Stark broadening parameters and transition probabilities of persistent lines of Tl II

Stark broadening parameters and transition probabilities of persistent lines of Tl II Abstract The presence of singly ionized thallium in the stellar atmosphere of the chemically peculiar star χ Lupi was reported by Leckrone et al. in 1999 by analysis of its stellar spectrum obtained with the Goddard High Resolution Spectrograph (GHRS) on board the Hubble Space Telescope. Atomic data about the spectral line of 1307.50 Å and about the hyperfine components of the spectral lines of 1321.71 Å and 1908.64 Å were taken from different sources and used to analyse the isotopic abundance of thallium II in the star χ Lupi. From their results the authors concluded that the photosphere of the star presents an anomalous isotopic composition of Tl II. A study of the atomic parameters of Tl II and of the broadening by the Stark effect of its spectral lines (and therefore of the possible overlaps of these lines) can help to clarify the conclusions about the spectral abundance of Tl II in different stars. In this paper we present calculated values of the atomic transition probabilities and Stark broadening parameters for 49 spectral lines of Tl II obtained by using the Cowan code including core polarization effects and the Griem semiempirical approach. Theoretical values of radiative lifetimes for 11 levels (eight with experimental values in the bibliography) are calculated and compared with the experimental values in order to test the quality of our results. Theoretical trends of the Stark width and shift parameters versus the temperature for spectral lines of astrophysical interest are displayed. Trends of our calculated Stark width for the isoelectronic sequence Tl II–Pb III–Bi IV are also displayed. atomic data, atomic processes 1 INTRODUCTION There are different industrial applications of singly ionized thallium (Tl II). In particular, its applications in the form of thallium sulphide in photocells can be mentioned because its conductivity increases when exposed to infrared light. In 1999, in the analysis of the stellar spectrum, obtained with the Goddard High Resolution Spectrograph (GHRS) on board the Hubble Space Telescope, of the chemically peculiar star χ Lupi, the presence of Tl II was detected by Leckrone et al. The transition probability for the spectral line of 1307.50 Å was calculated by the authors in their work by using the Cowan code (Cowan 1981) without taking into account the core polarization effects (CPE). The transition probabilities for the hyperfine components of the spectral lines of 1321.71 Å and 1908.64 Å were taken from different sources listed in the Kurucz data base (1993). These values were used to analyse the isotopic abundance of thallium II in the star χ Lupi. From their results the authors concluded that the photosphere of the star presents an anomalous isotopic composition of Tl II. A study of the transition probabilities of Tl II including CPE can help to clarify the conclusions about the spectral abundance of Tl II in other stars. Also, as the mechanism of broadening by collision with electrons is the main pressure mechanism of stellar line broadening in atmospheres of stars of type A and late B (Popović, Dimitrijević & Ryabchikova 1999) and in white dwarf atmospheres (Milovanović 2005), an analysis of the Stark broadening parameters seems necessary to solve some problems of possible overlaps of spectral lines. Tl II is a member of the isoelectronic sequence of mercury, as are Pb III and Bi IV. The atomic parameters of Pb III and Bi IV have already been measured and calculated by the present authors. Calculations of the Stark broadening parameters of spectral lines of Pb III and Bi IV, taking into account the effects of core polarization, were made by Zanón, Alonso-Medina & Colón (2010) and Colon et al. (2017). In this work we have done a theoretical study similar to the one performed for Pb III and Bi IV. There is an early analysis of the Tl II spectrum, by McLennan, McLay & Crawford (1929), which was extended by Ellis & Sawyer (1936). In this work, 76 energy levels are provided and 275 lines are listed, of which 160 are identified for the first time. This last work is collected in the tables of Moore (1958) and later by Sansonetti & Martin (2005). We have only found eight values of experimental lifetimes in the bibliography. The experimental lifetimes of six levels of Tl II were obtained, by means of the beam foil technique, in 1972 by Andersen & Sørensen. A new lifetime for the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level was measured months later by Andersen, Kirkegård Nielsen & Sørensen (1972) using the 600 kV heavy-ion accelerator at the University of Aarhus. The lifetimes of three of the levels provided by Andersen were again measured by Henderson & Curtis (1996), which also included the measurement of the lifetime of a new level. There are no experimental measurements for the transition probabilities of the Tl II spectral lines except for the line of 1321.64 Å that was obtained directly from the value of the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level lifetime, by Andersen et al. (1972). Theoretical transition probabilities are given by some authors: Theoretical values in the Dirac–Fock approximation (MCDF) were calculated by Brage, Proffitt & Leckrone (1999); in addition, in the same year the theoretical value of the transition probability for line 1307.59 Å in the relativistic Hartree–Fock approximation (HFR) was calculated by Leckrone et al. (1999). Subsequently, values derived from experimental lifetimes, by using theoretical branching ratios, were published by Curtis (2000). Stark broadening parameters for the lines of 1321.71 Å and 2531.65 Å were calculated in the modified semiempirical approach (SME) by Milovanović in 2005. In this paper we present theoretical values of transition probabilities, level lifetimes and Stark broadening parameters for 49 spectral lines of Tl II. We include those that appear in the NIST data base (Kramida et al. 2013) as persistent lines (10 lines) in addition to the other 39 lines also in the NIST data base that appear with high relative intensities. We present theoretical values of the transition probabilities and the Stark broadening parameters for 49 spectral lines of Tl II that arise from configurations 5d106sns (n = 7–9), 5d106p2, 5d106snp (n = 6, 7), 5d106snd (n = 6, 7, 8) and 5d106s5f. Theoretical values of radiative lifetimes for 11 levels (eight with experimental values in the bibliography) are calculated and compared with the experimental values. These calculations were obtained using a semiclassical approach taking into account the core polarization effects (CPE), similar to the calculations in Colón et al. (2017). The Stark broadening parameters are presented for a set of temperatures ranging from 5000 to 160 000 K and an electronic density of 1017 cm−3. The theoretical calculations are presented in Section 2. In Section 3 we describe our results, including the regularity of the Stark broadening parameters versus the temperature and a comparison of calculated Stark widths for Tl II, Pb III and Bi IV (same isoelectronic sequence). 2 THEORETICAL CALCULATIONS Our calculation procedure is similar to that presented by the authors in previous work (Colón et al. 2017). In order to obtain the transition probabilities and the level lifetimes, wavefunctions were calculated in an intermediate coupling scheme (IC) using the relativistic Hartree–Fock (HFR) approach by means of the computer code in Cowan (1981). As Tl II has a high atomic number, Z = 81, the core polarization effects (CPE) must be considered. The Cowan code was modified in order to include these effects in a similar way to that presented in Colón et al. (2017). The CP effects were included following the suggestions of Migdalek and Baylis (1978) and the expressions of Biémont, Froese Fischer & Godefroid (2000): The core polarization effects were written as the one-particle, VP1, and two-particle, VP2, potential models (expressions (1) and (2) in the original Biémont paper). A modification in the matrix element can be made in order to take into account the potential change. The <Pnl|r|Pn'l’ > is replaced by   \begin{eqnarray}&&\int_{0}^{\infty }{{{P_{nl}}r\left( {1 - \frac{{{\alpha _d}}}{{{{\left( {{r^2} + r_{\rm{c}}^2} \right)}^{{3 \mathord{\left/ {\vphantom {3 2}} \right.} 2}}}}}} \right)}}{P_{n'l'}}\,{\rm{d}r}\nonumber\\ &&- \frac{{{\alpha _d}}}{{r_{\rm{c}}^3}}\int_{0}^{{{r_{\rm{c}}}}}{{{P_{nl}}\left( r \right)r{P_{n'l'}}\left( r \right)}}\,{\rm{d}r,}\end{eqnarray} (1)where the core penetration term suggested by Hameed (1972) has also been included. For the dipole polarizability and the cutoff radius we use the values αd = 5.472 (in au) and rc = 1.349 (in au), computed by Migdalek & Baylis (1985). We have used in our calculations 26 configurations of Tl II: 5d106s2, 5d106p2, 5d106sns (n = 7–12), 5d106snd (n = 6–11) and 5d106sng (n = 5, 6) for even parity and 5d106snp (n = 6, 11), 5d106snf (n = 5–7) and 5d96s26p for odd parity. For the IC calculations we used all the experimental levels shown in the table in Moore (1958) based on Ellis & Sawyer (1936). A partial Grotrian energy level scheme of Tl II showing several spectral lines with experimental radiative lifetimes is displayed in Fig. 1. Figure 1. View largeDownload slide Partial Grotrian diagram of the Tl II energy levels (Ellis & Sawyer 1936; Sansonetti & Martin 2005), showing several spectral lines with experimental lifetimes. Figure 1. View largeDownload slide Partial Grotrian diagram of the Tl II energy levels (Ellis & Sawyer 1936; Sansonetti & Martin 2005), showing several spectral lines with experimental lifetimes. As usual, the number of adjustable parameters in the Cowan code exceeds the number of experimental levels available in the literature (39 for even parity and 37 for odd parity). Following the recommendations of Cowan, in those configurations with a reduced number of experimental levels certain parameters are excluded from the fitting process. In these cases a factor of 0.85 was used to decrease the values of radials integrals Fk, Gk and Rk that are excluded from the fitting process. To avoid transition probabilities excessively influenced by a mixture of forced configurations to obtain the best possible adjustment, we have allowed our theoretical levels to differ by 1 per cent from the experimental levels. The parameters obtained following this procedure do not differ by more than 10 per cent of the ab initio values and are available on request. In this way, the transition probabilities for the allowed lines in LS coupling and for the so-called forbidden transitions were obtained. Theoretical lifetimes for several levels were also obtained. To obtain the broadening parameters by using the matrix elements calculated from the Cowan code, wwe have used the semiempirical formulas obtained by Griem in 1968 (expressions (24) and (35) in the original paper) where was taken into account Baranger´s (1958) original formulation with semiempirical effective Gaunt factors, as proposed by Van Regemorter (1962) and Seaton (1962). As is well known (Griem 1968), a factor larger than 1.5 between calculated and experimental values can be expected with the use of this effective Gaunt factor. In this paper the Stark widths, ω, and Stark shifts, d, are presented in wavelength units. As the values obtained with the above-mentioned expressions are in frequency units, the full width at half maximum (FWHM) of the spectral line, ω, in wavelength units is obtained through the expression ω = ωse λ2/ (πc), where λ is the wavelength and c is the speed of light. 