H i recombination lines corresponding to the decays of the first eight series (starting with Balmer, |$n=2$|) up to |$n=10$| that have been tested in our pure hydrogen plasma model at |$T=10^4$| K. The columns in the right contain the maximum resolved principal quantum number n at which the line intensity converge for less than 5 per cent and 1 per cent with respect to the models with maximum resolved levels |$n^\text{res} = n-5$| (convergence ratios start to be calculated at |$n=15$|). We show these at two relevant hydrogen densities of |$\boldsymbol {n}_\text{H} = 1\,\text{cm}^{-3}$| (corresponding to the interstellar medium) and |$\boldsymbol {n}_\text{H} = 10^4\,\text{cm}^{-3}$| (H ii regions). For each density, the maximum percentage difference induced by changing the maximum resolved level from |$n = 70$| to |$n = 10$| is also shown (columns ‘Diff.’).
| |$\lambda$| . | transition . | comments . | Convergence at |$\mathbf {n}_\text{H}=1\text{cm}^{-3}$| . | Convergence at |$\mathbf {n}_\text{H}=10^4\text{cm}^{-3}$| . | ||||
|---|---|---|---|---|---|---|---|---|
| . | . | . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . |
| 1215.67 Å | |$1\, ^2S-2\, ^2P$| | Ly |$\alpha$| | 15 | 15 | 0.90 | 15 | 15 | 0.21 |
| 3797.90 Å | |$2\, ^2S-n= 10$| | 15 | 15 | 1.81 | 15 | 15 | 1.43 | |
| 3835.38 Å | |$2\, ^2S-n= 9$| | 15 | 15 | 1.84 | 15 | 15 | 1.45 | |
| 3889.05 Å | |$2\, ^2S-n= 8$| | 15 | 15 | 1.82 | 15 | 15 | 1.43 | |
| 3970.07 Å | |$2\, ^2S-n= 7$| | 15 | 15 | 1.78 | 15 | 15 | 1.39 | |
| 4101.73 Å | |$2\, ^2S-n= 6$| | 15 | 15 | 1.64 | 15 | 15 | 1.28 | |
| 4340.46 Å | |$2\, ^2S-n= 5$| | 15 | 15 | 1.32 | 15 | 15 | 1.03 | |
| 4861.32 Å | |$2\, ^2S-n= 4$| | H|$\beta$| | 15 | 15 | 0.46 | 15 | 15 | 0.47 |
| 6562.80 Å | |$2\, ^2S-n= 3$| | H|$\alpha$| | 15 | 20 | 2.75 | 15 | 20 | 2.02 |
| 9014.91 Å | |$n= 3-n= 10$| | 15 | 15 | 0.10 | 15 | 15 | 0.10 | |
| 9229.02 Å | |$n= 3-n= 9$| | 15 | 15 | 0.16 | 15 | 15 | 0.10 | |
| 9545.97 Å | |$n= 3-n= 8$| | 15 | 15 | 0.51 | 15 | 15 | 0.37 | |
| 1.00494 |$\mu$|m | |$n= 3-n= 7$| | 15 | 15 | 1.05 | 15 | 15 | 0.77 | |
| 1.09381 |$\mu$|m | |$n= 3-n= 6$| | 15 | 20 | 1.99 | 15 | 20 | 1.48 | |
| 1.28181|$\mu$|m | |$n= 3-n= 5$| | 15 | 20 | 4.06 | 15 | 20 | 3.00 | |
| 1.73621 |$\mu$|m | |$n= 4-n= 10$| | 15 | 20 | 3.23 | 15 | 20 | 2.41 | |
| 1.81741 |$\mu$|m | |$n= 4-n= 9$| | 15 | 20 | 3.87 | 15 | 20 | 2.89 | |
| 1.87510|$\mu$|m | |$n= 3-n= 4$| | 15 | 30 | 10.30 | 15 | 25 | 7.61 | |
| 1.94456|$\mu$|m | |$n= 4-n= 8$| | 15 | 25 | 4.79 | 15 | 20 | 3.57 | |
