Energy levels, radiative rates and electron impact excitation rates for transitions in Be-like Ti XIX

Emission lines of Ti ions, including Ti XIX, have been widely measured in laboratory plasmas [1–3], due to their interest for the development of x-ray lasers. Titanium is also often a material in the walls of fusion reactors, and hence many ionization stages of this element are observed in fusion spectra due to the high temperatures. Considering its importance, several calculations have been performed in the past [4–9] to determine atomic data for 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). Additionally, O'Mahony et al [10] have reported analytical expressions to derive values of ϒ for Ti XIX, based on R-matrix calculations for Be-like ions between Sc XVIII and Zn XXVII. However, all these data are for transitions among the lowest ten levels of the n = 2 configurations of Ti XIX, and no calculation has so far been performed with the R-matrix code which explicitly includes the contribution of resonances in the determination of ϒ. The resonance contribution to ϒ may be highly significant, particularly for the forbidden transitions, as we will demonstrate in section 6. Therefore, in this work we report atomic data for energy levels, A-values, Ω and ϒ for transitions among the lowest 98 levels of the n ⩽ 4 configurations of Ti XIX.

For calculations of energy levels and A-values we employ the fully relativistic general-purpose relativistic atomic structure package (grasp) code, which was originally developed by Grant et al [11] and revised by Dr P H Norrington. It is a fully relativistic code, and is based on the jj coupling scheme. Further relativistic corrections arising from the Breit (magnetic) interaction and quantum electrodynamics (QED) effects (vacuum polarization and Lamb shift) have also been included. Additionally, we have used the option of extended average level, in which a weighted (proportional to 2j + 1) trace of the Hamiltonian matrix is minimized. This produces a compromise set of orbitals describing closely lying states with moderate accuracy. For our calculations of Ω, we have adopted the Dirac atomic R-matrix code (darc) of P H Norrington and I P Grant (http://web.am.qub.ac.uk/DARC/). Finally, for comparison purposes, we have performed parallel calculations with the flexible atomic code (fac) of Gu [12], available from the website http://sprg.ssl.berkeley.edu/~mfgu/fac/. This is also a fully relativistic code which provides a variety of atomic parameters, and (generally) yields results for energy levels and radiative rates comparable to grasp—see, for example, Aggarwal et al [13]. However, differences in collision strengths and subsequently in effective collision strengths with those obtained from darc can be large, particularly for forbidden transitions, as demonstrated in some of our earlier papers [14–19], and also discussed below in sections 5 and 6. Hence results from fac will be helpful in assessing the accuracy of our energy levels and radiative rates, and in estimating the contribution of resonances to the determination of effective collision strengths, included in calculations from darc but not in fac.

The 17 configurations of Ti XIX, namely (1s²) 2ℓ2ℓ', 2ℓ3ℓ' and 2ℓ4ℓ', give rise to the lowest 98 levels listed in table 1, where we also provide our level energies calculated from grasp, without and with the inclusion of Breit and QED effects. Wiese and Fuhr [20] have compiled and critically evaluated experimentally measured energy levels of Ti XIX, listed at the NIST (National Institute of Standards and Technology) website http://www.nist.gov/pml/data/asd.cfm. These compilations are included in table 1 for comparisons. However, NIST energies are not available for many levels, particularly of the 2ℓ4ℓ' configurations, and for some of the levels their results are indistinguishable—see for example: 26/27 [(2p3p) ³D₂ and ¹P₁] and 41/42 [2p3d ³P^o_2,1]. Also included in the table are our calculations obtained from the fac code (FAC1), including the same CI (configuration interaction) as in grasp.