3 RESULTS AND DISCUSSION The probabilities of theoretical transitions obtained in this work for 13 spectral lines of Tl II of special interest (they appear in the NIST data base as persistent lines or have appeared in the bibliography for some reason) are displayed in Table 1. Our values are presented in column 4 of the table mentioned above. In columns 5 and 6 are the theoretical values (except for the line of 1321.64 Å that was obtained from the lifetime of the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level) provided by other authors. As can be seen, there is a good agreement even though they have been obtained by different procedures. In column 4 in parentheses we present the values obtained without taking into account core polarization effects (CPE). It should be noted that in the case of the 1307.50 Å line, this last value coincides with that obtained in the work of Leckrone et al. (1999) although the value obtained taking into account these effects is a factor of two lower. In later tables values obtained in this work are presented for the transition probabilities of other spectral lines collected by NIST but with lower relative intensities. Table 1. Calculated transition probabilities of persistent Tl II lines. Transition levels    Transition probabilities (108 s−1)  Upper  Lower  Wavelength λ (Å)a  This work  Curtis (2000)  Brage et al. (1999)c  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1321.64  13.02(24.1)  16.9  17.3  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  1593.26b  0.52  0.48  0.22  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_0^{\rm{o}}$$  1792.83  1.50    1.02  5d106s6d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1814.77  8.25    9.17  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1871.39b  0.14  0.01  0.21  5d106s7d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1307.50  1.92(3.17)    3.17  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1908.62  0.27  0.26  0.27  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  2298.06  3.47    3.79  5d106s6d1D2  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  2530.74  1.47  1.18  1.31  5d106s7s1S0  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  3091.57  3.83    3.34  5d106s5f3F3  5d106s6d3D2  5078.54  1.64      5d106s5f3F4  5d106s6d3D3  5152.14  1.77      5d106s7p$$^3{\rm{P}}_2^{\rm{o}}$$  5d106s7s3S1  5949.48  0.94      Transition levels    Transition probabilities (108 s−1)  Upper  Lower  Wavelength λ (Å)a  This work  Curtis (2000)  Brage et al. (1999)c  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1321.64  13.02(24.1)  16.9  17.3  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  1593.26b  0.52  0.48  0.22  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_0^{\rm{o}}$$  1792.83  1.50    1.02  5d106s6d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1814.77  8.25    9.17  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1871.39b  0.14  0.01  0.21  5d106s7d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1307.50  1.92(3.17)    3.17  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1908.62  0.27  0.26  0.27  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  2298.06  3.47    3.79  5d106s6d1D2  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  2530.74  1.47  1.18  1.31  5d106s7s1S0  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  3091.57  3.83    3.34  5d106s5f3F3  5d106s6d3D2  5078.54  1.64      5d106s5f3F4  5d106s6d3D3  5152.14  1.77      5d106s7p$$^3{\rm{P}}_2^{\rm{o}}$$  5d106s7s3S1  5949.48  0.94      Notes.aPersistent lines (NIST; Kramida et al. 2013). bNIST Kramida et al. (2013) and Curtis et al. (2001). cValues deduced from the author´s oscillator strengths. View Large In order to show the quality of our theoretical values of the transition probabilities (beyond a comparison with other theoretical values) we have compared the lifetime values obtained in this work with experimental lifetime values available in the bibliography. Our theoretical lifetime values for 11 levels of Tl II (of which eight have experimental values available in the bibliography) are presented in Table 2. In the last three columns of the table, the experimental values of different authors are collected. The ratio between the experimental values of radiative lives and the theoretical values obtained in this work for several levels of Tl II is less than 1.5, with the notable exception of the values of the 6s7s 3S1 level lifetime. Like Brague et al. (1999), we suggest that the lifetime of this level should be measured again. Table 2. Radiative lifetimes calculated for several levels of Tl II.   Radiative lifetimes τ (ns)  Level  This work  Other authors  5d106s7s3S1  1.15  1.31a  18±4b      5d106s7s1S0  2.15  2.77a  4.6±0.5b  3.0±0.4c    5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  36.67  36.5a    39±2c    5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  0.76  0567a    0.59±0.04c  0.65±0.08d  5d106s6d1D2  5.01  5.61a  5.0±1.0b  6.5±0.5c    5d106s6d3D1  0.73          5d106s6d3D2  0.89          5d106s6d3D3  1.21          5d106s5f$$^1{\rm{F}}_3^{\rm{o}}$$  5.12    6.8±0.8b      5d106s5f$$^3{\rm{F}}_3^{\rm{o}}$$  5.18    7.8±1.0b      5d106s6f$$^3{\rm{F}}_4^{\rm{o}}$$  14.8    9.3±1.5b        Radiative lifetimes τ (ns)  Level  This work  Other authors  5d106s7s3S1  1.15  1.31a  18±4b      5d106s7s1S0  2.15  2.77a  4.6±0.5b  3.0±0.4c    5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  36.67  36.5a    39±2c    5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  0.76  0567a    0.59±0.04c  0.65±0.08d  5d106s6d1D2  5.01  5.61a  5.0±1.0b  6.5±0.5c    5d106s6d3D1  0.73          5d106s6d3D2  0.89          5d106s6d3D3  1.21          5d106s5f$$^1{\rm{F}}_3^{\rm{o}}$$  5.12    6.8±0.8b      5d106s5f$$^3{\rm{F}}_3^{\rm{o}}$$  5.18    7.8±1.0b      5d106s6f$$^3{\rm{F}}_4^{\rm{o}}$$  14.8    9.3±1.5b      Notes.aBrage et al. (1999). bAndersen & Sørensen (1972). cHenderson & Curtis (1996). dAndersen et al. (1972). View Large All our results for the transition probabilities and the Stark broadening parameters are shown in Tables 3–6. Tables are displayed for temperatures ranging from 5000 to 160 000 K and an electronic density of 1017 cm−3. In the first three columns, the transition array, the multiplet and the wavelengths (in Å) for each studied transition are displayed. In the third column, spectral lines marked with superscript b are the NIST (Kramida et al. 2013) persistent lines. In the fourth column the transition probabilities are shown. Our theoretical Stark line widths and line shifts (a positive shift is red) are displayed (in Å) in the two last columns. As is well known (Griem 1968), a difference of a factor of 1.5 can be expected between the experimental values and our calculations. This could be due to the theoretical uncertainties. In our case the energy differences of the perturbing levels can reach 15 eV where the Gaunt factor used is 0.2 and, as was indicated by Griem, this approximation is acceptable. The theoretical values for the lines of 1321.71 Å and 2531.65 Å calculated by Milovanović in 2005 have not been included in the table. Although his approach is more sophisticated that our semiempirical calculations, they have been calculated using transition probabilities obtained in the Coulomb approximation (which only includes allowed LS transitions) and as usual are a factor of two lower than those presented in this work (de Andrés-García, Alonso-Medina & Colón 2016). Table 3. Tl II 5d106p2, 5d106sns (n = 7–9) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s7s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1792.83b  1.50  0.5  0.22  −0.18          1  0.16  −0.13          2  0.06  −0.04          3  0.09  −0.07          5  0.11  −0.10          10  0.12  −0.10          16  0.12  −0.10  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1892.72  3.66  0.5  0.29  −0.23          1  0.20  −0.17          2  0.08  −0.06          3  0.11  −0.09          5  0.13  −0.12          10  0.13  −0.12          16  0.14  −0.12  5d106s6p–5d106s7s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  2298.06b  3.47  0.5  0.47  −0.39          1  0.33  −0.28          2  0.15  −0.11          3  0.19  −0.16          5  0.20  −0.19          10  0.21  −0.19          16  0.22  −0.20  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1798.36  0.83  0.5  0.13  −0.10          1  0.09  −0.07          2  0.05  −0.04          3  0.05  −0.04          5  0.05  −0.05          10  0.05  −0.04          16  0.05  −0.04  5d106s6p–5d106s7s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  3091.57b  3.83  0.5  0.48  −0.35          1  0.34  −0.25          2  0.19  −0.13          3  0.19  −0.14          5  0.18  −0.14          10  0.17  −0.14          16  0.19  −0.15  5d106s6p–5d106s8s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1188.83  0.41  0.5  0.34  −0.20          1  0.19  −0.09          2  0.25  −0.20          3  0.28  −0.21          5  0.29  −0.21          10  0.28  −0.19          16  0.26  −0.17  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1231.81  1.05  0.5  0.38  −0.23          1  0.21  −0.11          2  0.28  −0.22          3  0.31  −0.23          5  0.32  −0.23          10  0.30  −0.21          16  0.28  −0.19  5d106s6p–5d106s8s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1391.88  1.30  0.5  0.51  −0.32          1  0.28  −0.15          2  0.36  −0.29          3  0.40  −0.30          5  0.41  −0.30          10  0.39  −0.27          16  0.37  −0.25  5d106s7p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  7144.9  0.40  0.5  17.12  −7.85          1  10.95  −2.69          2  11.79  −5.45          3  13.51  −6.07          5  14.36  −6.39          10  13.92  −6.18          16  13.03  −5.77  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1221.02  0.47  0.5  0.12  −0.07          1  0.07  −0.04          2  0.08  −0.06          3  0.09  −0.06          5  0.09  −0.06          10  0.09  −0.05          16  0.08  −0.05  5d106s6p–5d106s8s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  1705.55  0.92  0.5  0.26  −0.15          1  0.15  −0.09          2  0.18  −0.13          3  0.19  −0.13          5  0.19  −0.12          10  0.18  −0.11          16  0.17  −0.10  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1074.97  0.48  0.5  0.42  −0.25          1  0.72  −0.48          2  0.85  −0.51          3  0.85  −0.50          5  0.82  −0.47          10  0.73  −0.40          16  0.66  −0.36  5d106s6p–5d106s9s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1194.84  0.64  0.5  0.53  −0.33          1  0.89  −0.60          2  1.05  −0.64          3  1.06  −0.62          5  1.02  −0.58          10  0.91  −0.50          16  0.82  −0.45  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1072.99  0.19  0.5  0.11  −0.08          1  0.23  −0.11          2  0.27  −0.12          3  0.27  −0.12          5  0.26  −0.11          10  0.24  −0.09          16  0.21  −0.09  5d106s7p–5d106s9s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  4306.80  0.23  0.5  2.96  −1.31          1  4.25  −1.92          2  4.84  −1.94          3  5.09  −1.94          5  5.09  −1.87          10  4.72  −1.69          16  4.33  −1.53  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P0  1538.39  10.66  0.5  0.04  −0.03          1  0.03  −0.02          2  0.02  −0.02          3  0.02  −0.01          5  0.01  −0.01          10  0.01  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P1  1370.88  3.21  0.5  0.04  −0.02          1  0.02  −0.02          2  0.02  −0.01          3  0.01  −0.01          5  0.01  −0.01          10  0.00  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–3P1  1572.16  2.23  0.5  0.07  −0.05          1  0.05  −0.04          2  0.03  −0.03          3  0.03  −0.02          5  0.02  −0.01          10  0.01  −0.01          16  0.02  −0.01          3  1.36  −0.42          5  1.29  −0.40  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1246.00  1.34  0.5  0.68  −0.17          10  1.14  −0.36          16  1.03  −0.33          1  0.85  −0.25          2  0.94  −0.29          3  0.93  −0.29          5  0.88  −0.28          10  0.77  −0.25          16  0.70  −0.23  5d106s6p–5d106p2  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1507.82  9.29  0.5  1.00  −0.24          1  1.25  −0.36          2  1.37  −0.42          3  1.36  −0.42          5  1.29  −0.40          10  1.14  −0.36          16  1.03  −0.33  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s7s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1792.83b  1.50  0.5  0.22  −0.18          1  0.16  −0.13          2  0.06  −0.04          3  0.09  −0.07          5  0.11  −0.10          10  0.12  −0.10          16  0.12  −0.10  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1892.72  3.66  0.5  0.29  −0.23          1  0.20  −0.17          2  0.08  −0.06          3  0.11  −0.09          5  0.13  −0.12          10  0.13  −0.12          16  0.14  −0.12  5d106s6p–5d106s7s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  2298.06b  3.47  0.5  0.47  −0.39          1  0.33  −0.28          2  0.15  −0.11          3  0.19  −0.16          5  0.20  −0.19          10  0.21  −0.19          16  0.22  −0.20  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1798.36  0.83  0.5  0.13  −0.10          1  0.09  −0.07          2  0.05  −0.04          3  0.05  −0.04          5  0.05  −0.05          10  0.05  −0.04          16  0.05  −0.04  5d106s6p–5d106s7s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  3091.57b  3.83  0.5  0.48  −0.35          1  0.34  −0.25          2  0.19  −0.13          3  0.19  −0.14          5  0.18  −0.14          10  0.17  −0.14          16  0.19  −0.15  5d106s6p–5d106s8s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1188.83  0.41  0.5  0.34  −0.20          1  0.19  −0.09          2  0.25  −0.20          3  0.28  −0.21          5  0.29  −0.21          10  0.28  −0.19          16  0.26  −0.17  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1231.81  1.05  0.5  0.38  −0.23          1  0.21  −0.11          2  0.28  −0.22          3  0.31  −0.23          5  0.32  −0.23          10  0.30  −0.21          16  0.28  −0.19  5d106s6p–5d106s8s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1391.88  1.30  0.5  0.51  −0.32          1  0.28  −0.15          2  0.36  −0.29          3  0.40  −0.30          5  0.41  −0.30          10  0.39  −0.27          16  0.37  −0.25  5d106s7p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  7144.9  0.40  0.5  17.12  −7.85          1  10.95  −2.69          2  11.79  −5.45          3  13.51  −6.07          5  14.36  −6.39          10  13.92  −6.18          16  13.03  −5.77  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1221.02  0.47  0.5  0.12  −0.07          1  0.07  −0.04          2  0.08  −0.06          3  0.09  −0.06          5  0.09  −0.06          10  0.09  −0.05          16  0.08  −0.05  5d106s6p–5d106s8s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  1705.55  0.92  0.5  0.26  −0.15          1  0.15  −0.09          2  0.18  −0.13          3  0.19  −0.13          5  0.19  −0.12          10  0.18  −0.11          16  0.17  −0.10  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1074.97  0.48  0.5  0.42  −0.25          1  0.72  −0.48          2  0.85  −0.51          3  0.85  −0.50          5  0.82  −0.47          10  0.73  −0.40          16  0.66  −0.36  5d106s6p–5d106s9s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1194.84  0.64  0.5  0.53  −0.33          1  0.89  −0.60          2  1.05  −0.64          3  1.06  −0.62          5  1.02  −0.58          10  0.91  −0.50          16  0.82  −0.45  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1072.99  0.19  0.5  0.11  −0.08          1  0.23  −0.11          2  0.27  −0.12          3  0.27  −0.12          5  0.26  −0.11          10  0.24  −0.09          16  0.21  −0.09  5d106s7p–5d106s9s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  4306.80  0.23  0.5  2.96  −1.31          1  4.25  −1.92          2  4.84  −1.94          3  5.09  −1.94          5  5.09  −1.87          10  4.72  −1.69          16  4.33  −1.53  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P0  1538.39  10.66  0.5  0.04  −0.03          1  0.03  −0.02          2  0.02  −0.02          3  0.02  −0.01          5  0.01  −0.01          10  0.01  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P1  1370.88  3.21  0.5  0.04  −0.02          1  0.02  −0.02          2  0.02  −0.01          3  0.01  −0.01          5  0.01  −0.01          10  0.00  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–3P1  1572.16  2.23  0.5  0.07  −0.05          1  0.05  −0.04          2  0.03  −0.03          3  0.03  −0.02          5  0.02  −0.01          10  0.01  −0.01          16  0.02  −0.01          3  1.36  −0.42          5  1.29  −0.40  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1246.00  1.34  0.5  0.68  −0.17          10  1.14  −0.36          16  1.03  −0.33          1  0.85  −0.25          2  0.94  −0.29          3  0.93  −0.29          5  0.88  −0.28          10  0.77  −0.25          16  0.70  −0.23  5d106s6p–5d106p2  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1507.82  9.29  0.5  1.00  −0.24          1  1.25  −0.36          2  1.37  −0.42          3  1.36  −0.42          5  1.29  −0.40          10  1.14  −0.36          16  1.03  −0.33  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST; Kramida et al. 2013). View Large Table 4. Tl II 5d106snp (n = 6–7) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s2–5d106s6p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  1908.62b  0.27  0.5  0.07  −0.07          1  0.05  −0.05          2  0.03  −0.03          3  0.03  −0.03          5  0.02  −0.02          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s6p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  1321.64b  13.02  0.5  0.05  −0.04          1  0.04  −0.03          2  0.03  −0.02          3  0.02  −0.02          5  0.01  −0.01          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s7p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  836.34  0.01  0.5  0.07  −0.01          1  0.06  0.00          2  0.04  0.02          3  0.05  0.02          5  0.05  0.01          10  0.05  0.01          16  0.05  0.01  5d106s7s–5d106s7p  3S1–$$^3{\rm{P}}_2^{\rm{o}}$$  5949.48  0.94  0.5  6.99  −3.51          1  5.97  −1.48          2  3.41  0.74          3  4.45  0.26          5  5.20  −0.33          10  5.45  −0.71          16  5.27  −0.80  5d106s2–5d106s7p  1S0–$$^1{\rm{P}}_1^{\rm{o}}$$  817.18  1.31  0.5  0.05  −0.01          1  0.03  −0.01          2  0.02  −0.01          3  0.03  −0.01          5  0.03  −0.01          10  0.04  −0.01          16  0.03  −0.01  5d106s2–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  709.23  0.16  0.5  0.14  −0.07          1  0.16  −0.09          2  0.19  −0.09          3  0.20  −0.09          5  0.19  −0.08          10  0.17  −0.07          16  0.16  −0.07  5d106s6d–5d106s8p  1D2 –$$^1{\rm{P}}_1^{\rm{o}}$$  3869.15  0.12  0.5  5.06  −2.81          1  5.37  −3.11          2  6.23  −3.10          3  6.24  −2.93          5  6.18  −2.90          10  5.72  −2.66          16  5.24  −2.43  5d106s7s–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  3029.01  0.11  0.5  2.72  −1.36          1  3.08  −1.71          2  3.57  −1.66          3  3.69  −1.67          5  3.62  −1.61          10  3.30  −1.43          16  3.01  −1.29  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s2–5d106s6p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  1908.62b  0.27  0.5  0.07  −0.07          1  0.05  −0.05          2  0.03  −0.03          3  0.03  −0.03          5  0.02  −0.02          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s6p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  1321.64b  13.02  0.5  0.05  −0.04          1  0.04  −0.03          2  0.03  −0.02          3  0.02  −0.02          5  0.01  −0.01          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s7p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  836.34  0.01  0.5  0.07  −0.01          1  0.06  0.00          2  0.04  0.02          3  0.05  0.02          5  0.05  0.01          10  0.05  0.01          16  0.05  0.01  5d106s7s–5d106s7p  3S1–$$^3{\rm{P}}_2^{\rm{o}}$$  5949.48  0.94  0.5  6.99  −3.51          1  5.97  −1.48          2  3.41  0.74          3  4.45  0.26          5  5.20  −0.33          10  5.45  −0.71          16  5.27  −0.80  5d106s2–5d106s7p  1S0–$$^1{\rm{P}}_1^{\rm{o}}$$  817.18  1.31  0.5  0.05  −0.01          1  0.03  −0.01          2  0.02  −0.01          3  0.03  −0.01          5  0.03  −0.01          10  0.04  −0.01          16  0.03  −0.01  5d106s2–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  709.23  0.16  0.5  0.14  −0.07          1  0.16  −0.09          2  0.19  −0.09          3  0.20  −0.09          5  0.19  −0.08          10  0.17  −0.07          16  0.16  −0.07  5d106s6d–5d106s8p  1D2 –$$^1{\rm{P}}_1^{\rm{o}}$$  3869.15  0.12  0.5  5.06  −2.81          1  5.37  −3.11          2  6.23  −3.10          3  6.24  −2.93          5  6.18  −2.90          10  5.72  −2.66          16  5.24  −2.43  5d106s7s–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  3029.01  0.11  0.5  2.72  −1.36          1  3.08  −1.71          2  3.57  −1.66          3  3.69  −1.67          5  3.62  −1.61          10  3.30  −1.43          16  3.01  −1.29  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines NIST (Kramida et al. 2013). View Large Table 5. Tl II 5d106snd (n = 6–8) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s6d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1499.30  8.28  0.5  0.13  −0.11          1  0.12  −0.11          2  0.07  −0.06          3  0.08  −0.08          5  0.09  −0.09          10  0.09  −0.09          16  0.09  −0.08  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1568.57  5.16  0.5  0.17  −0.15          1  0.15  −0.13          2  0.09  −0.08          3  0.10  −0.09          5  0.11  −0.10          10  0.10  −0.10          16  0.10  −0.10  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1593.26  0.53  0.5  0.20  −0.18          1  0.13  −0.11          2  0.11  −0.10          3  0.08  −0.07          5  0.09  −0.08          10  0.09  −0.09          16  0.10  −0.09  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  2530.74b  1.47  0.5  0.58  −0.49          1  0.37  −0.30          2  0.31  −0.26          3  0.22  −0.18          5  0.24  −0.21          10  0.26  −0.23          16  0.27  −0.24  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1561.58  15.20  0.5  0.27  −0.23          1  0.22  −0.19          2  0.13  −0.11          3  0.15  −0.14          5  0.17  −0.15          10  0.16  −0.15          16  0.16  −0.15  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–3D2  2451.83  0.25  0.5  0.72  −0.59          1  0.58  −0.49          2  0.35  −0.29          3  0.40  −0.35          5  0.42  −0.38          10  0.41  −0.39          16  0.41  −0.38  5d106s6p–5d106s6d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1814.77b  8.25  0.5  0.40  −0.33          1  0.38  −0.33          2  0.23  −0.19          3  0.27  −0.24          5  0.30  −0.27          10  0.30  −0.28          16  0.30  −0.27  5d106s6p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1130.17  1.63  0.5  0.40  −0.14          1  0.33  −0.05          2  0.35  −0.11          3  0.36  −0.12          5  0.34  −0.12          10  0.31  −0.11          16  0.28  −0.10  5d106s7p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  5384.85  0.78  0.5  9.85  −3.06          1  8.20  −0.97          2  8.44  −2.16          3  8.70  −2.39          5  8.52  −2.49          10  7.74  −2.38          16  7.04  −2.21  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1183.41  1.24  0.5  0.22  −0.06          1  0.15  0.00          2  0.19  −0.07          3  0.21  −0.08          5  0.22  −0.08          10  0.20  −0.08          16  0.19  −0.08  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1330.40  3.28  0.5  0.30  −0.09          1  0.20  −0.02          2  0.24  −0.09          3  0.27  −0.10          5  0.28  −0.11          10  0.26  −0.10          16  0.25  −0.10  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1167.43  1.81  0.5  0.74  −0.31          1  0.63  −0.17          2  0.67  −0.27          3  0.68  −0.28          5  0.66  −0.27          10  0.59  −0.25          16  0.53  −0.23  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D2  1310.20  0.59  0.5  0.94  −0.40          1  0.80  −0.23          2  0.85  −0.35          3  0.86  −0.36          5  0.83  −0.35          10  0.74  −0.32          16  0.67  −0.29  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1307.50  1.92  0.5  1.20  −0.45          1  1.03  −0.23          2  1.14  −0.42          3  1.16  −0.45          5  1.12  −0.44          10  1.01  −0.41          16  0.92  −0.38  5d106s6p–5d106s8d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1018.85  0.64  0.5  0.94  −0.09          1  1.06  −0.25          2  1.07  −0.27          3  1.03  −0.27          5  0.95  −0.25          10  0.81  −0.22          16  0.72  −0.20  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1050.30  0.41  0.5  1.02  −0.11          1  1.14  −0.28          2  1.15  −0.30          3  1.10  −0.29          5  1.01  −0.27          10  0.87  −0.23          16  0.77  −0.21  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1049.73  0.77  0.5  1.69  −0.08          1  1.92  −0.38          2  1.94  −0.43          3  1.86  −0.43          5  1.71  −0.41          10  1.47  −0.36          16  1.30  −0.32  5d106s6p–5d106s8d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1373.52  6.44  0.5  