| 2.16553 |$\mu$|m | |$n= 4-n= 7$| | 15 | 25 | 6.33 | 15 | 25 | 4.70 | |
| 2.62515 |$\mu$|m | |$n= 4-n= 6$| | 15 | 30 | 9.40 | 15 | 25 | 6.92 | |
| 3.03837 |$\mu$|m | |$n= 5-n= 10$| | 15 | 25 | 7.71 | 15 | 25 | 5.72 | |
| 3.29609 |$\mu$|m | |$n= 5-n= 9$| | 15 | 25 | 9.03 | 15 | 25 | 6.69 | |
| 3.73954 |$\mu$|m | |$n= 5-n= 8$| | 20 | 30 | 11.10 | 20 | 25 | 8.69 | |
| 4.05115 |$\mu$|m | |$n= 4-n= 5$| | 20 | 35 | 17.16 | 20 | 30 | 12.65 | |
| 4.65251 |$\mu$|m | |$n= 5-n= 7$| | 20 | 35 | 14.92 | 20 | 30 | 10.89 | |
| 5.12726 |$\mu$|m | |$n= 6-n= 10$| | 20 | 30 | 13.89 | 20 | 25 | 9.82 | |
| 5.90660 |$\mu$|m | |$n= 6-n= 9$| | 20 | 35 | 15.93 | 20 | 30 | 11.62 | |
| 7.45782 |$\mu$|m | |$n= 5-n= 6$| | 20 | 40 | 23.20 | 20 | 30 | 17.11 | |
| 7.50045 |$\mu$|m | |$n= 6-n= 8$| | 20 | 35 | 20.22 | 20 | 30 | 14.66 | |
| 8.75768 |$\mu$|m | |$n= 7-n= 10$| | 20 | 35 | 20.53 | 20 | 30 | 14.83 | |
| 11.3056 |$\mu$|m | |$n= 7-n= 9$| | 20 | 40 | 25.06 | 20 | 30 | 18.08 | |
| 12.3685 |$\mu$|m | |$n= 6-n= 7$| | 25 | 45 | 28.31 | 25 | 35 | 20.94 | |
| 16.2047 |$\mu$|m | |$n= 8-n= 10$| | 25 | 45 | 29.22 | 25 | 35 | 21.01 | |
| 19.0567 |$\mu$|m | |$n= 7-n= 8$| | 25 | 50 | 32.43 | 25 | 35 | 24.16 | |
| 27.7958 |$\mu$|m | |$n= 8-n= 9$| | 25 | 50 | 35.60 | 25 | 35 | 26.80 | |
| |$\lambda$| . | transition . | comments . | Convergence at |$\mathbf {n}_\text{H}=1\text{cm}^{-3}$| . | Convergence at |$\mathbf {n}_\text{H}=10^4\text{cm}^{-3}$| . | ||||
|---|---|---|---|---|---|---|---|---|
| . | . | . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . |
| 1215.67 Å | |$1\, ^2S-2\, ^2P$| | Ly |$\alpha$| | 15 | 15 | 0.90 | 15 | 15 | 0.21 |
| 3797.90 Å | |$2\, ^2S-n= 10$| | 15 | 15 | 1.81 | 15 | 15 | 1.43 | |
| 3835.38 Å | |$2\, ^2S-n= 9$| | 15 | 15 | 1.84 | 15 | 15 | 1.45 | |
| 3889.05 Å | |$2\, ^2S-n= 8$| | 15 | 15 | 1.82 | 15 | 15 | 1.43 | |
| 3970.07 Å | |$2\, ^2S-n= 7$| | 15 | 15 | 1.78 | 15 | 15 | 1.39 | |
| 4101.73 Å | |$2\, ^2S-n= 6$| | 15 | 15 | 1.64 | 15 | 15 | 1.28 | |
| 4340.46 Å | |$2\, ^2S-n= 5$| | 15 | 15 | 1.32 | 15 | 15 | 1.03 | |
| 4861.32 Å | |$2\, ^2S-n= 4$| | H|$\beta$| | 15 | 15 | 0.46 | 15 | 15 | 0.47 |
| 6562.80 Å | |$2\, ^2S-n= 3$| | H|$\alpha$| | 15 | 20 | 2.75 | 15 | 20 | 2.02 |
| 9014.91 Å | |$n= 3-n= 10$| | 15 | 15 | 0.10 | 15 | 15 | 0.10 | |
| 9229.02 Å | |$n= 3-n= 9$| | 15 | 15 | 0.16 | 15 | 15 | 0.10 | |
| 9545.97 Å | |$n= 3-n= 8$| | 15 | 15 | 0.51 | 15 | 15 | 0.37 | |
| 1.00494 |$\mu$|m | |$n= 3-n= 7$| | 15 | 15 | 1.05 | 15 | 15 | 0.77 | |
| 1.09381 |$\mu$|m | |$n= 3-n= 6$| | 15 | 20 | 1.99 | 15 | 20 | 1.48 | |
