Atomic data for Ti XIX


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Poster presented by K. M. Aggarwal and F. P. Keenan at 11th International Conference on Atomic Processes in Plasmas, Queen's University Belfast, 19-22 July 2011

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Atomic data for Ti XIX

  1. 1. ATOMIC DATA FOR Ti XIX K. M. Aggarwal and F. P. Keenan Astrophysics Research Centre, School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN, Northern IrelandIntroductionEmission 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 ton=4 lines are of particular interest in the development of lasers due to populationinversion. To analyse observations, atomic data are required for a variety ofparameters, such as energy levels, radiative rates (A- values), and excitation rates orequivalently the effective collision strengths (ϒ), which are obtained from the electronimpact collision strengths (Ω). Similarly, atomic data for Ti ions are useful to analyseimpurity 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 ispaucity for accurate collisional atomic data for Ti XIX. Therefore, here we calculate acomplete set of results (namely energy levels, radiative rates, and effective collisionstrengths) for all transitions among the lowest 98 levels of Ti XIX. These levelsbelong 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.CalculationsFor our calculations of wavefunctions, we have adopted the fully relativistic (GRASP)code, which is based on the jj coupling scheme. Further relativistic correctionsarising from the Breit interaction and QED effects have also been included.Additionally, we have used the option of extended average level (EAL), in which aweighted (proportional to 2j+1) trace of the Hamiltonian matrix is minimized. For thecalculations of Ω, the Dirac atomic R-matrix code (DARC) of PH Norrington and IPGrant has been adopted. In our calculations, the R-matrix radius is 3.64 au, and 55continuum orbitals have been included for each channel angular momentum for theexpansion of the wavefunctions. The maximum number of channels for a partial waveis 428, and the corresponding size of the Hamiltonian matrix is 23579. This allows usto calculate values of Ω up to an energy of 1130 Ryd, and values of ϒ up to atemperature 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 ofbetter than 0.002 Ryd. Additionally, parallel calculations have also been performedwith the Flexible Atomic Code (FAC) of Gu, so that all atomic parameters can berigorously assessed for accuracy. At present resonances are being resolved as theirimportance 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.