3.51  −2.78          1  3.96  −3.10          2  3.92  −2.95          3  3.73  −2.77          5  3.41  −2.49          10  2.92  −2.10          16  2.57  −1.84  5d106s6p–5d106s8d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1162.55  0.79  0.5  2.71  −0.05          1  3.17  −0.59          2  3.24  −0.70          3  3.12  −0.71          5  2.89  −0.68          10  2.49  −0.60          16  2.21  −0.55  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s6d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1499.30  8.28  0.5  0.13  −0.11          1  0.12  −0.11          2  0.07  −0.06          3  0.08  −0.08          5  0.09  −0.09          10  0.09  −0.09          16  0.09  −0.08  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1568.57  5.16  0.5  0.17  −0.15          1  0.15  −0.13          2  0.09  −0.08          3  0.10  −0.09          5  0.11  −0.10          10  0.10  −0.10          16  0.10  −0.10  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1593.26  0.53  0.5  0.20  −0.18          1  0.13  −0.11          2  0.11  −0.10          3  0.08  −0.07          5  0.09  −0.08          10  0.09  −0.09          16  0.10  −0.09  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  2530.74b  1.47  0.5  0.58  −0.49          1  0.37  −0.30          2  0.31  −0.26          3  0.22  −0.18          5  0.24  −0.21          10  0.26  −0.23          16  0.27  −0.24  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1561.58  15.20  0.5  0.27  −0.23          1  0.22  −0.19          2  0.13  −0.11          3  0.15  −0.14          5  0.17  −0.15          10  0.16  −0.15          16  0.16  −0.15  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–3D2  2451.83  0.25  0.5  0.72  −0.59          1  0.58  −0.49          2  0.35  −0.29          3  0.40  −0.35          5  0.42  −0.38          10  0.41  −0.39          16  0.41  −0.38  5d106s6p–5d106s6d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1814.77b  8.25  0.5  0.40  −0.33          1  0.38  −0.33          2  0.23  −0.19          3  0.27  −0.24          5  0.30  −0.27          10  0.30  −0.28          16  0.30  −0.27  5d106s6p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1130.17  1.63  0.5  0.40  −0.14          1  0.33  −0.05          2  0.35  −0.11          3  0.36  −0.12          5  0.34  −0.12          10  0.31  −0.11          16  0.28  −0.10  5d106s7p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  5384.85  0.78  0.5  9.85  −3.06          1  8.20  −0.97          2  8.44  −2.16          3  8.70  −2.39          5  8.52  −2.49          10  7.74  −2.38          16  7.04  −2.21  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1183.41  1.24  0.5  0.22  −0.06          1  0.15  0.00          2  0.19  −0.07          3  0.21  −0.08          5  0.22  −0.08          10  0.20  −0.08          16  0.19  −0.08  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1330.40  3.28  0.5  0.30  −0.09          1  0.20  −0.02          2  0.24  −0.09          3  0.27  −0.10          5  0.28  −0.11          10  0.26  −0.10          16  0.25  −0.10  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1167.43  1.81  0.5  0.74  −0.31          1  0.63  −0.17          2  0.67  −0.27          3  0.68  −0.28          5  0.66  −0.27          10  0.59  −0.25          16  0.53  −0.23  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D2  1310.20  0.59  0.5  0.94  −0.40          1  0.80  −0.23          2  0.85  −0.35          3  0.86  −0.36          5  0.83  −0.35          10  0.74  −0.32          16  0.67  −0.29  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1307.50  1.92  0.5  1.20  −0.45          1  1.03  −0.23          2  1.14  −0.42          3  1.16  −0.45          5  1.12  −0.44          10  1.01  −0.41          16  0.92  −0.38  5d106s6p–5d106s8d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1018.85  0.64  0.5  0.94  −0.09          1  1.06  −0.25          2  1.07  −0.27          3  1.03  −0.27          5  0.95  −0.25          10  0.81  −0.22          16  0.72  −0.20  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1050.30  0.41  0.5  1.02  −0.11          1  1.14  −0.28          2  1.15  −0.30          3  1.10  −0.29          5  1.01  −0.27          10  0.87  −0.23          16  0.77  −0.21  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1049.73  0.77  0.5  1.69  −0.08          1  1.92  −0.38          2  1.94  −0.43          3  1.86  −0.43          5  1.71  −0.41          10  1.47  −0.36          16  1.30  −0.32  5d106s6p–5d106s8d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1373.52  6.44  0.5  3.51  −2.78          1  3.96  −3.10          2  3.92  −2.95          3  3.73  −2.77          5  3.41  −2.49          10  2.92  −2.10          16  2.57  −1.84  5d106s6p–5d106s8d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1162.55  0.79  0.5  2.71  −0.05          1  3.17  −0.59          2  3.24  −0.70          3  3.12  −0.71          5  2.89  −0.68          10  2.49  −0.60          16  2.21  −0.55  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST Kramida et al. 2013). View Large Table 6. Tl II 5d106s5f theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6d–5d106s5f  3D2–$$^3{\rm{P}}_3^{\rm{o}}$$  5078.54b  1.64  0.5  8.92  −6.07          1  7.76  −5.75          2  5.50  −5.35          3  6.32  −5.55          5  6.67  −5.44          10  6.43  −4.95          16  6.00  −4.50  5d106s6d–5d106s5f  3D3–$$^3{\rm{P}}_4^{\rm{o}}$$  5152.14b  1.77  0.5  14.60  −10.22          1  13.05  −9.98          2  8.99  −8.45          3  10.51  −9.20          5  11.29  −9.42          10  11.00  −8.88          16  10.35  −8.17  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6d–5d106s5f  3D2–$$^3{\rm{P}}_3^{\rm{o}}$$  5078.54b  1.64  0.5  8.92  −6.07          1  7.76  −5.75          2  5.50  −5.35          3  6.32  −5.55          5  6.67  −5.44          10  6.43  −4.95          16  6.00  −4.50  5d106s6d–5d106s5f  3D3–$$^3{\rm{P}}_4^{\rm{o}}$$  5152.14b  1.77  0.5  14.60  −10.22          1  13.05  −9.98          2  8.99  −8.45          3  10.51  −9.20          5  11.29  −9.42          10  11.00  −8.88          16  10.35  −8.17  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST Kramida et al. 2013). View Large Our values of the widths FWHM (ω(pm)) and the Stark line shifts (d(pm)) for the persistent lines of 1908.62 Å, 1321.63 Å and 3091.57 Å are plotted against temperature and shown in Fig. 2. A comparison of the calculated Stark widths of Bi IV, Pb III, and the calculated Stark width of Tl II (same isoelectronic sequence) are displayed for three transitions in Fig. 3. The values of Pb III and Bi IV Stark widths used in these comparisons were obtained by some of these same authors in previous works (Zanon et al. 2010); Colón et al. 2017). In the case of Pb III, the values used, not included in the cited work, have been calculated in this work following the procedure indicated for Tl II. As in our previous work (Colon et al. 2017), a dependence of the Stark widths compatible with Z−2 can also be observed. Figure 2. View largeDownload slide Calculated Stark width FWHM (ω (pm)) and shift (d (pm)) at an electron density of 1017 cm−3 versus temperature for several spectral lines of Tl II. Figure 2. View largeDownload slide Calculated Stark width FWHM (ω (pm)) and shift (d (pm)) at an electron density of 1017 cm−3 versus temperature for several spectral lines of Tl II. Figure 3. View largeDownload slide Theoretical Stark width FWHM (ω (in frequency units)) of five transitions at an electron density of 1017 cm−3 in Tl II (present work), Pb III (Zanón et al. 2010) and Bi IV (Colón et al. 2017) versus the ion charge (number Z) at a temperature of 20 000 K. Figure 3. View largeDownload slide Theoretical Stark width FWHM (ω (in frequency units)) of five transitions at an electron density of 1017 cm−3 in Tl II (present work), Pb III (Zanón et al. 2010) and Bi IV (Colón et al. 2017) versus the ion charge (number Z) at a temperature of 20 000 K. In conclusion, in this work we have calculated the transition probabilities and the Stark widths and shifts of 49 Tl II spectral lines. Radiative lifetimes of 11 levels of Tl II were also calculated. Core polarization effects (CPE) were taken into account in the Cowan code, which was used to calculate the required matrix elements in this work. Griem´s semiempirical model was used in order to obtain the Stark broadening parameters. The dependence of these values on temperature and charge number Z has also been studied. Acknowledgements This work was financially supported by the Spanish Ministry of Science and Technology (DGI project MAT2013-44964-R. REFERENCES Andersen T., Kirkegård Nielsen A., Sørensen G., 1972, Phys. Scr. , 6 122 https://doi.org/10.1088/0031-8949/6/2-3/004 CrossRef Search ADS   Andersen T., Sørensen G., 1972, Phys. Rev. A , 5, 2447 https://doi.org/10.1103/PhysRevA.5.2447 CrossRef Search ADS   Baranger M., 1958, Phys. Rev. , 112, 855 https://doi.org/10.1103/PhysRev.112.855 CrossRef Search ADS   Biémont E., Fischer C. F., Godefroid M. R., Palmeri P., Quinet P., 2000, Phys. Rev. A , 62, 032512 https://doi.org/10.1103/PhysRevA.62.032512 CrossRef Search ADS   Brage T., Proffitt C. R., Leckrone E. S., 1999, J. Phys. B: Atomic Molecular Optical Phys. , 32, 3183 https://doi.org/10.1088/0953-4075/32/13/308 CrossRef Search ADS   Colón C., Moreno-Díaz C., de Andrés-García I., Alonso-Medina A., 2017, MNRAS , 470, 2179 https://doi.org/10.1093/mnras/stx1320 CrossRef Search ADS   Cowan R. D., 1981, The Theory of Atomic Structure and Spectra . Univ. California Press, Berkeley, CA Curtis L. J., 2000, Phys. Scr. , 62, 31 https://doi.org/10.1238/Physica.Regular.062a00031 CrossRef Search ADS   Curtis L. J., Irving R. E., Henderson M., Matulioniene R., Fischer C. F., Pinnington E. H., 2001, Phys. Rev. A , 63, 042502 https://doi.org/10.1103/PhysRevA.63.042502 CrossRef Search ADS   de Andrés-García I., Alonso-Medina A., Colón C., 2016, MNRAS , 455, 1145 https://doi.org/10.1093/mnras/stv2170 CrossRef Search ADS   Ellis C. B., Sawyer R. A., 1936, Phys. Rev. , 49, 145 https://doi.org/10.1103/PhysRev.49.145 CrossRef Search ADS   Griem H. R., 1968, Phys. Rev. , 165, 258 https://doi.org/10.1103/PhysRev.165.258 CrossRef Search ADS   Hameed S., 1972, J. Phys. B: Atomic Molecular Phys. , 5, 746 https://doi.org/10.1088/0022-3700/5/4/009 CrossRef Search ADS   Henderson M., Curtis L. J., 1996, J. Phys. B: Atomic Molecular Optical Phys. , 29, L629 https://doi.org/10.1088/0953-4075/29/17/001 CrossRef Search ADS   Kramida A., Ralchenko Y., Reader J., NIST ASD Team, 2013, NIST Atomic Spectra Database  (v.5.3). Available at: http://physics.nist.gov/asd Kurucz R. L., 1993, CD-ROM 18: SYNTHE Spectrum Synthesis Programs and Line Data.  Smithsonian Astrophys. Obs., Cambridge, MA Leckrone E. S., Proffitt C. R., Wahlgren G. M., Johansson S., Brage T., 1999, AJ , 117, 1454 https://doi.org/10.1086/300776 CrossRef Search ADS   McLennan J. C., McLay A. B., Crawford M. F., 1929, Proc. R. Soc. A: Math. Phys. Eng. Sci., A  125, 570 https://doi.org/10.1098/rspa.1929.0186 CrossRef Search ADS   Migdalek J., Baylis W. E., 1978, J. Phys. B: Atomic Molecular Phys. , 11, L497 https://doi.org/10.1088/0022-3700/11/17/001 CrossRef Search ADS   Migdalek J., Baylis W. E., 1985, J. Phys. B: Atomic Molecular Phys. , 18, 1533 https://doi.org/10.1088/0022-3700/18/8/012 CrossRef Search ADS   Milovanović N., 2005, Memorie della Supplementi. Societa Astronomica Italiana , 7, 132 Moore C. E., 1958, Atomic Energy Levels:  NBS Circular 467 Vol. III. National Bureau of Standards, Washington, DC, 213 Popović L. C., Dimitrijević M. S., Ryabchikova T., 1999, A&A , 350, 719 Sansonetti J. E., Martin W. C., 2005, J. Phys. Chem. Reference Data , 34, 1559 https://doi.org/10.1063/1.1800011 CrossRef Search ADS   Seaton M. J., 1962, in Bates D. R., ed., Atomic and Molecular Processes.  Academic Press, New York Van Regemorter H., 1962, ApJ , 136, 906 https://doi.org/10.1086/147445 CrossRef Search ADS   Zanón A., Alonso-Medina A., Colón C., 2010, Int. Rev. At. Mol. Phys. , 1, 1 © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society Oxford University Press

Stark broadening parameters and transition probabilities of persistent lines of Tl II

Loading next page...
 
/lp/ou_press/stark-broadening-parameters-and-transition-probabilities-of-persistent-f8NvfCBnMn
Publisher
The Royal Astronomical Society
Copyright
© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
ISSN
0035-8711
eISSN
1365-2966
D.O.I.