| 1.28181|$\mu$|m | |$n= 3-n= 5$| | 15 | 20 | 4.06 | 15 | 20 | 3.00 | |
| 1.73621 |$\mu$|m | |$n= 4-n= 10$| | 15 | 20 | 3.23 | 15 | 20 | 2.41 | |
| 1.81741 |$\mu$|m | |$n= 4-n= 9$| | 15 | 20 | 3.87 | 15 | 20 | 2.89 | |
| 1.87510|$\mu$|m | |$n= 3-n= 4$| | 15 | 30 | 10.30 | 15 | 25 | 7.61 | |
| 1.94456|$\mu$|m | |$n= 4-n= 8$| | 15 | 25 | 4.79 | 15 | 20 | 3.57 | |
| 2.16553 |$\mu$|m | |$n= 4-n= 7$| | 15 | 25 | 6.33 | 15 | 25 | 4.70 | |
| 2.62515 |$\mu$|m | |$n= 4-n= 6$| | 15 | 30 | 9.40 | 15 | 25 | 6.92 | |
| 3.03837 |$\mu$|m | |$n= 5-n= 10$| | 15 | 25 | 7.71 | 15 | 25 | 5.72 | |
| 3.29609 |$\mu$|m | |$n= 5-n= 9$| | 15 | 25 | 9.03 | 15 | 25 | 6.69 | |
| 3.73954 |$\mu$|m | |$n= 5-n= 8$| | 20 | 30 | 11.10 | 20 | 25 | 8.69 | |
| 4.05115 |$\mu$|m | |$n= 4-n= 5$| | 20 | 35 | 17.16 | 20 | 30 | 12.65 | |
| 4.65251 |$\mu$|m | |$n= 5-n= 7$| | 20 | 35 | 14.92 | 20 | 30 | 10.89 | |
| 5.12726 |$\mu$|m | |$n= 6-n= 10$| | 20 | 30 | 13.89 | 20 | 25 | 9.82 | |
| 5.90660 |$\mu$|m | |$n= 6-n= 9$| | 20 | 35 | 15.93 | 20 | 30 | 11.62 | |
| 7.45782 |$\mu$|m | |$n= 5-n= 6$| | 20 | 40 | 23.20 | 20 | 30 | 17.11 | |
| 7.50045 |$\mu$|m | |$n= 6-n= 8$| | 20 | 35 | 20.22 | 20 | 30 | 14.66 | |
| 8.75768 |$\mu$|m | |$n= 7-n= 10$| | 20 | 35 | 20.53 | 20 | 30 | 14.83 | |
| 11.3056 |$\mu$|m | |$n= 7-n= 9$| | 20 | 40 | 25.06 | 20 | 30 | 18.08 | |
| 12.3685 |$\mu$|m | |$n= 6-n= 7$| | 25 | 45 | 28.31 | 25 | 35 | 20.94 | |
| 16.2047 |$\mu$|m | |$n= 8-n= 10$| | 25 | 45 | 29.22 | 25 | 35 | 21.01 | |
| 19.0567 |$\mu$|m | |$n= 7-n= 8$| | 25 | 50 | 32.43 | 25 | 35 | 24.16 | |
| 27.7958 |$\mu$|m | |$n= 8-n= 9$| | 25 | 50 | 35.60 | 25 | 35 | 26.80 | |
H i recombination lines corresponding to the decays of the first eight series (starting with Balmer, |$n=2$|) up to |$n=10$| that have been tested in our pure hydrogen plasma model at |$T=10^4$| K. The columns in the right contain the maximum resolved principal quantum number n at which the line intensity converge for less than 5 per cent and 1 per cent with respect to the models with maximum resolved levels |$n^\text{res} = n-5$| (convergence ratios start to be calculated at |$n=15$|). We show these at two relevant hydrogen densities of |$\boldsymbol {n}_\text{H} = 1\,\text{cm}^{-3}$| (corresponding to the interstellar medium) and |$\boldsymbol {n}_\text{H} = 10^4\,\text{cm}^{-3}$| (H ii regions). For each density, the maximum percentage difference induced by changing the maximum resolved level from |$n = 70$| to |$n = 10$| is also shown (columns ‘Diff.’).
