\begin{table}%t1 \caption{\label{tab_level}Energy levels (in Ryd) of Si$^{9+}$.} \par %\centering \small \begin{tabular}{lcccccc|lcccccc} \hline\hline %&&&&&&&&&&&&& \\[-8pt] {\rm ID} & {\rm Conf.} & $^{2S+1}L_J^{\pi}$ & ${\rm NIST}^a$ & ${\rm AS}^b$ & ${\rm FAC}^c$ & ${\rm ZS94}^d$ & {\rm ID} & {\rm Conf.} & $^{2S+1}L_J^{\pi}$ & ${\rm NIST}^a$ & {\rm AS} & {\rm FAC} & {\rm ZS94} \\[2pt] \hline %&&&&&&&&&&&&& \\[-8pt] 1 & ${\rm 2s^2 2p}$ & ${\rm ^2P^{o}_{1/2} }$ & & & & & 64 & ${\rm 2p^2 3s}$ & ${\rm ^4P^{e}_{3/2} }$ & & 20.8084 & 20.8434 & 20.7610 \\ 2 & ${\rm 2s^2 2p}$ & ${\rm ^2P^{o}_{3/2} }$ & 0.0637 & 0.0664 & 0.0623 & 0.0637 & 65 & ${\rm 2p^2 3s}$ & ${\rm ^4P^{e}_{5/2} }$ & & 20.8453 & 20.8776 & 20.7951 \\ 3 & ${\rm 2s 2p^2}$ & ${\rm ^4P^{e}_{1/2} }$ & 1.4672 & 1.4370 & 1.4335 & 1.4672 & 66 & ${\rm 2s 2p 3d }$ & ${\rm ^2F^{o}_{7/2} }$ & 20.9582 & 21.0562 & 21.0263 & 21.0180 \\ 4 & ${\rm 2s 2p^2}$ & ${\rm ^4P^{e}_{3/2} }$ & 1.4898 & 1.4610 & 1.4567 & 1.4898 & 67 & ${\rm 2s 2p 3d }$ & ${\rm ^2F^{o}_{5/2} }$ & 20.9582 & 21.0575 & 21.0282 & 21.0191 \\ 5 & ${\rm 2s 2p^2}$ & ${\rm ^4P^{e}_{5/2} }$ & 1.5224 & 1.4985 & 1.4880 & 1.5224 & 68 & ${\rm 2s 2p 3d }$ & ${\rm ^2D^{o}_{3/2} }$ & 21.0551 & 21.1356 & 21.1353 & 21.0838 \\ 6 & ${\rm 2s 2p^2}$ & ${\rm ^2D^{e}_{3/2} }$ & 2.6231 & 2.6815 & 2.6620 & 2.6231 & 69 & ${\rm 2s 2p 3d }$ & ${\rm ^2D^{o}_{5/2} }$ & 21.0629 & 21.1425 & 21.1416 & 21.0900 \\ 7 & ${\rm 2s 2p^2}$ & ${\rm ^2D^{e}_{5/2} }$ & 2.6234 & 2.6833 & 2.6622 & 2.6234 & 70 & ${\rm 2p^2 3s}$ & ${\rm ^2P^{e}_{1/2} }$ & & 21.2186 & 21.2463 & 21.1318 \\ 8 & ${\rm 2s 2p^2}$ & ${\rm ^2S^{e}_{1/2} }$ & 3.3505 & 3.4221 & 3.4029 & 3.3505 & 71 & ${\rm 2p^2 3s}$ & ${\rm ^2P^{e}_{3/2} }$ & & 21.2590 & 21.2825 & 21.1699 \\ 9 & ${\rm 2s 2p^2}$ & ${\rm ^2P^{e}_{1/2} }$ & 3.5543 & 3.6491 & 3.6325 & 3.5543 & 72 & ${\rm 2s 2p 3d }$ & ${\rm ^2P^{o}_{1/2} }$ & & 21.2731 & 21.2686 & 21.2200 \\ 10 & ${\rm 2s 2p^2}$ & ${\rm ^2P^{e}_{3/2} }$ & 3.5907 & 3.6895 & 3.6687 & 3.5907 & 73 & ${\rm 2s 2p 3d }$ & ${\rm ^2P^{o}_{3/2} }$ & & 21.2800 & 21.2732 & 21.2246 \\ 11 & ${\rm 2p^3}$ & ${\rm ^4S^{o}_{3/2} }$ & 4.6414 & 4.6641 & 4.6274 & 4.6414 & 74 & ${\rm 2p^2 3p}$ & ${\rm ^2S^{o}_{1/2} }$ & & 21.2878 & 21.3255 & 21.2422 \\ 12 & ${\rm 2p^3}$ & ${\rm ^2D^{o}_{3/2} }$ & 5.2437 & 5.3479 & 5.2973 & 5.2437 & 75 & ${\rm 2p^2 3p}$ & ${\rm ^4D^{o}_{1/2} }$ & & 21.3792 & 21.4234 & 21.3370 \\ 13 & ${\rm 2p^3}$ & ${\rm ^2D^{o}_{5/2} }$ & 5.2439 & 5.3517 & 5.2984 & 5.2439 & 76 & ${\rm 2p^2 3p}$ & ${\rm ^4D^{o}_{3/2} }$ & & 21.3931 & 21.4355 & 21.3510 \\ 14 & ${\rm 2p^3}$ & ${\rm ^2P^{o}_{1/2} }$ & 5.8937 & 6.0271 & 5.9806 & 5.8937 & 77 & ${\rm 2p^2 3p}$ & ${\rm ^4D^{o}_{5/2} }$ & & 21.4168 & 21.4567 & 21.3744 \\ 15 & ${\rm 2p^3}$ & ${\rm ^2P^{o}_{3/2} }$ & 5.8994 & 6.0348 & 5.9832 & 5.8995 & 78 & ${\rm 2p^2 3s}$ & ${\rm ^2D^{e}_{5/2} }$ & & 21.4443 & 21.4737 & 21.3951 \\ 16 & ${\rm 2s^2 3s}$ & ${\rm ^2S^{e}_{1/2} }$ & & 16.5450 & 16.5368 & 16.4970 & 79 & ${\rm 2p^2 3s}$ & ${\rm ^2D^{e}_{3/2} }$ & & 21.4455 & 21.4748 & 21.3956 \\ 17 & ${\rm 2s^2 3p}$ & ${\rm ^2P^{o}_{1/2} }$ & & 17.2856 & 17.2881 & 17.2366 & 80 & ${\rm 2p^2 3p}$ & ${\rm ^4D^{o}_{7/2} }$ & & 21.4503 & 21.4879 & 21.4061 \\ 18 & ${\rm 2s^2 3p}$ & ${\rm ^2P^{o}_{3/2} }$ & & 17.3019 & 17.3046 & 17.2548 & 81 & ${\rm 2p^2 3p}$ & ${\rm ^4P^{o}_{1/2} }$ & & 21.4860 & 21.5255 & 21.4449 \\ 19 & ${\rm 2s^2 3d}$ & ${\rm ^2D^{e}_{3/2} }$ & 18.0363 & 18.0030 & 17.9972 & 17.9443 & 82 & ${\rm 2p^2 3p}$ & ${\rm ^4P^{o}_{3/2} }$ & & 21.4956 & 21.5349 & 21.4531 \\ 20 & ${\rm 2s^2 3d}$ & ${\rm ^2D^{e}_{5/2} }$ & 18.0406 & 18.0078 & 18.0014 & 17.9493 & 83 & ${\rm 2p^2 3p}$ & ${\rm ^4P^{o}_{5/2} }$ & & 21.5166 & 21.5535 & 21.4733 \\ 21 & ${\rm 2s 2p 3s }$ & ${\rm ^4P^{o}_{1/2} }$ & 18.1600 & 18.1070 & 18.1088 & 18.0608 & 84 & ${\rm 2p^2 3p}$ & ${\rm ^2D^{o}_{3/2} }$ & & 21.5945 & 21.6406 & 21.5462 \\ 22 & ${\rm 2s 2p 3s }$ & ${\rm ^4P^{o}_{3/2} }$ & 18.1810 & 18.1289 & 18.1293 & 18.0818 & 85 & ${\rm 2p^2 3p}$ & ${\rm ^2D^{o}_{5/2} }$ & & 21.6397 & 21.6836 & 21.5903 \\ 23 & ${\rm 2s 2p 3s }$ & ${\rm ^4P^{o}_{5/2} }$ & 18.2215 & 18.1681 & 18.1675 & 18.1209 & 86 & ${\rm 2p^2 3p}$ & ${\rm ^4S^{o}_{3/2} }$ & & 21.7785 & 21.8273 & 21.6973 \\ 24 & ${\rm 2s 2p 3s }$ & ${\rm ^2P^{o}_{1/2} }$ & 18.5084 & 18.4910 & 18.5012 & 18.4184 & 87 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{3/2} }$ & & 21.7866 & 21.8347 & 21.7384 \\ 25 & ${\rm 2s 2p 3s }$ & ${\rm ^2P^{o}_{3/2} }$ & 18.5521 & 18.5346 & 18.5431 & 18.4615 & 88 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{1/2} }$ & & 21.7908 & 21.8588 & 21.7342 \\ 26 & ${\rm 2s 2p 3p }$ & ${\rm ^4D^{e}_{1/2} }$ & & 18.7682 & 18.7772 & 18.7209 & 89 & ${\rm 2p^2 3d}$ & ${\rm ^4F^{e}_{3/2} }$ & & 21.9403 & 21.9761 & 21.8967 \\ 27 & ${\rm 2s 2p 3p }$ & ${\rm ^4D^{e}_{3/2} }$ & & 18.7885 & 18.7954 & 18.7405 & 90 & ${\rm 2p^2 3d}$ & ${\rm ^4F^{e}_{5/2} }$ & & 21.9537 & 21.9902 & 21.9094 \\ 28 & ${\rm 2s 2p 3p }$ & ${\rm ^2P^{e}_{1/2} }$ & 18.8139 & 18.8058 & 18.8146 & 18.7593 & 91 & ${\rm 2p^2 3d}$ & ${\rm ^4F^{e}_{7/2} }$ & & 21.9731 & 22.0079 & 21.9278 \\ 29 & ${\rm 2s 2p 3p }$ & ${\rm ^2P^{e}_{3/2} }$ & 18.8336 & 18.8152 & 18.8238 & 18.7683 & 92 & ${\rm 2p^2 3d}$ & ${\rm ^4F^{e}_{9/2} }$ & & 21.9993 & 22.0288 & 21.9520 \\ 30 & ${\rm 2s 2p 3p }$ & ${\rm ^4D^{e}_{5/2} }$ & & 18.8220 & 18.8269 & 18.7769 & 93 & ${\rm 2p^2 3p}$ & ${\rm ^2F^{o}_{5/2} }$ & & 22.0439 & 22.0825 & 22.0050 \\ 31 & ${\rm 2s 2p 3p }$ & ${\rm ^4D^{e}_{7/2} }$ & & 18.8560 & 18.8607 & 18.8121 & 94 & ${\rm 2p^2 3p}$ & ${\rm ^2F^{o}_{7/2} }$ & & 22.0554 & 22.0939 & 22.0171 \\ 32 & ${\rm 2s 2p 3p }$ & ${\rm ^4S^{e}_{3/2} }$ & & 18.9487 & 18.9586 & 18.9056 & 95 & ${\rm 2p^2 3d}$ & ${\rm ^2P^{e}_{3/2} }$ & & 22.0733 & 22.1139 & 22.0267 \\ 33 & ${\rm 2s 2p 3p }$ & ${\rm ^4P^{e}_{1/2} }$ & & 19.0525 & 19.0822 & 18.9858 & 96 & ${\rm 2p^2 3d}$ & ${\rm ^4D^{e}_{1/2} }$ & & 22.0776 & 22.1154 & 22.0355 \\ 34 & ${\rm 2s 2p 3p }$ & ${\rm ^4P^{e}_{3/2} }$ & & 19.0711 & 19.0993 & 19.0046 & 97 & ${\rm 2p^2 3d}$ & ${\rm ^4D^{e}_{5/2} }$ & & 22.0953 & 22.1334 & 22.0516 \\ 35 & ${\rm 2s 2p 3p }$ & ${\rm ^4P^{e}_{5/2} }$ & & 19.0913 & 19.1179 & 19.0227 & 98 & ${\rm 2p^2 3d}$ & ${\rm ^4D^{e}_{3/2} }$ & & 22.1032 & 22.1447 & 22.0571 \\ 36 & ${\rm 2s 2p 3p }$ & ${\rm ^2D^{e}_{3/2} }$ & 19.1890 & 19.1704 & 19.1919 & 19.1028 & 99 & ${\rm 2p^2 3d}$ & ${\rm ^4D^{e}_{7/2} }$ & & 22.1066 & 22.1403 & 22.0621 \\ 37 & ${\rm 2s 2p 3p }$ & ${\rm ^2D^{e}_{5/2} }$ & 19.2301 & 19.2114 & 19.2327 & 19.1437 & 100 & ${\rm 2p^2 3d}$ & ${\rm ^2P^{e}_{1/2} }$ & & 22.1345 & 22.1755 & 22.0831 \\ 38 & ${\rm 2s 2p 3d }$ & ${\rm ^4F^{o}_{3/2} }$ & & 19.3897 & 19.3973 & 19.3414 & 101 & ${\rm 2p^2 3d}$ & ${\rm ^2F^{e}_{5/2} }$ & & 22.1703 & 22.2021 & 22.1259 \\ 39 & ${\rm 2s 2p 3d }$ & ${\rm ^4F^{o}_{5/2} }$ & & 19.4030 & 19.4121 & 19.3544 & 102 & ${\rm 2p^2 3d}$ & ${\rm ^2F^{e}_{7/2} }$ & & 22.2179 & 22.2450 & 22.1725 \\ 40 & ${\rm 2s 2p 3d }$ & ${\rm ^4F^{o}_{7/2} }$ & & 19.4226 & 19.4318 & 19.3738 & 103 & ${\rm 2p^2 3d}$ & ${\rm ^4P^{e}_{5/2} }$ & 22.2756 & 22.2494 & 22.2927 & 22.1978 \\ 41 & ${\rm 2s 2p 3p }$ & ${\rm ^2S^{e}_{1/2} }$ & 19.4337 & 19.4284 & 19.4463 & 19.3548 & 104 & ${\rm 2p^2 3p}$ & ${\rm ^2D^{o}_{5/2} }$ & & 22.2642 & 22.3481 & 22.1825 \\ 42 & ${\rm 2s 2p 3d }$ & ${\rm ^4F^{o}_{9/2} }$ & & 19.4499 & 19.4548 & 19.4014 & 105 & ${\rm 2p^2 3d}$ & ${\rm ^4P^{e}_{3/2} }$ & 22.2896 & 22.2649 & 22.3069 & 22.2135 \\ 43 & ${\rm 2s 2p 3d }$ & ${\rm ^4D^{o}_{1/2} }$ & 19.6004 & 19.5602 & 19.5722 & 19.5081 & 106 & ${\rm 2p^2 3p}$ & ${\rm ^2D^{o}_{3/2} }$ & & 22.2651 & 22.3514 & 22.1856 \\ 44 & ${\rm 2s 2p 3d }$ & ${\rm ^4D^{o}_{3/2} }$ & 19.6004 & 19.5622 & 19.5757 & 19.5096 & 107 & ${\rm 2p^2 3d}$ & ${\rm ^4P^{e}_{1/2} }$ & & 22.2731 & 22.3158 & 22.2216 \\ 45 & ${\rm 2s 2p 3d }$ & ${\rm ^4D^{o}_{5/2} }$ & 19.6046 & 19.5664 & 19.5820 & 19.5130 & 108 & ${\rm 2p^2 3s}$ & ${\rm ^2S^{e}_{1/2} }$ & & 22.4339 & 22.4660 & 22.4001 \\ 46 & ${\rm 2s 2p 3d }$ & ${\rm ^4D^{o}_{7/2} }$ & 19.6271 & 19.5879 & 19.5997 & 19.5349 & 109 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{1/2} }$ & & 22.4519 & 22.5090 & 22.3612 \\ 47 & ${\rm 2s 2p 3d }$ & ${\rm ^2D^{o}_{3/2} }$ & 19.6260 & 19.6072 & 19.6198 & 19.5313 & 110 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{3/2} }$ & & 22.4792 & 22.5387 & 22.3865 \\ 48 & ${\rm 2s 2p 3d }$ & ${\rm ^2D^{o}_{5/2} }$ & 19.6331 & 19.6112 & 19.6240 & 19.5390 & 111 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{3/2} }$ & & 22.5927 & 22.6130 & 22.5328 \\ 49 & ${\rm 2s 2p 3d }$ & ${\rm ^4P^{o}_{5/2} }$ & 19.6917 & 19.6450 & 19.6568 & 19.5923 & 112 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{5/2} }$ & & 22.5934 & 22.6147 & 22.5347 \\ 50 & ${\rm 2s 2p 3d }$ & ${\rm ^4P^{o}_{3/2} }$ & 19.7025 & 19.6516 & 19.6655 & 19.6026 & 113 & ${\rm 2p^2 3d}$ & ${\rm ^2G^{e}_{7/2} }$ & & 22.6011 & 22.6272 & 22.5608 \\ 51 & ${\rm 2s 2p 3d }$ & ${\rm ^4P^{o}_{1/2} }$ & & 19.6576 & 19.6736 & 19.6098 & 114 & ${\rm 2p^2 3d}$ & ${\rm ^2G^{e}_{9/2} }$ & & 22.6062 & 22.6303 & 22.5653 \\ 52 & ${\rm 2s 2p 3s }$ & ${\rm ^2P^{o}_{1/2} }$ & & 19.7078 & 19.7031 & 