Our level energies obtained without the Breit and QED effects (GRASP1) are higher than the NIST values by up to ∼0.15 Ryd for some of the levels, such as: 9 (2p^{2 1}D₂), 10 (2p^{2 1}S₀) and 17 (2s3d ³D₁). Furthermore, the ordering is also mostly the same as that of NIST. However, there are also striking differences, in both ordering and magnitude, for some of the levels, namely 45/46 [(2p3d) ¹F^o₃ and ¹P^o₁], 53/54 [2s4d ³D_1,2] and 85 [2d4d ³P^o₂] , for which the discrepancy is up to 0.4 Ryd. The inclusion of Breit and QED effects (GRASP2) lowers the energies by a maximum of ∼0.065 Ryd, indicating that for this ion the higher relativistic effects are not too important. In addition, the ordering has slightly altered in a few instances, see for example levels 37/38 [2p3p ¹D₂ and 2p3d ³F^o₄] and 60/61 [2s4f ¹F^o₃ and 2p4s ³P^o₀]. However, the energy differences for these swapped levels are very small. Our FAC1 level energies agree with our GRASP2 calculations within 0.04 Ryd for all levels and the orderings are also the same. Small differences in the grasp and fac energies arise mostly by the ways calculations of central potential for radial orbitals and recoupling schemes of angular parts have been performed—see detailed discussion in the fac manual. A further inclusion of the 2ℓ5ℓ' configurations, labelled FAC2 calculations in table 1, makes no appreciable difference either in the magnitude or ordering of the levels. Therefore, we are confident of our energy levels listed in table 1, and assess these to be accurate to better than 0.5%.

Since currently available A-values in the literature are limited to transitions among the lowest ten levels of Ti XIX, we here provide a complete set of data for all transitions among the 98 levels and for four types, namely electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2), as these are required in a plasma model. Furthermore, the absorption oscillator strength (f_ij) and radiative rate A_ji (in s⁻¹) for a transition i → j are related by the following expression [21]:

$$\begin{equation} f_{ij} = \frac{mc}{8{\pi}^2{e^2}}{\lambda^2_{ji}} \frac{{\omega}_j}{{\omega}_i} A_{ji} = 1.49 \times 10^{-16} \lambda^2_{ji} (\omega_j/\omega_i) A_{ji}, \end{equation} \tag{ 1 }$$

where m and e are the electron mass and charge, respectively, c is the velocity of light, λ_ji is the transition energy/wavelength in Å, and ω_i and ω_j are the statistical weights of the lower (i) and upper (j) levels, respectively. Similarly, the oscillator strength f_ij (dimensionless) and the line strength S (in atomic unit, 1 au = 6.460 × 10⁻³⁶ cm² esu²) are related by the standard equations given below [21–23].

For the electric dipole (E1) transitions

$$\begin{equation} A_{ji} = \frac{2.0261\times{10^{18}}}{{{\omega}_j}\lambda^3_{ji}} S^{{\rm E1}} \quad {\rm and} \quad f_{ij} = \frac{303.75}{\lambda_{ji}\omega_i} S^{{\rm E1}}, \end{equation}\noindent \tag{ 2 }$$

for the magnetic dipole (M1) transitions

$$\begin{equation} A_{ji} = \frac{2.6974\times{10^{13}}}{{{\omega}_j}\lambda^3_{ji}} S^{{\rm M1}} \quad {\rm and} \quad f_{ij} = \frac{4.044\times{10^{-3}}}{\lambda_{ji}\omega_i} S^{{\rm M1}}, \end{equation} \tag{ 3 }$$

for the electric quadrupole (E2) transitions

$$\begin{equation} A_{ji} = \frac{1.1199\times{10^{18}}}{{{\omega}_j}\lambda^5_{ji}} S^{{\rm E2}} \quad {\rm and} \quad f_{ij} = \frac{167.89}{\lambda^3_{ji}\omega_i} S^{{\rm E2}} \end{equation}\noindent \tag{ 4 }$$

and for the magnetic quadrupole (M2) transitions

$$\begin{equation} A_{ji} = \frac{1.4910\times{10^{13}}}{{{\omega}_j}\lambda^5_{ji}} S^{{\rm M2}} \quad {\rm and} \quad f_{ij} = \frac{2.236\times{10^{-3}}}{\lambda^3_{ji}\omega_i} S^{{\rm M2}}. \end{equation}\noindent \tag{ 5 }$$

In table 2 (available in the supplementary data at stacks.iop.org/PhysScr/86/055301/mmedia) we present transition energies/wavelengths (λ, in Å), radiative rates (A_ji, in s⁻¹), oscillator strengths (f_ij, dimensionless) and line strengths (S, in au), in length form only, for all 1468 electric dipole (E1) transitions among the 98 levels of Ti XIX. The indices used to represent the lower and upper levels of a transition have already been defined in table 1. Similarly, there are 1754 electric quadrupole (E2), 1424 magnetic dipole (M1) and 1792 magnetic quadrupole (M2) transitions among the 98 levels. However, for these transitions only the A-values are listed in table 2, and the corresponding results for f- or S-values can be easily obtained using equations (1)–(5).