| |$\lambda$| . | transition . | comments . | Convergence at |$\mathbf {n}_\text{H}=1\text{cm}^{-3}$| . | Convergence at |$\mathbf {n}_\text{H}=10^4\text{cm}^{-3}$| . | ||||
|---|---|---|---|---|---|---|---|---|
| . | . | . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . |
| 1215.67 Å | |$1\, ^2S-2\, ^2P$| | Ly |$\alpha$| | 15 | 15 | 0.90 | 15 | 15 | 0.21 |
| 3797.90 Å | |$2\, ^2S-n= 10$| | 15 | 15 | 1.81 | 15 | 15 | 1.43 | |
| 3835.38 Å | |$2\, ^2S-n= 9$| | 15 | 15 | 1.84 | 15 | 15 | 1.45 | |
| 3889.05 Å | |$2\, ^2S-n= 8$| | 15 | 15 | 1.82 | 15 | 15 | 1.43 | |
| 3970.07 Å | |$2\, ^2S-n= 7$| | 15 | 15 | 1.78 | 15 | 15 | 1.39 | |
| 4101.73 Å | |$2\, ^2S-n= 6$| | 15 | 15 | 1.64 | 15 | 15 | 1.28 | |
| 4340.46 Å | |$2\, ^2S-n= 5$| | 15 | 15 | 1.32 | 15 | 15 | 1.03 | |
| 4861.32 Å | |$2\, ^2S-n= 4$| | H|$\beta$| | 15 | 15 | 0.46 | 15 | 15 | 0.47 |
| 6562.80 Å | |$2\, ^2S-n= 3$| | H|$\alpha$| | 15 | 20 | 2.75 | 15 | 20 | 2.02 |
| 9014.91 Å | |$n= 3-n= 10$| | 15 | 15 | 0.10 | 15 | 15 | 0.10 | |
| 9229.02 Å | |$n= 3-n= 9$| | 15 | 15 | 0.16 | 15 | 15 | 0.10 | |
| 9545.97 Å | |$n= 3-n= 8$| | 15 | 15 | 0.51 | 15 | 15 | 0.37 | |
| 1.00494 |$\mu$|m | |$n= 3-n= 7$| | 15 | 15 | 1.05 | 15 | 15 | 0.77 | |
| 1.09381 |$\mu$|m | |$n= 3-n= 6$| | 15 | 20 | 1.99 | 15 | 20 | 1.48 | |
| 1.28181|$\mu$|m | |$n= 3-n= 5$| | 15 | 20 | 4.06 | 15 | 20 | 3.00 | |
| 1.73621 |$\mu$|m | |$n= 4-n= 10$| | 15 | 20 | 3.23 | 15 | 20 | 2.41 | |
| 1.81741 |$\mu$|m | |$n= 4-n= 9$| | 15 | 20 | 3.87 | 15 | 20 | 2.89 | |
| 1.87510|$\mu$|m | |$n= 3-n= 4$| | 15 | 30 | 10.30 | 15 | 25 | 7.61 | |
| 1.94456|$\mu$|m | |$n= 4-n= 8$| | 15 | 25 | 4.79 | 15 | 20 | 3.57 | |
| 2.16553 |$\mu$|m | |$n= 4-n= 7$| | 15 | 25 | 6.33 | 15 | 25 | 4.70 | |
| 2.62515 |$\mu$|m | |$n= 4-n= 6$| | 15 | 30 | 9.40 | 15 | 25 | 6.92 | |
| 3.03837 |$\mu$|m | |$n= 5-n= 10$| | 15 | 25 | 7.71 | 15 | 25 | 5.72 | |
| 3.29609 |$\mu$|m | |$n= 5-n= 9$| | 15 | 25 | 9.03 | 15 | 25 | 6.69 | |
| 3.73954 |$\mu$|m | |$n= 5-n= 8$| | 20 | 30 | 11.10 | 20 | 25 | 8.69 | |
