References

Bhatia,A.K., Landi, E., 2007, ADNDT 93,742

Chidichimo,M. C., Del Zanna, G.,Mason, H.E., Badnell,N. R., Tully, J.A., Berrington, K.A., 2005, A&A,430,331

Feldman, U., Doschek, G. A., Sch¨uhle, U., & Wilhelm, K. 1999, ApJ, 518, 500

Keenan, F. P., Berrington, K. A., Burke, P. G., Dufton, P. L., & Kingston, A. E. 1986, Phys. Scr, 34, 216

Sampson, 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 of

1.35 MK by Feldman et al. (1999). The CHIANTI model indicates a lower temperature of 1 MK.

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