This document discusses theoretical atomic and molecular physics research being conducted on recombination lines in nebulae spectra. The research group is investigating two recombination processes, radiative and dielectronic recombination, using atomic structure and R-matrix codes. They are studying carbon and magnesium ions to analyze planetary nebulae and draw conclusions about nebula conditions and compositions.

1. Theoretical Atomic and Molecular Physics and Astrophysics
Recombination Lines in the Spectrum of Nebulae
Taha Sochi & Peter Storey

2. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Recombination Processes
Our primary interest is in two recombination processes:
• Radiative recombination:
Xn+ + e−
→ X∗
(n−1)+ + hν
where Xn+ is an ion of effective charge n and X∗
(n−1)+ is an
excited bound state of the recombined ion.
This process is dominant in low-density low-temperature plasmas.
• Dielectronic recombination:
Xn+ + e−
↔ X∗∗
(n−1)+ → X∗
(n−1)+ + hν
where X∗∗
(n−1)+ is a doubly-excited autoionising state.
This process is dominant at high temperatures, but also is very
significant at low temperatures.

3. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Planetary Nebula
An expanding shell of gas ejected by a red giant star late in its life.
How planetary nebulae form?
• A star can no longer support itself by fusion reactions in its centre.
• The gravity forces the inner parts to condense and heat up.
• The high temperature central region drives the outer part away
in a stellar wind.
• The remaining core remnant ionizes and heats the distant gases
and causes them to radiate.

4. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Why Studying Planetary Nebulae?
Some reasons are:
• They are relatively abundant in the neighborhood (about 1500
are known in our galaxy).
• In other galaxies, they may be the only objects observable enough
to yield useful information about chemical abundances.
• They are important objects because they play a crucial role in
the chemical evolution of the galaxy, returning material to the
interstellar medium which has been enriched in heavy elements.
• Their physics is relatively well understood.

5. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Tools
The main tools of our research are:
• Autostructure code: a general purpose atomic structure program.
• R-Matrix code: a program for electron-atom and electron-ion
scattering calculations.
• Astronomical observations and experimental spectral data:
from databases (e.g. ELCAT and NIST), scientific literature and
possibly by request.

6. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Autostructure Code
Some of the Autostructure features:
• Calculates term energies, energy levels in LS and IC couplings,
radiative data e.g. permitted and forbidden transition probabili-
ties, and cascade coefficients.
• Uses multi-configuration type expansions.
• Relativistic corrections are made by means of the Breit-Pauli ap-
proximation.
• Wave functions are effectively expanded in Slater determinants.
• Radial functions can be either statistical-model functions or user-
supplied functions.
• The wide range of atomic structure data which the program can
calculate makes it highly suitable for astrophysical applications.

7. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Atomic R-Matrix Code
Some of the R-Matrix features:
• Calculates atomic continuum processes using the R -matrix method,
including electron-atom and electron-ion scattering.
• Calculates radiative processes, such as bound-bound transitions,
and polarizabilities.
• Calculates energy levels, collision strengths, resonances, oscillator
strengths and photoionisation cross-sections.
• Calculations can be either in LS-coupling, or in intermediate-
coupling scheme by including some terms of Breit-Pauli Hamil-
tonian (spin-orbit interaction).

8. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Pertinent Previous Work
• Storey (1981) calculated rate coefficients for dielectronic recom-
bination for several ions at the planetary nebulae conditions.
• Storey (1994) calculated rate coefficients for O II lines at nebular
densities and temperatures.
• Davey, Kisielius and Storey (1995-2002) investigated the recom-
bination spectrum of C II, N II, Ne II and O III in LS coupling
with application to planetary nebulae.
• Bastin and Storey (2005) investigated the dielectronic recombi-
nation in C II to work out the theoretical line transitions and
strengths in planetary nebulae. They also investigated the re-
combination lines of O II in intermediate-coupling.

9. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on C II
Why C II?
• Davey et al. investigated only the doublet states of C II because
at that time the atomic R-Matrix code was not available in IC
coupling scheme.
• The quartet states of C II, which are a valuable diagnostic tool
on the nebulae conditions such as the temperature of the lines-
emitting regions, need to be investigated. This is possible now
because the current R-Matrix code can run under the IC scheme.
What we will investigate?
• Mainly quartets, which give rise to C II lines from low-lying au-
toionizing states. Some examples are:

10. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on C II

11. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on C II

12. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on C II
How to do it?
• The R-Matrix code will be used to calculate the radiative and
dielectronic recombination data of doubly-ionized carbon, i.e.
C2+
+ e−
, in IC scheme.
• One way (stgqb) of processing the data is:
∆res → Γa
u, Γr
u → bu → Nu → εul
• Another way (stgbf) is:
σω(l→u) → αeff → εul
• The conclusions about the nebula(e) conditions will be drawn
accordingly.

13. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on Mg II
Why Mg II?
• The recombination lines
observed suggest high
abundance of CNO
relative to H.
• The knots preferentially
emit the CNO lines.
• There are two possibilities:
1. H-poor with normal abundance of CNO → Mg is enhanced.
2. H-normal with enhanced CNO → Mg is NOT enhanced.

14. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Our Work on Mg II
What we will do?
• Prepare theoretical data for the Mg II lines to be investigated.
• Explore databases for raw data.
• Search for strong lines by astronomical observation.
How to do it?
• Mainly the Autostructure and R-Matrix codes will be used to
carry out complete atomic data calculations as in the C II case.
• The theoretical emissivity results obtained for the Mg II lines will
be compared to the observational data.
• Conclusions about the structure and conditions of the planetary
nebula(e) of concern will be drawn accordingly.

15. Group of Theoretical Atomic and Molecular Physics and Astrophysics
Thank You
Questions?