| 4.05115 |$\mu$|m | |$n= 4-n= 5$| | 20 | 35 | 17.16 | 20 | 30 | 12.65 | |
| 4.65251 |$\mu$|m | |$n= 5-n= 7$| | 20 | 35 | 14.92 | 20 | 30 | 10.89 | |
| 5.12726 |$\mu$|m | |$n= 6-n= 10$| | 20 | 30 | 13.89 | 20 | 25 | 9.82 | |
| 5.90660 |$\mu$|m | |$n= 6-n= 9$| | 20 | 35 | 15.93 | 20 | 30 | 11.62 | |
| 7.45782 |$\mu$|m | |$n= 5-n= 6$| | 20 | 40 | 23.20 | 20 | 30 | 17.11 | |
| 7.50045 |$\mu$|m | |$n= 6-n= 8$| | 20 | 35 | 20.22 | 20 | 30 | 14.66 | |
| 8.75768 |$\mu$|m | |$n= 7-n= 10$| | 20 | 35 | 20.53 | 20 | 30 | 14.83 | |
| 11.3056 |$\mu$|m | |$n= 7-n= 9$| | 20 | 40 | 25.06 | 20 | 30 | 18.08 | |
| 12.3685 |$\mu$|m | |$n= 6-n= 7$| | 25 | 45 | 28.31 | 25 | 35 | 20.94 | |
| 16.2047 |$\mu$|m | |$n= 8-n= 10$| | 25 | 45 | 29.22 | 25 | 35 | 21.01 | |
| 19.0567 |$\mu$|m | |$n= 7-n= 8$| | 25 | 50 | 32.43 | 25 | 35 | 24.16 | |
| 27.7958 |$\mu$|m | |$n= 8-n= 9$| | 25 | 50 | 35.60 | 25 | 35 | 26.80 | |
| |$\lambda$| . | transition . | comments . | Convergence at |$\mathbf {n}_\text{H}=1\text{cm}^{-3}$| . | Convergence at |$\mathbf {n}_\text{H}=10^4\text{cm}^{-3}$| . | ||||
|---|---|---|---|---|---|---|---|---|
| . | . | . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . | n (|$<$|5 per cent) . | n (|$<$|1 per cent) . | Diff. (per cent) . |
| 1215.67 Å | |$1\, ^2S-2\, ^2P$| | Ly |$\alpha$| | 15 | 15 | 0.90 | 15 | 15 | 0.21 |
| 3797.90 Å | |$2\, ^2S-n= 10$| | 15 | 15 | 1.81 | 15 | 15 | 1.43 | |
| 3835.38 Å | |$2\, ^2S-n= 9$| | 15 | 15 | 1.84 | 15 | 15 | 1.45 | |
| 3889.05 Å | |$2\, ^2S-n= 8$| | 15 | 15 | 1.82 | 15 | 15 | 1.43 | |
| 3970.07 Å | |$2\, ^2S-n= 7$| | 15 | 15 | 1.78 | 15 | 15 | 1.39 | |
| 4101.73 Å | |$2\, ^2S-n= 6$| | 15 | 15 | 1.64 | 15 | 15 | 1.28 | |
| 4340.46 Å | |$2\, ^2S-n= 5$| | 15 | 15 | 1.32 | 15 | 15 | 1.03 | |
| 4861.32 Å | |$2\, ^2S-n= 4$| | H|$\beta$| | 15 | 15 | 0.46 | 15 | 15 | 0.47 |
| 6562.80 Å | |$2\, ^2S-n= 3$| | H|$\alpha$| | 15 | 20 | 2.75 | 15 | 20 | 2.02 |
| 9014.91 Å | |$n= 3-n= 10$| | 15 | 15 | 0.10 | 15 | 15 | 0.10 | |