10.1093/mnras/sty167
Publisher site
See Article on Publisher Site

Abstract

Abstract The presence of singly ionized thallium in the stellar atmosphere of the chemically peculiar star χ Lupi was reported by Leckrone et al. in 1999 by analysis of its stellar spectrum obtained with the Goddard High Resolution Spectrograph (GHRS) on board the Hubble Space Telescope. Atomic data about the spectral line of 1307.50 Å and about the hyperfine components of the spectral lines of 1321.71 Å and 1908.64 Å were taken from different sources and used to analyse the isotopic abundance of thallium II in the star χ Lupi. From their results the authors concluded that the photosphere of the star presents an anomalous isotopic composition of Tl II. A study of the atomic parameters of Tl II and of the broadening by the Stark effect of its spectral lines (and therefore of the possible overlaps of these lines) can help to clarify the conclusions about the spectral abundance of Tl II in different stars. In this paper we present calculated values of the atomic transition probabilities and Stark broadening parameters for 49 spectral lines of Tl II obtained by using the Cowan code including core polarization effects and the Griem semiempirical approach. Theoretical values of radiative lifetimes for 11 levels (eight with experimental values in the bibliography) are calculated and compared with the experimental values in order to test the quality of our results. Theoretical trends of the Stark width and shift parameters versus the temperature for spectral lines of astrophysical interest are displayed. Trends of our calculated Stark width for the isoelectronic sequence Tl II–Pb III–Bi IV are also displayed. atomic data, atomic processes 1 INTRODUCTION There are different industrial applications of singly ionized thallium (Tl II). In particular, its applications in the form of thallium sulphide in photocells can be mentioned because its conductivity increases when exposed to infrared light. In 1999, in the analysis of the stellar spectrum, obtained with the Goddard High Resolution Spectrograph (GHRS) on board the Hubble Space Telescope, of the chemically peculiar star χ Lupi, the presence of Tl II was detected by Leckrone et al. The transition probability for the spectral line of 1307.50 Å was calculated by the authors in their work by using the Cowan code (Cowan 1981) without taking into account the core polarization effects (CPE). The transition probabilities for the hyperfine components of the spectral lines of 1321.71 Å and 1908.64 Å were taken from different sources listed in the Kurucz data base (1993). These values were used to analyse the isotopic abundance of thallium II in the star χ Lupi. From their results the authors concluded that the photosphere of the star presents an anomalous isotopic composition of Tl II. A study of the transition probabilities of Tl II including CPE can help to clarify the conclusions about the spectral abundance of Tl II in other stars. Also, as the mechanism of broadening by collision with electrons is the main pressure mechanism of stellar line broadening in atmospheres of stars of type A and late B (Popović, Dimitrijević & Ryabchikova 1999) and in white dwarf atmospheres (Milovanović 2005), an analysis of the Stark broadening parameters seems necessary to solve some problems of possible overlaps of spectral lines. Tl II is a member of the isoelectronic sequence of mercury, as are Pb III and Bi IV. The atomic parameters of Pb III and Bi IV have already been measured and calculated by the present authors. Calculations of the Stark broadening parameters of spectral lines of Pb III and Bi IV, taking into account the effects of core polarization, were made by Zanón, Alonso-Medina & Colón (2010) and Colon et al. (2017). In this work we have done a theoretical study similar to the one performed for Pb III and Bi IV. There is an early analysis of the Tl II spectrum, by McLennan, McLay & Crawford (1929), which was extended by Ellis & Sawyer (1936). In this work, 76 energy levels are provided and 275 lines are listed, of which 160 are identified for the first time. This last work is collected in the tables of Moore (1958) and later by Sansonetti & Martin (2005). We have only found eight values of experimental lifetimes in the bibliography. The experimental lifetimes of six levels of Tl II were obtained, by means of the beam foil technique, in 1972 by Andersen & Sørensen. A new lifetime for the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level was measured months later by Andersen, Kirkegård Nielsen & Sørensen (1972) using the 600 kV heavy-ion accelerator at the University of Aarhus. The lifetimes of three of the levels provided by Andersen were again measured by Henderson & Curtis (1996), which also included the measurement of the lifetime of a new level. There are no experimental measurements for the transition probabilities of the Tl II spectral lines except for the line of 1321.64 Å that was obtained directly from the value of the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level lifetime, by Andersen et al. (1972). Theoretical transition probabilities are given by some authors: Theoretical values in the Dirac–Fock approximation (MCDF) were calculated by Brage, Proffitt & Leckrone (1999); in addition, in the same year the theoretical value of the transition probability for line 1307.59 Å in the relativistic Hartree–Fock approximation (HFR) was calculated by Leckrone et al. (1999). Subsequently, values derived from experimental lifetimes, by using theoretical branching ratios, were published by Curtis (2000). Stark broadening parameters for the lines of 1321.71 Å and 2531.65 Å were calculated in the modified semiempirical approach (SME) by Milovanović in 2005. In this paper we present theoretical values of transition probabilities, level lifetimes and Stark broadening parameters for 49 spectral lines of Tl II. We include those that appear in the NIST data base (Kramida et al. 2013) as persistent lines (10 lines) in addition to the other 39 lines also in the NIST data base that appear with high relative intensities. We present theoretical values of the transition probabilities and the Stark broadening parameters for 49 spectral lines of Tl II that arise from configurations 5d106sns (n = 7–9), 5d106p2, 5d106snp (n = 6, 7), 5d106snd (n = 6, 7, 8) and 5d106s5f. Theoretical values of radiative lifetimes for 11 levels (eight with experimental values in the bibliography) are calculated and compared with the experimental values. These calculations were obtained using a semiclassical approach taking into account the core polarization effects (CPE), similar to the calculations in Colón et al. (2017). The Stark broadening parameters are presented for a set of temperatures ranging from 5000 to 160 000 K and an electronic density of 1017 cm−3. The theoretical calculations are presented in Section 2. In Section 3 we describe our results, including the regularity of the Stark broadening parameters versus the temperature and a comparison of calculated Stark widths for Tl II, Pb III and Bi IV (same isoelectronic sequence). 2 THEORETICAL CALCULATIONS Our calculation procedure is similar to that presented by the authors in previous work (Colón et al. 2017). In order to obtain the transition probabilities and the level lifetimes, wavefunctions were calculated in an intermediate coupling scheme (IC) using the relativistic Hartree–Fock (HFR) approach by means of the computer code in Cowan (1981). As Tl II has a high atomic number, Z = 81, the core polarization effects (CPE) must be considered. The Cowan code was modified in order to include these effects in a similar way to that presented in Colón et al. (2017). The CP effects were included following the suggestions of Migdalek and Baylis (1978) and the expressions of Biémont, Froese Fischer & Godefroid (2000): The core polarization effects were written as the one-particle, VP1, and two-particle, VP2, potential models (expressions (1) and (2) in the original Biémont paper). A modification in the matrix element can be made in order to take into account the potential change. The <Pnl|r|Pn'l’ > is replaced by   \begin{eqnarray}&&\int_{0}^{\infty }{{{P_{nl}}r\left( {1 - \frac{{{\alpha _d}}}{{{{\left( {{r^2} + r_{\rm{c}}^2} \right)}^{{3 \mathord{\left/ {\vphantom {3 2}} \right.} 2}}}}}} \right)}}{P_{n'l'}}\,{\rm{d}r}\nonumber\\ &&- \frac{{{\alpha _d}}}{{r_{\rm{c}}^3}}\int_{0}^{{{r_{\rm{c}}}}}{{{P_{nl}}\left( r \right)r{P_{n'l'}}\left( r \right)}}\,{\rm{d}r,}\end{eqnarray} (1)where the core penetration term suggested by Hameed (1972) has also been included. For the dipole polarizability and the cutoff radius we use the values αd = 5.472 (in au) and rc = 1.349 (in au), computed by Migdalek & Baylis (1985). We have used in our calculations 26 configurations of Tl II: 5d106s2, 5d106p2, 5d106sns (n = 7–12), 5d106snd (n = 6–11) and 5d106sng (n = 5, 6) for even parity and 5d106snp (n = 6, 11), 5d106snf (n = 5–7) and 5d96s26p for odd parity. For the IC calculations we used all the experimental levels shown in the table in Moore (1958) based on Ellis & Sawyer (1936). A partial Grotrian energy level scheme of Tl II showing several spectral lines with experimental radiative lifetimes is displayed in Fig. 1. Figure 1. View largeDownload slide Partial Grotrian diagram of the Tl II energy levels (Ellis & Sawyer 1936; Sansonetti & Martin 2005), showing several spectral lines with experimental lifetimes. Figure 1. View largeDownload slide Partial Grotrian diagram of the Tl II energy levels (Ellis & Sawyer 1936; Sansonetti & Martin 2005), showing several spectral lines with experimental lifetimes. As usual, the number of adjustable parameters in the Cowan code exceeds the number of experimental levels available in the literature (39 for even parity and 37 for odd parity). Following the recommendations of Cowan, in those configurations with a reduced number of experimental levels certain parameters are excluded from the fitting process. In these cases a factor of 0.85 was used to decrease the values of radials integrals Fk, Gk and Rk that are excluded from the fitting process. To avoid transition probabilities excessively influenced by a mixture of forced configurations to obtain the best possible adjustment, we have allowed our theoretical levels to differ by 1 per cent from the experimental levels. The parameters obtained following this procedure do not differ by more than 10 per cent of the ab initio values and are available on request. In this way, the transition probabilities for the allowed lines in LS coupling and for the so-called forbidden transitions were obtained. Theoretical lifetimes for several levels were also obtained. To obtain the broadening parameters by using the matrix elements calculated from the Cowan code, wwe have used the semiempirical formulas obtained by Griem in 1968 (expressions (24) and (35) in the original paper) where was taken into account Baranger´s (1958) original formulation with semiempirical effective Gaunt factors, as proposed by Van Regemorter (1962) and Seaton (1962). As is well known (Griem 1968), a factor larger than 1.5 between calculated and experimental values can be expected with the use of this effective Gaunt factor. In this paper the Stark widths, ω, and Stark shifts, d, are presented in wavelength units. As the values obtained with the above-mentioned expressions are in frequency units, the full width at half maximum (FWHM) of the spectral line, ω, in wavelength units is obtained through the expression ω = ωse λ2/ (πc), where λ is the wavelength and c is the speed of light. 