As noted earlier, A-values in the literature for Ti XIX are only available for a limited number of transitions. Therefore, we have performed another calculation with the fac code of Gu [12]. In table 3 we compare our A-values from both the grasp and fac codes for some transitions among the lowest 20 levels of Ti XIX. Also included in this table are f-values from grasp because they give an indication of the strength of a transition. Similarly, to facilitate easy comparison between the two calculations, we have also listed the ratio of A-values obtained with the grasp and fac codes. For these (and many other) transitions, the agreement between the two sets of A-values is better than 20%. Indeed, for most strong transitions (f ⩾ 0.01), the A-values from grasp and fac agree to better than 20%, and the only exceptions are three transitions, namely 2–32 (2s2p ³P^o₀–2p3p ³S₁), 32–71 (2p3p ³S₁–2p4d ³D^o₂) and 32–83 (2p3p ³S₁–2p4d ¹D^o₂), for which the discrepancies are up to 40%. These discrepancies mainly arise from the corresponding differences in the energy levels. Furthermore, for a majority (80%) of the strong E1 transitions (f ⩾ 0.01) the length and velocity forms in our grasp calculations agree within 20%, and discrepancies for the others are mostly within a factor of two. However, for a few (∼13%) weaker transitions (f ⩽ 10⁻³) the two forms of the f-value differ by up to several orders of magnitude, and examples include: 4–24 (f ∼ 3 × 10⁻¹⁰), 4–92 (f ∼ 4 × 10⁻⁷), 29–31 (f ∼ 5 × 10⁻⁹), 30–31 (f ∼ 6 × 10⁻⁷) and 33–34 (f ∼ 3 × 10⁻⁶). Finally, as for the energy levels, the effect of additional CI is negligible on the A-values, as results for all strong E1 transitions agree within ∼20% with those obtained with the inclusion of the n = 5 configurations. To conclude, we may state that for almost all strong E1 transitions, our radiative rates are accurate to better than 20%. However, for the weaker transitions the accuracy is comparatively poorer.

The lifetime τ for a level j is defined as follows [24]:

$$\begin{equation} {\tau}_j = \frac{1}{{\sum_{i}} A_{ji}}. \end{equation}\noindent \tag{ 6 }$$

Since this is a measurable parameter, it provides a check on the accuracy of the calculations. Therefore, in table 1 we have also listed our calculated lifetimes, which include the contributions from four types of transitions, i.e. E1, E2, M1 and M2. To our knowledge, no calculations or measurements are available for lifetimes for any of the Ti XIX levels. However, we hope the present results will be useful for future comparisons and may encourage experimentalists to measure lifetimes, particularly for the level 2s2p ³P^o₂ which has a comparatively large value of ∼1 ms.

Collision strengths (Ω) are related to the more commonly known parameter collision cross section (σ_ij, πa₀²) by the following relationship [25]:

$$\begin{equation} \Omega_{ij}(E) = {k^2_i}\omega_i\sigma_{ij}(E), \end{equation} \tag{ 7 }$$

where k²_i is the incident energy of the electron and ω_i is the statistical weight of the initial state. Results for collisional data are preferred in the form of Ω because it is a symmetric and dimensionless quantity.

For the computation of collision strengths Ω, we have employed the darc, which includes the relativistic effects in a systematic way, in both the target description and the scattering model. It is based on the jj coupling scheme, and uses the Dirac–Coulomb Hamiltonian in the R-matrix approach. The R-matrix radius adopted for Ti XIX is 3.64 au, and 55 continuum orbitals have been included for each channel angular momentum in the expansion of the wavefunction, allowing us to compute Ω up to an energy of 1150 Ryd, i.e. ∼1070 Ryd above the highest threshold, equivalent to ∼1.7 × 10⁸ K. This energy range is sufficient to calculate values of effective collision strength ϒ (see section 6) up to T_e = 10^7.7 K, well above the temperature of maximum abundance in ionization equilibrium for Ti XIX, i.e. 10^6.9 K [26]. The maximum number of channels for a partial wave is 428, and the corresponding size of the Hamiltonian matrix is 23 579. To obtain convergence of Ω for all transitions and at all energies, we have included all partial waves with angular momentum J ⩽ 40.5, although a larger number would have been preferable for the convergence of some allowed transitions, especially at higher energies. However, to account for higher neglected partial waves, we have included a top-up, based on the Coulomb–Bethe approximation [27] for allowed transitions and geometric series for others.