| 9229.02 Å | |$n= 3-n= 9$| | 15 | 15 | 0.16 | 15 | 15 | 0.10 | |
| 9545.97 Å | |$n= 3-n= 8$| | 15 | 15 | 0.51 | 15 | 15 | 0.37 | |
| 1.00494 |$\mu$|m | |$n= 3-n= 7$| | 15 | 15 | 1.05 | 15 | 15 | 0.77 | |
| 1.09381 |$\mu$|m | |$n= 3-n= 6$| | 15 | 20 | 1.99 | 15 | 20 | 1.48 | |
| 1.28181|$\mu$|m | |$n= 3-n= 5$| | 15 | 20 | 4.06 | 15 | 20 | 3.00 | |
| 1.73621 |$\mu$|m | |$n= 4-n= 10$| | 15 | 20 | 3.23 | 15 | 20 | 2.41 | |
| 1.81741 |$\mu$|m | |$n= 4-n= 9$| | 15 | 20 | 3.87 | 15 | 20 | 2.89 | |
| 1.87510|$\mu$|m | |$n= 3-n= 4$| | 15 | 30 | 10.30 | 15 | 25 | 7.61 | |
| 1.94456|$\mu$|m | |$n= 4-n= 8$| | 15 | 25 | 4.79 | 15 | 20 | 3.57 | |
| 2.16553 |$\mu$|m | |$n= 4-n= 7$| | 15 | 25 | 6.33 | 15 | 25 | 4.70 | |
| 2.62515 |$\mu$|m | |$n= 4-n= 6$| | 15 | 30 | 9.40 | 15 | 25 | 6.92 | |
| 3.03837 |$\mu$|m | |$n= 5-n= 10$| | 15 | 25 | 7.71 | 15 | 25 | 5.72 | |
| 3.29609 |$\mu$|m | |$n= 5-n= 9$| | 15 | 25 | 9.03 | 15 | 25 | 6.69 | |
| 3.73954 |$\mu$|m | |$n= 5-n= 8$| | 20 | 30 | 11.10 | 20 | 25 | 8.69 | |
| 4.05115 |$\mu$|m | |$n= 4-n= 5$| | 20 | 35 | 17.16 | 20 | 30 | 12.65 | |
| 4.65251 |$\mu$|m | |$n= 5-n= 7$| | 20 | 35 | 14.92 | 20 | 30 | 10.89 | |
| 5.12726 |$\mu$|m | |$n= 6-n= 10$| | 20 | 30 | 13.89 | 20 | 25 | 9.82 | |
| 5.90660 |$\mu$|m | |$n= 6-n= 9$| | 20 | 35 | 15.93 | 20 | 30 | 11.62 | |
| 7.45782 |$\mu$|m | |$n= 5-n= 6$| | 20 | 40 | 23.20 | 20 | 30 | 17.11 | |
| 7.50045 |$\mu$|m | |$n= 6-n= 8$| | 20 | 35 | 20.22 | 20 | 30 | 14.66 | |
| 8.75768 |$\mu$|m | |$n= 7-n= 10$| | 20 | 35 | 20.53 | 20 | 30 | 14.83 | |
| 11.3056 |$\mu$|m | |$n= 7-n= 9$| | 20 | 40 | 25.06 | 20 | 30 | 18.08 | |
| 12.3685 |$\mu$|m | |$n= 6-n= 7$| | 25 | 45 | 28.31 | 25 | 35 | 20.94 | |
| 16.2047 |$\mu$|m | |$n= 8-n= 10$| | 25 | 45 | 29.22 | 25 | 35 | 21.01 | |
| 19.0567 |$\mu$|m | |$n= 7-n= 8$| | 25 | 50 | 32.43 | 25 | 35 | 24.16 | |
| 27.7958 |$\mu$|m | |$n= 8-n= 9$| | 25 | 50 | 35.60 | 25 | 35 | 26.80 | |
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