3 RESULTS AND DISCUSSION The probabilities of theoretical transitions obtained in this work for 13 spectral lines of Tl II of special interest (they appear in the NIST data base as persistent lines or have appeared in the bibliography for some reason) are displayed in Table 1. Our values are presented in column 4 of the table mentioned above. In columns 5 and 6 are the theoretical values (except for the line of 1321.64 Å that was obtained from the lifetime of the 5d106s6p $$^1{\rm{P}}_1^{\rm{o}}$$ level) provided by other authors. As can be seen, there is a good agreement even though they have been obtained by different procedures. In column 4 in parentheses we present the values obtained without taking into account core polarization effects (CPE). It should be noted that in the case of the 1307.50 Å line, this last value coincides with that obtained in the work of Leckrone et al. (1999) although the value obtained taking into account these effects is a factor of two lower. In later tables values obtained in this work are presented for the transition probabilities of other spectral lines collected by NIST but with lower relative intensities. Table 1. Calculated transition probabilities of persistent Tl II lines. Transition levels    Transition probabilities (108 s−1)  Upper  Lower  Wavelength λ (Å)a  This work  Curtis (2000)  Brage et al. (1999)c  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1321.64  13.02(24.1)  16.9  17.3  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  1593.26b  0.52  0.48  0.22  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_0^{\rm{o}}$$  1792.83  1.50    1.02  5d106s6d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1814.77  8.25    9.17  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1871.39b  0.14  0.01  0.21  5d106s7d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1307.50  1.92(3.17)    3.17  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1908.62  0.27  0.26  0.27  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  2298.06  3.47    3.79  5d106s6d1D2  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  2530.74  1.47  1.18  1.31  5d106s7s1S0  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  3091.57  3.83    3.34  5d106s5f3F3  5d106s6d3D2  5078.54  1.64      5d106s5f3F4  5d106s6d3D3  5152.14  1.77      5d106s7p$$^3{\rm{P}}_2^{\rm{o}}$$  5d106s7s3S1  5949.48  0.94      Transition levels    Transition probabilities (108 s−1)  Upper  Lower  Wavelength λ (Å)a  This work  Curtis (2000)  Brage et al. (1999)c  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1321.64  13.02(24.1)  16.9  17.3  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  1593.26b  0.52  0.48  0.22  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_0^{\rm{o}}$$  1792.83  1.50    1.02  5d106s6d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1814.77  8.25    9.17  5d106s6d1D2  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1871.39b  0.14  0.01  0.21  5d106s7d3D3  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  1307.50  1.92(3.17)    3.17  5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  5d106s2 1S0  1908.62  0.27  0.26  0.27  5d106s7s3S1  5d106s6p$$^3{\rm{P}}_2^{\rm{o}}$$  2298.06  3.47    3.79  5d106s6d1D2  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  2530.74  1.47  1.18  1.31  5d106s7s1S0  5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  3091.57  3.83    3.34  5d106s5f3F3  5d106s6d3D2  5078.54  1.64      5d106s5f3F4  5d106s6d3D3  5152.14  1.77      5d106s7p$$^3{\rm{P}}_2^{\rm{o}}$$  5d106s7s3S1  5949.48  0.94      Notes.aPersistent lines (NIST; Kramida et al. 2013). bNIST Kramida et al. (2013) and Curtis et al. (2001). cValues deduced from the author´s oscillator strengths. View Large In order to show the quality of our theoretical values of the transition probabilities (beyond a comparison with other theoretical values) we have compared the lifetime values obtained in this work with experimental lifetime values available in the bibliography. Our theoretical lifetime values for 11 levels of Tl II (of which eight have experimental values available in the bibliography) are presented in Table 2. In the last three columns of the table, the experimental values of different authors are collected. The ratio between the experimental values of radiative lives and the theoretical values obtained in this work for several levels of Tl II is less than 1.5, with the notable exception of the values of the 6s7s 3S1 level lifetime. Like Brague et al. (1999), we suggest that the lifetime of this level should be measured again. Table 2. Radiative lifetimes calculated for several levels of Tl II.   Radiative lifetimes τ (ns)  Level  This work  Other authors  5d106s7s3S1  1.15  1.31a  18±4b      5d106s7s1S0  2.15  2.77a  4.6±0.5b  3.0±0.4c    5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  36.67  36.5a    39±2c    5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  0.76  0567a    0.59±0.04c  0.65±0.08d  5d106s6d1D2  5.01  5.61a  5.0±1.0b  6.5±0.5c    5d106s6d3D1  0.73          5d106s6d3D2  0.89          5d106s6d3D3  1.21          5d106s5f$$^1{\rm{F}}_3^{\rm{o}}$$  5.12    6.8±0.8b      5d106s5f$$^3{\rm{F}}_3^{\rm{o}}$$  5.18    7.8±1.0b      5d106s6f$$^3{\rm{F}}_4^{\rm{o}}$$  14.8    9.3±1.5b        Radiative lifetimes τ (ns)  Level  This work  Other authors  5d106s7s3S1  1.15  1.31a  18±4b      5d106s7s1S0  2.15  2.77a  4.6±0.5b  3.0±0.4c    5d106s6p$$^3{\rm{P}}_1^{\rm{o}}$$  36.67  36.5a    39±2c    5d106s6p$$^1{\rm{P}}_1^{\rm{o}}$$  0.76  0567a    0.59±0.04c  0.65±0.08d  5d106s6d1D2  5.01  5.61a  5.0±1.0b  6.5±0.5c    5d106s6d3D1  0.73          5d106s6d3D2  0.89          5d106s6d3D3  1.21          5d106s5f$$^1{\rm{F}}_3^{\rm{o}}$$  5.12    6.8±0.8b      5d106s5f$$^3{\rm{F}}_3^{\rm{o}}$$  5.18    7.8±1.0b      5d106s6f$$^3{\rm{F}}_4^{\rm{o}}$$  14.8    9.3±1.5b      Notes.aBrage et al. (1999). bAndersen & Sørensen (1972). cHenderson & Curtis (1996). dAndersen et al. (1972). View Large All our results for the transition probabilities and the Stark broadening parameters are shown in Tables 3–6. Tables are displayed for temperatures ranging from 5000 to 160 000 K and an electronic density of 1017 cm−3. In the first three columns, the transition array, the multiplet and the wavelengths (in Å) for each studied transition are displayed. In the third column, spectral lines marked with superscript b are the NIST (Kramida et al. 2013) persistent lines. In the fourth column the transition probabilities are shown. Our theoretical Stark line widths and line shifts (a positive shift is red) are displayed (in Å) in the two last columns. As is well known (Griem 1968), a difference of a factor of 1.5 can be expected between the experimental values and our calculations. This could be due to the theoretical uncertainties. In our case the energy differences of the perturbing levels can reach 15 eV where the Gaunt factor used is 0.2 and, as was indicated by Griem, this approximation is acceptable. The theoretical values for the lines of 1321.71 Å and 2531.65 Å calculated by Milovanović in 2005 have not been included in the table. Although his approach is more sophisticated that our semiempirical calculations, they have been calculated using transition probabilities obtained in the Coulomb approximation (which only includes allowed LS transitions) and as usual are a factor of two lower than those presented in this work (de Andrés-García, Alonso-Medina & Colón 2016). Table 3. Tl II 5d106p2, 5d106sns (n = 7–9) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s7s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1792.83b  1.50  0.5  0.22  −0.18          1  0.16  −0.13          2  0.06  −0.04          3  0.09  −0.07          5  0.11  −0.10          10  0.12  −0.10          16  0.12  −0.10  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1892.72  3.66  0.5  0.29  −0.23          1  0.20  −0.17          2  0.08  −0.06          3  0.11  −0.09          5  0.13  −0.12          10  0.13  −0.12          16  0.14  −0.12  5d106s6p–5d106s7s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  2298.06b  3.47  0.5  0.47  −0.39          1  0.33  −0.28          2  0.15  −0.11          3  0.19  −0.16          5  0.20  −0.19          10  0.21  −0.19          16  0.22  −0.20  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1798.36  0.83  0.5  0.13  −0.10          1  0.09  −0.07          2  0.05  −0.04          3  0.05  −0.04          5  0.05  −0.05          10  0.05  −0.04          16  0.05  −0.04  5d106s6p–5d106s7s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  3091.57b  3.83  0.5  0.48  −0.35          1  0.34  −0.25          2  0.19  −0.13          3  0.19  −0.14          5  0.18  −0.14          10  0.17  −0.14          16  0.19  −0.15  5d106s6p–5d106s8s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1188.83  0.41  0.5  0.34  −0.20          1  0.19  −0.09          2  0.25  −0.20          3  0.28  −0.21          5  0.29  −0.21          10  0.28  −0.19          16  0.26  −0.17  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1231.81  1.05  0.5  0.38  −0.23          1  0.21  −0.11          2  0.28  −0.22          3  0.31  −0.23          5  0.32  −0.23          10  0.30  −0.21          16  0.28  −0.19  5d106s6p–5d106s8s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1391.88  1.30  0.5  0.51  −0.32          1  0.28  −0.15          2  0.36  −0.29          3  0.40  −0.30          5  0.41  −0.30          10  0.39  −0.27          16  0.37  −0.25  5d106s7p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  7144.9  0.40  0.5  17.12  −7.85          1  10.95  −2.69          2  11.79  −5.45          3  13.51  −6.07          5  14.36  −6.39          10  13.92  −6.18          16  13.03  −5.77  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1221.02  0.47  0.5  0.12  −0.07          1  0.07  −0.04          2  0.08  −0.06          3  0.09  −0.06          5  0.09  −0.06          10  0.09  −0.05          16  0.08  −0.05  5d106s6p–5d106s8s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  1705.55  0.92  0.5  0.26  −0.15          1  0.15  −0.09          2  0.18  −0.13          3  0.19  −0.13          5  0.19  −0.12          10  0.18  −0.11          16  0.17  −0.10  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1074.97  0.48  0.5  0.42  −0.25          1  0.72  −0.48          2  0.85  −0.51          3  0.85  −0.50          5  0.82  −0.47          10  0.73  −0.40          16  0.66  −0.36  5d106s6p–5d106s9s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1194.84  0.64  0.5  0.53  −0.33          1  0.89  −0.60          2  1.05  −0.64          3  1.06  −0.62          5  1.02  −0.58          10  0.91  −0.50          16  0.82  −0.45  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1072.99  0.19  0.5  0.11  −0.08          1  0.23  −0.11          2  0.27  −0.12          3  0.27  −0.12          5  0.26  −0.11          10  0.24  −0.09          16  0.21  −0.09  5d106s7p–5d106s9s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  4306.80  0.23  0.5  2.96  −1.31          1  4.25  −1.92          2  4.84  −1.94          3  5.09  −1.94          5  5.09  −1.87          10  4.72  −1.69          16  4.33  −1.53  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P0  1538.39  10.66  0.5  0.04  −0.03          1  0.03  −0.02          2  0.02  −0.02          3  0.02  −0.01          5  0.01  −0.01          10  0.01  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P1  1370.88  3.21  0.5  0.04  −0.02          1  0.02  −0.02          2  0.02  −0.01          3  0.01  −0.01          5  0.01  −0.01          10  0.00  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–3P1  1572.16  2.23  0.5  0.07  −0.05          1  0.05  −0.04          2  0.03  −0.03          3  0.03  −0.02          5  0.02  −0.01          10  0.01  −0.01          16  0.02  −0.01          3  1.36  −0.42          5  1.29  −0.40  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1246.00  1.34  0.5  0.68  −0.17          10  1.14  −0.36          16  1.03  −0.33          1  0.85  −0.25          2  0.94  −0.29          3  0.93  −0.29          5  0.88  −0.28          10  0.77  −0.25          16  0.70  −0.23  5d106s6p–5d106p2  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1507.82  9.29  0.5  1.00  −0.24          1  1.25  −0.36          2  1.37  −0.42          3  1.36  −0.42          5  1.29  −0.40          10  1.14  −0.36          16  1.03  −0.33  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s7s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1792.83b  1.50  0.5  0.22  −0.18          1  0.16  −0.13          2  0.06  −0.04          3  0.09  −0.07          5  0.11  −0.10          10  0.12  −0.10          16  0.12  −0.10  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1892.72  3.66  0.5  0.29  −0.23          1  0.20  −0.17          2  0.08  −0.06          3  0.11  −0.09          5  0.13  −0.12          10  0.13  −0.12          16  0.14  −0.12  5d106s6p–5d106s7s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  2298.06b  3.47  0.5  0.47  −0.39          1  0.33  −0.28          2  0.15  −0.11          3  0.19  −0.16          5  0.20  −0.19          10  0.21  −0.19          16  0.22  −0.20  5d106s6p–5d106s7s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1798.36  