For illustration, in figures 1–3 we show the variation of Ω with angular momentum J for three transitions of Ti XIX, namely 1–5 (2s^{2 1}S₀–2s2p ¹P^o₁), 2–4 (2s2p ³P^o₀–2s2p ³P^o₂) and 9–10 (2p^{2 1}D₀–2p^{2 1}S₀), and at three energies of 100, 500 and 900 Ryd. The values of Ω have not converged for allowed transitions as shown in figure 1, for which a top-up has been included as mentioned above, and has been found to be appreciable. However, for all forbidden transitions, the values of Ω have fully converged as shown in figures 2 and 3. It is also clear from figures 2 and 3 that a large range of partial waves is required for the convergence of Ω for some of the forbidden transitions, particularly towards the higher end of the energy range.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In table 4 we list our values of Ω for resonance transitions of Ti XIX at energies above thresholds. The indices used to represent the levels of a transition have already been defined in table 1. Unfortunately, no similar data are available for comparison purposes as already noted in section 1. Therefore, to make an accuracy assessment for Ω, we have performed another calculation using the fac code of Gu [12]. This code is also fully relativistic, and is based on the well-known and widely-used distorted-wave (DW) method—see for example [28, 29] and the FAC manual. Furthermore, the same CI is included in fac as in the calculations from darc. Therefore, also included in table 4 for comparison purposes are the Ω values from fac at a single excited energy E_j, which corresponds to an incident energy of ∼700 Ryd for Ti XIX. For ∼60% of the Ti XIX transitions, the values of Ω with the darc and fac codes agree within 20% at an energy of 700 Ryd. However, the discrepancies for others are much higher, particularly for weaker transitions, such as: 1–30/31/35/39/73/77/83/89/91. Most of these are weak (Ω ⩽ 10⁻⁶) and forbidden, i.e. the values of Ω have fully converged at all energies within our adopted range of partial waves in the calculations with the darc code. For such weak transitions, values of Ω from the fac code are not assessed to be accurate. Additionally, for a few transitions, such as 49–87, 50–72/86/98, 51–66/69/71/83/85, 52–68/72/86/98 and 53–63/64/77/95, the values of Ω from the fac code show a sudden increase, by orders of magnitude at some random energies, generally towards the higher end. This problem is common for many ions and examples of this can be seen in figure 6 of Aggarwal and Keenan [17, 18]. The sudden anomalous behaviour in Ω with the fac code is also responsible for the differences noted above for many transitions. Such anomalies for some transitions (both allowed and forbidden) from the fac calculations arise primarily because of the interpolation and extrapolation techniques employed in the code. In order to expedite calculations, i.e. to generate a large amount of atomic data in a comparatively very short period of time, and without too large loss of accuracy, calculations of Ω are not performed at each partial wave, but only at each J up to 5, and then the interval between successive calculations is doubled every two points, i.e. the grid is almost logarithmic—see the fac manual for further details. Similarly, some differences in Ω are expected because the DW method generally overestimates results due to the exclusion of channel coupling.

As a further comparison between the darc and fac values of Ω, in figure 4 we show the variation of Ω with energy for three allowed transitions among the excited levels of Ti XIX, namely 4–19 (2s2p ³P^o₂–2s3d ³D₃), 5–20 (2s2p ¹P^o₁–2s3d ¹D₂) and 8–40 (2p^{2 3}P₂–2p3d ³D^o₃). For many transitions there are no discrepancies between the f- values obtained with the two different codes (grasp and fac) as demonstrated in table 3, and therefore the values of Ω also agree to better than 20%. Similar comparisons between the two calculations with darc and fac are shown in figure 5 for three forbidden transitions of Ti XIX, namely 1–12 (2s^{2 1}S₀–2s3s ¹S₀), 2–4 (2s2p ³P^o₀–2s2p ³P^o₂) and 3–4 (2s2p ³P^o₁–2s2p ³P^o₂). As in the case of the allowed transitions, for these forbidden ones the agreement between the two calculations is generally satisfactory, although there are some differences towards the lower end of the energy range. Therefore, on the basis of these and other comparisons discussed above, collision strengths from our darc code are assessed to be accurate to better than 20%. However, similar data from fac are not assessed to be accurate for all transitions over an entire energy range.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Excitation rates, in addition to energy levels and radiative rates, are required for plasma modelling, and are determined from the collision strengths (Ω). Since the threshold energy region is dominated by numerous closed-channel (Feshbach) resonances, values of Ω need to be calculated in a fine energy mesh to accurately account for their contribution. Furthermore, in a plasma electrons have a wide distribution of velocities, and therefore values of Ω are generally averaged over a Maxwellian distribution as follows [25]:

