Atomic data for Ti XIX

K. M. Aggarwal and F. P. Keenan (Astrophysics Research Centre,
School of Mathematics and Physics, Queen’s University, Belfast BT7 1NN, Northern Ireland, UK)

Emission lines from several ionisation stages of titanium, including Be-like Ti XIX, have been observed [1] in laser produced plasmas in the 12–15 Å region. The n=2 to n=4 lines are of particular interest in the development of lasers due to population inversion. However, to analyse observations, atomic data are required for a variety of parameters, such as energy levels, radiative rates (A-values), and excitation rates or equivalently the effective collision strengths (Y), which are obtained from the electron impact collision strengths (Ω). Similarly, atomic data for Ti ions are useful to analyse impurity content and transport in tokamak plasmas [2].

Experimentally, energy levels are available for Ti XIX on the NIST website. Similarly, A-values are also available for some transitions on the NIST website, but there is paucity for accurate collisional atomic data for Ti XIX. Therefore, in this paper we report a
complete set of results (namely energy levels, radiative rates, and effective
collision strengths) for all transitions among the lowest 98 levels of Ti XIX.
These levels belong to the (1s2) 2s2, 2s2p, 2p2, 2s3l, 2p3l, 2s4l, and 2p4l
configurations. Finally, we also report the A-values for four types of transitions, namely
electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and
magnetic quadrupole (M2), because these are also required for plasma modelling.
For our calculations of wavefunctions, we have adopted the fully relativistic
GRASP code, which is based on the jj coupling scheme. Further relativistic corrections
arising from the Breit interaction and QED effects have also been included.
Additionally, we have used the option of extended average level (EAL), in which a weighted (proportional to 2j+1) trace of the Hamiltonian matrix is minimized. For the calculations of , the Dirac atomic R-matrix code (DARC) of PH Norrington and IP Grant has been adopted. In our calculations, the R-matrix radius is 3.64 au, and 55
continuum orbitals have been included for each channel angular momentum for the
expansion of the wavefunctions. The maximum number of channels for a partial
wave is 428, and the corresponding size of the Hamiltonian matrix is 23579.
This allows us to calculate values of up to an energy of 1130 Ryd, and values of
Y up to a temperature of 107.7 K, suitable for applications in a
variety of plasmas. Furthermore, resonances in the thresholds region are being
resolved in a fine energy mesh of better than 0.002 Ry. Additionally, parallel
calculations have also been performed with the Flexible Atomic Code (FAC) of Gu [3], so that all atomic
parameters can be rigorously assessed for accuracy. At present calculations are
in progress and hopefully detailed data along with comparisons will be
presented during the conference.

Poster presented at the 17th International Conference on Atomic Processes in Plasmas, Queen’s University Belfast, 19-22 July 2011.



  1. J. C. Moreno et al., J. Opt. Soc. Am. B4, 1931 (1987)
  2. A. P. Zwicker et al., J. X-ray Sci. Tech. 4, 57 (1993)
  3. M. F. Gu, ApJ 582, 1241 (2003)
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