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Table 3:

The lowest $\Delta n_{{\rm c}} = 0, 1$ core excitation thresholds (in Rydbergs) for K II and Ca III.
    ${\rm K}^{+}$     ${\rm Ca}^{2+}$
K Config. Level(mix) Presenta NISTb MCHFc K Config. Level(mix) Presenta NISTd MCHFc

1 $\rm 3s^{2}3p^{6} $ $\rm {}^{1}\hspace*{-.5mm}S_{0}~(96.3\%)$ 0.000000 0.000000 0.000000 1 $\rm 3s^{2}3p^{6} $ $\rm {}^{1}\hspace*{-.5mm}S_{0}~(99.0\%)$ 0.000000 0.000000 0.000000
2 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(93.2\%)$ 1.480381 1.480834 1.400644 2 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{0}^{{\rm o}}~(95.7\%)$ 1.879530 1.853273 1.760169
3 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{1}^{{\rm o}}~(59.7\%)$ 1.487826 1.487481 1.408491 3 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{1}^{{\rm o}}~(95.6\%)$ 1.884279 1.857636 1.764514
4 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{0}^{{\rm o}}~(70.9\%)$ 1.490116 1.489303 1.431384 4 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(95.2\%)$ 1.893907 1.866664 1.773134
5 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{1}^{{\rm o}}~(59.5\%)$ 1.499706 1.498961 1.430119 5 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{4}^{{\rm o}}~(95.1\%)$ 1.952880 1.934711 1.844004
6 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(81.1\%)$ 1.505571 1.502934 1.436726 6 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{3}^{{\rm o}}~(93.9\%)$ 1.963210 1.944456 1.853118
7 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{0}^{{\rm o}}~(82.4\%)$ 1.506735 1.504916 1.414847 7 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{2}^{{\rm o}}~(94.0\%)$ 1.972601 1.953156 1.861216
8 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(74.8\%)$ 1.517409 1.516872 1.437439 8 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}D_{2}^{{\rm o}}~(58.9\%)$ 2.086507 2.057880 1.972081
9 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{4}^{{\rm o}}~(82.4\%)$ 1.547896 1.549602 1.480702 9 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{3}^{{\rm o}}~(53.7\%)$ 2.080602 2.062503 1.976286
10 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{3}^{{\rm o}}~(81.1\%)$ 1.555741 1.556728 1.488382 10 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{1}^{{\rm o}}~(92.9\%)$ 2.093231 2.072514 1.985320
11 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}F_{2}^{{\rm o}}~(81.3\%)$ 1.562998 1.563029 1.494070 11 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{2}^{{\rm o}}~(54.0\%)$ 2.095232 2.072117 1.984866
12 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{3}^{{\rm o}}~(35.7\%)$ 1.633040 1.634775 1.561671 12 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}F_{3}^{{\rm o}}~(57.8\%)$ 2.081461 2.097941 1.995780
13 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}D_{2}^{{\rm o}}~(41.6\%)$ 1.639503 1.634350 1.560836 13 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(99.4\%)$ 2.313063 2.210253 2.114045
14 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{1}^{{\rm o}}~(71.5\%)$ 1.644348 1.644371 1.570061 14 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{1}^{{\rm o}}~(88.0\%)$ 2.327118 2.222858 2.126335
15 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{3}\hspace*{-.5mm}D_{2}^{{\rm o}}~(41.9\%)$ 1.645874 1.643859 1.569134 15 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{3}\hspace*{-.5mm}P_{0}^{{\rm o}}~(99.4\%)$ 2.341390 2.238180 2.140287
16 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}F_{3}^{{\rm o}}~(34.1\%)$ 1.645999 1.645919 1.571404 16 $\rm 3s^{2}3p^{5}4s$ $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(87.6\%)$ 2.369020 2.257176 2.160581
17 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}S_{1}~(97.7\%)$ 1.663215 1.669479 1.591351 17 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(63.1\%)$$^{\bigstar}$ 2.545658 2.545658 2.492690
18 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}D_{3}~(99.9\%)$ 1.693675 1.698454 1.618318            
19 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}D_{2}~(75.5\%)$ 1.697258 1.701166 1.621064            
20 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}D_{1}~(76.3\%)$ 1.705934 1.708872 1.628229            
21 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{1}\hspace*{-.5mm}D_{2}~(51.0\%)$ 1.712827 1.714552 1.633790            
22 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{1}\hspace*{-.5mm}P_{1}~(52.5\%)$ 1.724516 1.724477 1.643195            
23 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}P_{2}~(55.9\%)$ 1.727938 1.728285 1.646621            
24 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}P_{0}~(99.5\%)$ 1.730260 1.729293 1.648054            
25 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{3}\hspace*{-.5mm}P_{1}~(65.5\%)$ 1.733330 1.732598 1.650821            
26 $\rm 3s^{2}3p^{5}4p$ $\rm {}^{1}\hspace*{-.5mm}S_{0}~(95.2\%)$ 1.829238 1.774895 1.702454            
27 $\rm 3s^{2}3p^{5}3d$ $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(90.5\%)$$^{\bigstar}$ 1.840715 1.840373 1.817999            
  $\rm 3s^{2}3p^{5}4d$ $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(90.0\%)$ 2.033261 2.033256              

Notes. For brevity, we show only the core excitations that are below the dominant $\rm 3p^6({}^1S_{0})\to 3p^53d({}^1P_{1}^{{\rm o}})$threshold. The exception is the $\rm 3p^54d\;({}^1P_{1}^{{\rm o}})$threshold in K II whose configuration is marked as questionable by Sugar & Corliss (1985) and only recently properly identified by Pettersen et al. (2007). (a) present work: 51-level ( ${\rm K}^{+}$) and 69-level ( ${\rm Ca}^{2+}$) MCBP results; (b) UV spark spectroscopy experimental data of Pettersen et al. (2007); (c) MCHF results of Froese-Fischer & Tachiev (2006); (d) critically compiled experimental data of Sugar & Corliss (1985); $^{(\bigstar)}$ dominant excitation threshold - see Table 2.


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