$$\begin{equation} \Upsilon(T_{\rm e}) = \int_{0}^{\infty} {\Omega}(E) {\rm exp}(-E_j/kT_{\rm e}) \mathrm{d}(E_j/{kT_{\rm e}}), \end{equation} \tag{ 8 }$$

where k is Boltzmann constant, T_e electron temperature in K and E_j the electron energy with respect to the final (excited) state. Once the value of ϒ is known the corresponding results for the excitation q(i,j) and de-excitation q(j,i) rates can be easily obtained from the following equations:

$$\begin{equation} q(i,j) = \frac{8.63 \times 10^{-6}}{{\omega_i}{T_{\rm e}^{1/2}}} \Upsilon {\rm exp}(-E_{ij}/{kT_{\rm e}}) \, {\rm cm}^3\,{\rm s}^{-1} \end{equation} \tag{ 9 }$$

and

$$\begin{equation} q(j,i) = \frac{8.63 \times 10^{-6}}{{\omega_j}{T_{\rm e}^{1/2}}} \Upsilon \, {\rm cm}^3\,{\rm s}^{-1}, \end{equation} \tag{ 10 }$$

where ω_i and ω_j are the statistical weights of the initial (i) and final (j) states, respectively, and E_ij is the transition energy. The contribution of resonances may enhance the values of ϒ over those of the background collision strengths (Ω_B), especially for the forbidden transitions, by up to an order of magnitude (or even more) depending on the transition and/or the temperature. Similarly, values of Ω need to be calculated over a wide energy range (above thresholds) to obtain convergence of the integral in equation (8), as demonstrated in figure 7 of Aggarwal and Keenan [30]. It may be noted that if for practical reasons calculations of Ω are performed only up to a limited range of energy then the high energy limits for a range of transitions can be invoked through the expressions suggested by Burgess and Tully [25]. However, there is no such need in the present work as calculations for Ω have been performed up to a reasonably high energy range, as noted in section 5.

To delineate resonances, we have performed our calculations of Ω at over ∼41 000 energies in the thresholds region. Close to thresholds (∼0.1 Ryd above a threshold) the energy mesh is 0.001 Ryd, and away from thresholds is 0.002 Ryd. Hence care has been taken to include as many resonances as possible, and with as fine a resolution as is computationally feasible. The density and importance of resonances can be appreciated from figures 6–11, where we plot Ω as a function of energy in the thresholds region for the 1–2 (2s^{2 1}S₀–2s2p ³P^o₀), 1–3 (2s^{2 1}S₀–2s2p ³P^o₁), 1–4 (2s^{2 1}S₀–2s2p ³P^o₂), 2–3 (2s2p ³P^o₀–2s2p ³P^o₁), 2–4 (2s2p ³P^o₀–2s2p ³P^o₂) and 3–4 (2s2p ³P^o₁–2s2p ³P^o₂) transitions, respectively. For all these (and many other) transitions the resonances are dense over the entire thresholds energy range, and hence make a significant contribution to ϒ over a wide range of temperatures. Since for many transitions, resonances are dense and have high magnitude at energies close to the thresholds, a slight displacement in their positions can significantly affect the calculations of ϒ, mostly at the low temperatures, but not at the higher ones required for Ti XIX.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Our calculated values of ϒ are listed in table 5 (available in the supplementary data at stacks.iop.org/PhysScr/86/055301/mmedia) over a wide temperature range up to 10^7.7 K, suitable for applications to a variety of plasmas. Corresponding data at any other temperature/s and/or in a different format in a machine readable form can also be requested from any one of the authors. As stated in section 1, there are only limited results available for comparison purposes. Therefore, we have also calculated values of ϒ from our non-resonant Ω data obtained with the fac code, and these are included at the lowest and the highest calculated temperatures. These calculations are particularly helpful in providing an estimate of the importance of resonances in the determination of excitation rates. Furthermore, Zhang and Sampson [7] (ZS) have reported values of ϒ for transitions among the lowest ten levels of Ti XIX. In their calculations, they have adopted the Coulomb–Born-exchange method and their results are stored in the chianti database at http://www.chiantidatabase.org/chianti_direct_data.html. In table 6 we compare our results for ϒ, from both darc and fac, with those of ZS at three temperatures of 10^6.3, 10^6.9 and 10^7.5 K. Values of ϒ from fac generally agree with those of ZS within 20%, because both calculations are based on the DW method and do not include the contribution of resonances. However, our corresponding results from darc are higher, by up to a factor of 4, for many transitions, mostly forbidden. This is because of the inclusion of resonances in the calculations with darc. Moreover, since resonances are spread over a wide energy range, as noted in figures 6–11, higher values of ϒ are sustained over the entire range of temperatures over which the calculations have been performed—see for example transitions 1–2/4/6/7/8/9/10.