19.6708 & 115 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{3/2} }$ & & 22.7474 & 22.7877 & 22.7047 \\ 53 & ${\rm 2s 2p 3s }$ & ${\rm ^2P^{o}_{3/2} }$ & 19.6682 & 19.7092 & 19.7045 & 19.6714 & 116 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{5/2} }$ & & 22.7651 & 22.8000 & 22.7200 \\ 54 & ${\rm 2s 2p 3d }$ & ${\rm ^2F^{o}_{5/2} }$ & 19.9439 & 19.9522 & 19.9611 & 19.9023 & 117 & ${\rm 2p^2 3d}$ & ${\rm ^2F^{e}_{7/2} }$ & & 22.8084 & 22.8288 & 22.7608 \\ 55 & ${\rm 2s 2p 3d }$ & ${\rm ^2F^{o}_{7/2} }$ & 19.9858 & 19.9925 & 19.9999 & 19.9430 & 118 & ${\rm 2p^2 3d}$ & ${\rm ^2F^{e}_{5/2} }$ & & 22.8222 & 22.8440 & 22.7754 \\ 56 & ${\rm 2s 2p 3d }$ & ${\rm ^2P^{o}_{3/2} }$ & 20.0407 & 20.0350 & 20.0399 & 19.9648 & 119 & ${\rm 2p^2 3d}$ & ${\rm ^2P^{e}_{1/2} }$ & & 22.9527 & 22.9918 & 22.8744 \\ 57 & ${\rm 2s 2p 3d }$ & ${\rm ^2P^{o}_{1/2} }$ & 20.0642 & 20.0575 & 20.0621 & 19.9866 & 120 & ${\rm 2p^2 3d}$ & ${\rm ^2P^{e}_{3/2} }$ & & 22.9693 & 23.0067 & 22.8888 \\ 58 & ${\rm 2s 2p 3p }$ & ${\rm ^2P^{e}_{1/2} }$ & & 20.4168 & 20.4263 & 20.3749 & 121 & ${\rm 2p^2 3d}$ & ${\rm ^2S^{e}_{1/2} }$ & & 23.0395 & 23.0746 & 23.0057 \\ 59 & ${\rm 2s 2p 3p }$ & ${\rm ^2P^{e}_{3/2} }$ & & 20.4271 & 20.4346 & 20.3836 & 122 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{1/2} }$ & & 23.1746 & 23.2319 & 23.1418 \\[2pt] \hline 60 & ${\rm 2s 2p 3p }$ & ${\rm ^2D^{e}_{3/2} }$ & & 20.4412 & 20.4468 & 20.3963 & 123 & ${\rm 2p^2 3p}$ & ${\rm ^2P^{o}_{3/2} }$ & & 23.1805 & 23.2360 & 23.1486 \\ 61 & ${\rm 2s 2p 3p }$ & ${\rm ^2D^{e}_{5/2} }$ & & 20.4424 & 20.4463 & 20.3977 & 124 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{5/2} }$ & & 23.7640 & 23.7756 & 23.7376 \\ 62 & ${\rm 2s 2p 3p }$ & ${\rm ^2S^{e}_{1/2} }$ & 20.4698 & 20.6368 & 20.6169 & 20.5801 & 125 & ${\rm 2p^2 3d}$ & ${\rm ^2D^{e}_{3/2} }$ & & 23.7716 & 23.7839 & 23.7456 \\ 63 & ${\rm 2p^2 3s}$ & ${\rm ^4P^{e}_{1/2} }$ & & 20.7850 & 20.8237 & 20.7382 & & & & & & & \\[2pt] \hline \end{tabular} \medskip $^{a}$ \url{http://physics.nist.gov/PhysRefData/ASD/levels_form.html}; $^{b}$ {\sc autostructure} (present work); $^{c}$ Liang et~al. (\cite{LZZ07}); $^{d}$ Zhang \& Sampson (\cite{ZS94}), their 15~lowest-lying levels are observed values from Zhang et~al. (\cite{ZGP94}). \end{table}