This document discusses calculations of atomic data for the titanium ion Ti XIX. It presents results for energy levels, radiative rates, and effective collision strengths for transitions among the lowest 98 levels of Ti XIX. Calculations were performed using the fully relativistic GRASP code and Dirac atomic R-matrix code DARC. Results for energy levels agree well with available measurements within 0.1 Ryd, except for three levels. Radiative rates and effective collision strengths are calculated up to temperatures of 107.7 K for applications in plasma modeling.

1. ATOMIC DATA FOR Ti XIX
K. M. Aggarwal and F. P. Keenan
Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland
Introduction
Emission lines from several ionisation stages of titanium, including Be-like Ti XIX,
have been observed 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. 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 (ϒ), 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.
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, here we calculate 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.
Calculations
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 Ω, 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 Ω up to an energy of 1130 Ryd, and values of ϒ 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 Ryd. Additionally, parallel calculations have also been performed
with the Flexible Atomic Code (FAC) of Gu, so that all atomic parameters can be
rigorously assessed for accuracy. At present resonances are being resolved as their
importance can be appreciated from Figs. 6-11 shown here.
Results and Conclusions
 Energy levels and their lifetimes are listed in Table 1.
 Measurements of many energy levels are not available and some measurements are non-degenerate.
 All levels agree within 0.1 Ryd with the measurements, except three (32, 46 and 85) which differ by up to 0.3 Ryd.
 Inclusion of n=5 levels makes no appreciable difference either to energies or to their orderings.
 GRASP and FAC energy levels agree within 0.05 Ryd and orderings are also the same.