The comparison of ϒ in table 6 is limited to the 45 transitions among the lowest ten levels of Ti XIX. For a larger range of transitions, about half have a discrepancy of more than 20% over the entire range of temperatures. At lower temperatures, the differences are generally within a factor of 5, but are higher (up to two orders of magnitude) for some, such as: 2–38 (2s2p ³P^o₀–2p3d ³F^o₄), 6–11 (2p^{2 3}P₀–2s3s ³S₁), 7–11 (2p^{2 3}P₁–2s3s ³S₁), 8–11 (2p^{2 3}P₂–2s3s ³S₁) and 9–51 (2p^{2 1}D₂–2s4p ³P^o₂). Similarly, towards higher temperatures, the discrepancies for most transitions are within a factor of 2, but are larger by up to orders of magnitude for a few, such as: 2–38/43, 6–11/14/16/17 and 7–11/18/19. In most cases, our results from darc are higher because of the inclusion of resonances. However, in a few cases the values of ϒ from fac are abnormally greater because of the anomaly in the calculated values of Ω, as discussed in section 5.

In this paper we have presented results for energy levels and radiative rates for four types of transitions (E1, E2, M1 and M2) among the lowest 98 levels of Ti XIX belonging to the n ⩽ 4 configurations. Additionally, lifetimes of all the calculated levels have been reported, although no measurements or other theoretical results are available for comparison. However, based on a variety of comparisons among various calculations with the grasp and fac codes, our results for radiative rates, oscillator strengths, line strengths, lifetimes and collision strengths are judged to be accurate to better than 20% for a majority of the strong transitions (levels). Furthermore, for calculations of ϒ, resonances in the thresholds energy region are noted to be dominant for many transitions, and inclusion of their contribution has significantly enhanced the results. In the absence of other similar calculations, it is difficult to fully assess the accuracy of our ϒ results. However, since we have considered a large range of partial waves to achieve convergence of Ω at all energies, included a wide energy range to calculate values of ϒ up to T_e = 10^7.7 K, and resolved resonances in a fine energy mesh to account for their contributions, we see no apparent deficiency in our reported data. Therefore, based on the comparisons made in section 6 and our past experience with calculations on other ions, we estimate the accuracy of our results for ϒ to be better than 20% for most transitions. Nevertheless, the present data for ϒ for transitions involving the levels of the n = 4 configurations may perhaps be improved by the inclusion of the levels of the n = 5 configurations. Furthermore, for some highly charged ions, particularly He-like, the effect of radiation damping may reduce the contribution of resonances in the determination of effective collision strengths. While this may be true for a few transitions towards the lower end of the temperature range, as demonstrated by several workers, see for example [31–33], the effect is not appreciable at high temperatures at which data are applied in the modelling of plasmas, as discussed in some of our earlier papers, such as [17–19, 34]. Nevertheless, scope remains for improvement in the reported data but until then we believe the present set of complete results for radiative and excitation rates for transitions in Ti XIX will be highly useful for the modelling of a variety of plasmas.