0.83  0.5  0.13  −0.10          1  0.09  −0.07          2  0.05  −0.04          3  0.05  −0.04          5  0.05  −0.05          10  0.05  −0.04          16  0.05  −0.04  5d106s6p–5d106s7s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  3091.57b  3.83  0.5  0.48  −0.35          1  0.34  −0.25          2  0.19  −0.13          3  0.19  −0.14          5  0.18  −0.14          10  0.17  −0.14          16  0.19  −0.15  5d106s6p–5d106s8s  $$^3{\rm{P}}_0^{\rm{o}}$$–3S1  1188.83  0.41  0.5  0.34  −0.20          1  0.19  −0.09          2  0.25  −0.20          3  0.28  −0.21          5  0.29  −0.21          10  0.28  −0.19          16  0.26  −0.17  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1231.81  1.05  0.5  0.38  −0.23          1  0.21  −0.11          2  0.28  −0.22          3  0.31  −0.23          5  0.32  −0.23          10  0.30  −0.21          16  0.28  −0.19  5d106s6p–5d106s8s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1391.88  1.30  0.5  0.51  −0.32          1  0.28  −0.15          2  0.36  −0.29          3  0.40  −0.30          5  0.41  −0.30          10  0.39  −0.27          16  0.37  −0.25  5d106s7p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  7144.9  0.40  0.5  17.12  −7.85          1  10.95  −2.69          2  11.79  −5.45          3  13.51  −6.07          5  14.36  −6.39          10  13.92  −6.18          16  13.03  −5.77  5d106s6p–5d106s8s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1221.02  0.47  0.5  0.12  −0.07          1  0.07  −0.04          2  0.08  −0.06          3  0.09  −0.06          5  0.09  −0.06          10  0.09  −0.05          16  0.08  −0.05  5d106s6p–5d106s8s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  1705.55  0.92  0.5  0.26  −0.15          1  0.15  −0.09          2  0.18  −0.13          3  0.19  −0.13          5  0.19  −0.12          10  0.18  −0.11          16  0.17  −0.10  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–3S1  1074.97  0.48  0.5  0.42  −0.25          1  0.72  −0.48          2  0.85  −0.51          3  0.85  −0.50          5  0.82  −0.47          10  0.73  −0.40          16  0.66  −0.36  5d106s6p–5d106s9s  $$^3{\rm{P}}_2^{\rm{o}}$$–3S1  1194.84  0.64  0.5  0.53  −0.33          1  0.89  −0.60          2  1.05  −0.64          3  1.06  −0.62          5  1.02  −0.58          10  0.91  −0.50          16  0.82  −0.45  5d106s6p–5d106s9s  $$^3{\rm{P}}_1^{\rm{o}}$$–1S0  1072.99  0.19  0.5  0.11  −0.08          1  0.23  −0.11          2  0.27  −0.12          3  0.27  −0.12          5  0.26  −0.11          10  0.24  −0.09          16  0.21  −0.09  5d106s7p–5d106s9s  $$^1{\rm{P}}_1^{\rm{o}}$$–1S0  4306.80  0.23  0.5  2.96  −1.31          1  4.25  −1.92          2  4.84  −1.94          3  5.09  −1.94          5  5.09  −1.87          10  4.72  −1.69          16  4.33  −1.53  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P0  1538.39  10.66  0.5  0.04  −0.03          1  0.03  −0.02          2  0.02  −0.02          3  0.02  −0.01          5  0.01  −0.01          10  0.01  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_1^{\rm{o}}$$–3P1  1370.88  3.21  0.5  0.04  −0.02          1  0.02  −0.02          2  0.02  −0.01          3  0.01  −0.01          5  0.01  −0.01          10  0.00  0.00          16  0.01  −0.01  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–3P1  1572.16  2.23  0.5  0.07  −0.05          1  0.05  −0.04          2  0.03  −0.03          3  0.03  −0.02          5  0.02  −0.01          10  0.01  −0.01          16  0.02  −0.01          3  1.36  −0.42          5  1.29  −0.40  5d106s6p–5d106p2  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1246.00  1.34  0.5  0.68  −0.17          10  1.14  −0.36          16  1.03  −0.33          1  0.85  −0.25          2  0.94  −0.29          3  0.93  −0.29          5  0.88  −0.28          10  0.77  −0.25          16  0.70  −0.23  5d106s6p–5d106p2  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1507.82  9.29  0.5  1.00  −0.24          1  1.25  −0.36          2  1.37  −0.42          3  1.36  −0.42          5  1.29  −0.40          10  1.14  −0.36          16  1.03  −0.33  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST; Kramida et al. 2013). View Large Table 4. Tl II 5d106snp (n = 6–7) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s2–5d106s6p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  1908.62b  0.27  0.5  0.07  −0.07          1  0.05  −0.05          2  0.03  −0.03          3  0.03  −0.03          5  0.02  −0.02          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s6p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  1321.64b  13.02  0.5  0.05  −0.04          1  0.04  −0.03          2  0.03  −0.02          3  0.02  −0.02          5  0.01  −0.01          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s7p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  836.34  0.01  0.5  0.07  −0.01          1  0.06  0.00          2  0.04  0.02          3  0.05  0.02          5  0.05  0.01          10  0.05  0.01          16  0.05  0.01  5d106s7s–5d106s7p  3S1–$$^3{\rm{P}}_2^{\rm{o}}$$  5949.48  0.94  0.5  6.99  −3.51          1  5.97  −1.48          2  3.41  0.74          3  4.45  0.26          5  5.20  −0.33          10  5.45  −0.71          16  5.27  −0.80  5d106s2–5d106s7p  1S0–$$^1{\rm{P}}_1^{\rm{o}}$$  817.18  1.31  0.5  0.05  −0.01          1  0.03  −0.01          2  0.02  −0.01          3  0.03  −0.01          5  0.03  −0.01          10  0.04  −0.01          16  0.03  −0.01  5d106s2–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  709.23  0.16  0.5  0.14  −0.07          1  0.16  −0.09          2  0.19  −0.09          3  0.20  −0.09          5  0.19  −0.08          10  0.17  −0.07          16  0.16  −0.07  5d106s6d–5d106s8p  1D2 –$$^1{\rm{P}}_1^{\rm{o}}$$  3869.15  0.12  0.5  5.06  −2.81          1  5.37  −3.11          2  6.23  −3.10          3  6.24  −2.93          5  6.18  −2.90          10  5.72  −2.66          16  5.24  −2.43  5d106s7s–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  3029.01  0.11  0.5  2.72  −1.36          1  3.08  −1.71          2  3.57  −1.66          3  3.69  −1.67          5  3.62  −1.61          10  3.30  −1.43          16  3.01  −1.29  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s2–5d106s6p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  1908.62b  0.27  0.5  0.07  −0.07          1  0.05  −0.05          2  0.03  −0.03          3  0.03  −0.03          5  0.02  −0.02          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s6p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  1321.64b  13.02  0.5  0.05  −0.04          1  0.04  −0.03          2  0.03  −0.02          3  0.02  −0.02          5  0.01  −0.01          10  0.01  −0.01          16  0.01  −0.01  5d106s2–5d106s7p  1S0–$$^3{\rm{P}}_1^{\rm{o}}$$  836.34  0.01  0.5  0.07  −0.01          1  0.06  0.00          2  0.04  0.02          3  0.05  0.02          5  0.05  0.01          10  0.05  0.01          16  0.05  0.01  5d106s7s–5d106s7p  3S1–$$^3{\rm{P}}_2^{\rm{o}}$$  5949.48  0.94  0.5  6.99  −3.51          1  5.97  −1.48          2  3.41  0.74          3  4.45  0.26          5  5.20  −0.33          10  5.45  −0.71          16  5.27  −0.80  5d106s2–5d106s7p  1S0–$$^1{\rm{P}}_1^{\rm{o}}$$  817.18  1.31  0.5  0.05  −0.01          1  0.03  −0.01          2  0.02  −0.01          3  0.03  −0.01          5  0.03  −0.01          10  0.04  −0.01          16  0.03  −0.01  5d106s2–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  709.23  0.16  0.5  0.14  −0.07          1  0.16  −0.09          2  0.19  −0.09          3  0.20  −0.09          5  0.19  −0.08          10  0.17  −0.07          16  0.16  −0.07  5d106s6d–5d106s8p  1D2 –$$^1{\rm{P}}_1^{\rm{o}}$$  3869.15  0.12  0.5  5.06  −2.81          1  5.37  −3.11          2  6.23  −3.10          3  6.24  −2.93          5  6.18  −2.90          10  5.72  −2.66          16  5.24  −2.43  5d106s7s–5d106s8p  1S0 –$$^1{\rm{P}}_1^{\rm{o}}$$  3029.01  0.11  0.5  2.72  −1.36          1  3.08  −1.71          2  3.57  −1.66          3  3.69  −1.67          5  3.62  −1.61          10  3.30  −1.43          16  3.01  −1.29  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines NIST (Kramida et al. 2013). View Large Table 5. Tl II 5d106snd (n = 6–8) theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s6d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1499.30  8.28  0.5  0.13  −0.11          1  0.12  −0.11          2  0.07  −0.06          3  0.08  −0.08          5  0.09  −0.09          10  0.09  −0.09          16  0.09  −0.08  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1568.57  5.16  0.5  0.17  −0.15          1  0.15  −0.13          2  0.09  −0.08          3  0.10  −0.09          5  0.11  −0.10          10  0.10  −0.10          16  0.10  −0.10  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1593.26  0.53  0.5  0.20  −0.18          1  0.13  −0.11          2  0.11  −0.10          3  0.08  −0.07          5  0.09  −0.08          10  0.09  −0.09          16  0.10  −0.09  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  2530.74b  1.47  0.5  0.58  −0.49          1  0.37  −0.30          2  0.31  −0.26          3  0.22  −0.18          5  0.24  −0.21          10  0.26  −0.23          16  0.27  −0.24  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1561.58  15.20  0.5  0.27  −0.23          1  0.22  −0.19          2  0.13  −0.11          3  0.15  −0.14          5  0.17  −0.15          10  0.16  −0.15          16  0.16  −0.15  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–3D2  2451.83  0.25  0.5  0.72  −0.59          1  0.58  −0.49          2  0.35  −0.29          3  0.40  −0.35          5  0.42  −0.38          10  0.41  −0.39          16  0.41  −0.38  5d106s6p–5d106s6d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1814.77b  8.25  0.5  0.40  −0.33          1  0.38  −0.33          2  0.23  −0.19          3  0.27  −0.24          5  0.30  −0.27          10  0.30  −0.28          16  0.30  −0.27  5d106s6p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1130.17  1.63  0.5  0.40  −0.14          1  0.33  −0.05          2  0.35  −0.11          3  0.36  −0.12          5  0.34  −0.12          10  0.31  −0.11          16  0.28  −0.10  5d106s7p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  5384.85  0.78  0.5  9.85  −3.06          1  8.20  −0.97          2  8.44  −2.16          3  8.70  −2.39          5  8.52  −2.49          10  7.74  −2.38          16  7.04  −2.21  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1183.41  1.24  0.5  0.22  −0.06          1  0.15  0.00          2  0.19  −0.07          3  0.21  −0.08          5  0.22  −0.08          10  0.20  −0.08          16  0.19  −0.08  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1330.40  3.28  0.5  0.30  −0.09          1  0.20  −0.02          2  0.24  −0.09          3  0.27  −0.10          5  0.28  −0.11          10  0.26  −0.10          16  0.25  −0.10  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1167.43  1.81  0.5  0.74  −0.31          1  0.63  −0.17          2  0.67  −0.27          3  0.68  −0.28          5  0.66  −0.27          10  0.59  −0.25          16  0.53  −0.23  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D2  1310.20  0.59  0.5  0.94  −0.40          1  0.80  −0.23          2  0.85  −0.35          3  0.86  −0.36          5  0.83  −0.35          10  0.74  −0.32          16  0.67  −0.29  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1307.50  1.92  0.5  1.20  −0.45          1  1.03  −0.23          2  1.14  −0.42          3  1.16  −0.45          5  1.12  −0.44          10  1.01  −0.41          16  0.92  −0.38  5d106s6p–5d106s8d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1018.85  0.64  0.5  0.94  −0.09          1  1.06  −0.25          2  1.07  −0.27          3  1.03  −0.27          5  0.95  −0.25          10  0.81  −0.22          16  0.72  −0.20  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1050.30  0.41  0.5  1.02  −0.11          1  1.14  −0.28          2  1.15  −0.30          3  1.10  −0.29          5  1.01  −0.27          10  0.87  −0.23          16  0.77  −0.21  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1049.73  0.77  0.5  1.69  −0.08          1  1.92  −0.38          2  1.94  −0.43          3  1.86  −0.43          5  1.71  −0.41          10  1.47  −0.36          16  1.30  −0.32  5d106s6p–5d106s8d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1373.52  6.44  0.5  3.51  −2.78          1  3.96  −3.10          2  3.92  −2.95          3  3.73  −2.77          5  3.41  −2.49          10  2.92  −2.10          16  2.57  −1.84  5d106s6p–5d106s8d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1162.55  0.79  0.5  2.71  −0.05          1  3.17  −0.59          2  3.24  −0.70          3  3.12  −0.71          5  2.89  −0.68          10  2.49  −0.60          16  2.21  −0.55  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6p–5d106s6d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1499.30  8.28  0.5  0.13  −0.11          1  0.12  −0.11          2  0.07  −0.06          3  0.08  −0.08          5  0.09  −0.09          10  0.09  −0.09          16  0.09  −0.08  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1568.57  5.16  0.5  0.17  −0.15          1  0.15  −0.13          2  0.09  −0.08          3  0.10  −0.09          5  0.11  −0.10          10  0.10  −0.10          16  0.10  −0.10  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1593.26  0.53  0.5  0.20  −0.18          1  0.13  −0.11          2  0.11  −0.10          3  0.08  −0.07          5  0.09  −0.08          10  0.09  −0.09          16  0.10  −0.09  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  2530.74b  1.47  0.5  0.58  −0.49          1  0.37  −0.30          2  0.31  −0.26          3  0.22  −0.18          5  0.24  −0.21          10  0.26  −0.23          16  0.27  −0.24  5d106s6p–5d106s6d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1561.58  15.20  0.5  0.27  −0.23          1  0.22  −0.19          2  0.13  −0.11          3  0.15  −0.14          5  0.17  −0.15          10  0.16  −0.15          16  0.16  −0.15  5d106s6p–5d106s6d  $$^1{\rm{P}}_1^{\rm{o}}$$–3D2  2451.83  0.25  0.5  0.72  −0.59          1  0.58  −0.49          2  0.35  −0.29          3  0.40  −0.35          5  0.42  −0.38          10  0.41  −0.39          16  0.41  −0.38  5d106s6p–5d106s6d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1814.77b  8.25  0.5  0.40  −0.33          1  0.38  −0.33          2  0.23  −0.19          3  0.27  −0.24          5  0.30  −0.27          10  0.30  −0.28          16  0.30  −0.27  5d106s6p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1130.17  1.63  0.5  0.40  −0.14          1  0.33  −0.05          2  0.35  −0.11          3  0.36  −0.12          5  0.34  −0.12          10  0.31  −0.11          16  0.28  −0.10  5d106s7p–5d106s7d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  5384.85  0.78  0.5  9.85  −3.06          1  8.20  −0.97          2  8.44  −2.16          3  8.70  −2.39          5  8.52  −2.49          10  7.74  −2.38          16  7.04  −2.21  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–1D2  1183.41  1.24  0.5  0.22  −0.06          1  0.15  0.00          2  0.19  −0.07          3  0.21  −0.08          5  0.22  −0.08          10  0.20  −0.08          16  0.19  −0.08  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–1D2  1330.40  3.28  0.5  0.30  −0.09          1  0.20  −0.02          2  0.24  −0.09          3  0.27  −0.10          5  0.28  −0.11          10  0.26  −0.10          16  0.25  −0.10  5d106s6p–5d106s7d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1167.43  1.81  0.5  0.74  −0.31          1  0.63  −0.17          2  0.67  −0.27          3  0.68  −0.28          5  0.66  −0.27          10  0.59  −0.25          16  0.53  −0.23  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D2  1310.20  0.59  0.5  0.94  −0.40          1  0.80  −0.23          2  0.85  −0.35          3  0.86  −0.36          5  0.83  −0.35          10  0.74  −0.32          16  0.67  −0.29  5d106s6p–5d106s7d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1307.50  1.92  0.5  1.20  −0.45          1  1.03  −0.23          2  1.14  −0.42          3  1.16  −0.45          5  1.12  −0.44          10  1.01  −0.41          16  0.92  −0.38  5d106s6p–5d106s8d  $$^3{\rm{P}}_0^{\rm{o}}$$–3D1  1018.85  0.64  0.5  0.94  −0.09          1  1.06  −0.25          2  1.07  −0.27          3  1.03  −0.27          5  0.95  −0.25          10  0.81  −0.22          16  0.72  −0.20  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D1  1050.30  0.41  0.5  1.02  −0.11          1  1.14  −0.28          2  1.15  −0.30          3  1.10  −0.29          5  1.01  −0.27          10  0.87  −0.23          16  0.77  −0.21  5d106s6p–5d106s8d  $$^3{\rm{P}}_1^{\rm{o}}$$–3D2  1049.73  0.77  0.5  1.69  −0.08          1  1.92  −0.38          2  1.94  −0.43          3  1.86  −0.43          5  1.71  −0.41          10  1.47  −0.36          16  1.30  −0.32  5d106s6p–5d106s8d  $$^1{\rm{P}}_1^{\rm{o}}$$–1D2  1373.52  6.44  0.5  3.51  −2.78          1  3.96  −3.10          2  3.92  −2.95          3  3.73  −2.77          5  3.41  −2.49          10  2.92  −2.10          16  2.57  −1.84  5d106s6p–5d106s8d  $$^3{\rm{P}}_2^{\rm{o}}$$–3D3  1162.55  0.79  0.5  2.71  −0.05          1  3.17  −0.59          2  3.24  −0.70          3  3.12  −0.71          5  2.89  −0.68          10  2.49  −0.60          16  2.21  −0.55  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST Kramida et al. 2013). View Large Table 6. Tl II 5d106s5f theoretical transition probabilities Aij (108 s−1) and line widths (FWHM), ω (Å), and shifts, d (Å), normalized to an electron density, Ne = 1017 cm−3. Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6d–5d106s5f  3D2–$$^3{\rm{P}}_3^{\rm{o}}$$  5078.54b  1.64  0.5  8.92  −6.07          1  7.76  −5.75          2  5.50  −5.35          3  6.32  −5.55          5  6.67  −5.44          10  6.43  −4.95          16  6.00  −4.50  5d106s6d–5d106s5f  3D3–$$^3{\rm{P}}_4^{\rm{o}}$$  5152.14b  1.77  0.5  14.60  −10.22          1  13.05  −9.98          2  8.99  −8.45          3  10.51  −9.20          5  11.29  −9.42          10  11.00  −8.88          16  10.35  −8.17  Transition array  Multiplet  λ (Å)a  Aij (108 s−1)  T (104 K)  ω (Å)  d (Å)  5d106s6d–5d106s5f  3D2–$$^3{\rm{P}}_3^{\rm{o}}$$  5078.54b  1.64  0.5  8.92  −6.07          1  7.76  −5.75          2  5.50  −5.35          3  6.32  −5.55          5  6.67  −5.44          10  6.43  −4.95          16  6.00  −4.50  5d106s6d–5d106s5f  3D3–$$^3{\rm{P}}_4^{\rm{o}}$$  5152.14b  1.77  0.5  14.60  −10.22          1  13.05  −9.98          2  8.99  −8.45          3  10.51  −9.20          5  11.29  −9.42          10  11.00  −8.88          16  10.35  −8.17  Note. A positive shift is red. aEllis & Sawyer (1936). bPersistent lines (NIST Kramida et al. 2013). View Large Our values of the widths FWHM (ω(pm)) and the Stark line shifts (d(pm)) for the persistent lines of 1908.62 Å, 1321.63 Å and 3091.57 Å are plotted against temperature and shown in Fig. 2. A comparison of the calculated Stark widths of Bi IV, Pb III, and the calculated Stark width of Tl II (same isoelectronic sequence) are displayed for three transitions in Fig. 3. The values of Pb III and Bi IV Stark widths used in these comparisons were obtained by some of these same authors in previous works (Zanon et al. 2010); Colón et al. 2017). In the case of Pb III, the values used, not included in the cited work, have been calculated in this work following the procedure indicated for Tl II. As in our previous work (Colon et al. 2017), a dependence of the Stark widths compatible with Z−2 can also be observed. Figure 2. View largeDownload slide Calculated Stark width FWHM (ω (pm)) and shift (d (pm)) at an electron density of 1017 cm−3 versus temperature for several spectral lines of Tl II. Figure 2. View largeDownload slide Calculated Stark width FWHM (ω (pm)) and shift (d (pm)) at an electron density of 1017 cm−3 versus temperature for several spectral lines of Tl II. Figure 3. View largeDownload slide Theoretical Stark width FWHM (ω (in frequency units)) of five transitions at an electron density of 1017 cm−3 in Tl II (present work), Pb III (Zanón et al. 2010) and Bi IV (Colón et al. 2017) versus the ion charge (number Z) at a temperature of 20 000 K. Figure 3. View largeDownload slide Theoretical Stark width FWHM (ω (in frequency units)) of five transitions at an electron density of 1017 cm−3 in Tl II (present work), Pb III (Zanón et al. 2010) and Bi IV (Colón et al. 2017) versus the ion charge (number Z) at a temperature of 20 000 K. In conclusion, in this work we have calculated the transition probabilities and the Stark widths and shifts of 49 Tl II spectral lines. Radiative lifetimes of 11 levels of Tl II were also calculated. Core polarization effects (CPE) were taken into account in the Cowan code, which was used to calculate the required matrix elements in this work. Griem´s semiempirical model was used in order to obtain the Stark broadening parameters. The dependence of these values on temperature and charge number Z has also been studied. Acknowledgements This work was financially supported by the Spanish Ministry of Science and Technology (DGI project MAT2013-44964-R. REFERENCES Andersen T., Kirkegård Nielsen A., Sørensen G., 1972, Phys. Scr. , 6 122 https://doi.org/10.1088/0031-8949/6/2-3/004 CrossRef Search ADS   Andersen T., Sørensen G., 1972, Phys. Rev. A , 5, 2447 https://doi.org/10.1103/PhysRevA.5.2447 CrossRef Search ADS   Baranger M., 1958, Phys. Rev. , 112, 855 https://doi.org/10.1103/PhysRev.112.855 CrossRef Search ADS   Biémont E., Fischer C. F., Godefroid M. R., Palmeri P., Quinet P., 2000, Phys. Rev. A , 62, 032512 https://doi.org/10.1103/PhysRevA.62.032512 CrossRef Search ADS   Brage T., Proffitt C. R., Leckrone E. S., 1999, J. Phys. B: Atomic Molecular Optical Phys. , 32, 3183 https://doi.org/10.1088/0953-4075/32/13/308 CrossRef Search ADS   Colón C., Moreno-Díaz C., de Andrés-García I., Alonso-Medina A., 2017, MNRAS , 470, 2179 https://doi.org/10.1093/mnras/stx1320 CrossRef Search ADS   Cowan R. D., 1981, The Theory of Atomic Structure and Spectra . Univ. California Press, Berkeley, CA Curtis L. J., 2000, Phys. Scr. , 62, 31 https://doi.org/10.1238/Physica.Regular.062a00031 CrossRef Search ADS   Curtis L. J., Irving R. E., Henderson M., Matulioniene R., Fischer C. F., Pinnington E. H., 2001, Phys. Rev. A , 63, 042502 https://doi.org/10.1103/PhysRevA.63.042502 CrossRef Search ADS   de Andrés-García I., Alonso-Medina A., Colón C., 2016, MNRAS , 455, 1145 https://doi.org/10.1093/mnras/stv2170 CrossRef Search ADS   Ellis C. B., Sawyer R. A., 1936, Phys. Rev. , 49, 145 https://doi.org/10.1103/PhysRev.49.145 CrossRef Search ADS   Griem H. R., 1968, Phys. Rev. , 165, 258 https://doi.org/10.1103/PhysRev.165.258 CrossRef Search ADS   Hameed S., 1972, J. Phys. B: Atomic Molecular Phys. , 5, 746 https://doi.org/10.1088/0022-3700/5/4/009 CrossRef Search ADS   Henderson M., Curtis L. J., 1996, J. Phys. B: Atomic Molecular Optical Phys. , 29, L629 https://doi.org/10.1088/0953-4075/29/17/001 CrossRef Search ADS   Kramida A., Ralchenko Y., Reader J., NIST ASD Team, 2013, NIST Atomic Spectra Database  (v.5.3). Available at: http://physics.nist.gov/asd Kurucz R. L., 1993, CD-ROM 18: SYNTHE Spectrum Synthesis Programs and Line Data.  Smithsonian Astrophys. Obs., Cambridge, MA Leckrone E. S., Proffitt C. R., Wahlgren G. M., Johansson S., Brage T., 1999, AJ , 117, 1454 https://doi.org/10.1086/300776 CrossRef Search ADS   McLennan J. C., McLay A. B., Crawford M. F., 1929, Proc. R. Soc. A: Math. Phys. Eng. Sci., A  125, 570 https://doi.org/10.1098/rspa.1929.0186 CrossRef Search ADS   Migdalek J., Baylis W. E., 1978, J. Phys. B: Atomic Molecular Phys. , 11, L497 https://doi.org/10.1088/0022-3700/11/17/001 CrossRef Search ADS   Migdalek J., Baylis W. E., 1985, J. Phys. B: Atomic Molecular Phys. , 18, 1533 https://doi.org/10.1088/0022-3700/18/8/012 CrossRef Search ADS   Milovanović N., 2005, Memorie della Supplementi. Societa Astronomica Italiana , 7, 132 Moore C. E., 1958, Atomic Energy Levels:  NBS Circular 467 Vol. III. National Bureau of Standards, Washington, DC, 213 Popović L. C., Dimitrijević M. S., Ryabchikova T., 1999, A&A , 350, 719 Sansonetti J. E., Martin W. C., 2005, J. Phys. Chem. Reference Data , 34, 1559 https://doi.org/10.1063/1.1800011 CrossRef Search ADS   Seaton M. J., 1962, in Bates D. R., ed., Atomic and Molecular Processes.  Academic Press, New York Van Regemorter H., 1962, ApJ , 136, 906 https://doi.org/10.1086/147445 CrossRef Search ADS   Zanón A., Alonso-Medina A., Colón C., 2010, Int. Rev. At. Mol. Phys. , 1, 1 © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society

Journal

Monthly Notices of the Royal Astronomical SocietyOxford University Press

Published: May 1, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off