\begin{table}%t3 \caption{\label{Tab:K:Ca:tar-str}The lowest $\Delta n_{{\rm c}} = 0, 1$ core excitation thresholds (in Rydbergs) for \ion{K}{ii} and \ion{Ca}{iii}.} \par %\centering \par \begin{tabular}{r l l l r r c l l r r r} % 12 columns \hline \hline \noalign{\smallskip} %\multicolumn{12}{c}{\vspace*{-2mm}} \\ & & \multicolumn{4}{c}{${\rm K}^{+}$} & & & \multicolumn{4}{c}{${\rm Ca}^{2+}$} \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ %\cline{3-6}\cline{9-12} %\multicolumn{12}{c}{\vspace*{-2mm}} \\ K & Config. & Level(mix) & Present\tablefootmark{a} & NIST\tablefootmark{b} & MCHF\tablefootmark{c} & K & Config. & Level(mix) & Present\tablefootmark{a} & NIST\tablefootmark{d} & MCHF\tablefootmark{c} \\ \hline \multicolumn{12}{c}{\vspace*{-2mm}} \\ %K Configuration Level Present NIST MCHF 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} $ & $\rm {}^{1}\hspace*{-.5mm}S_{0}~(99.0\%)$ & $0.000000$ & $0.000000$ & $0.000000$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 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 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(95.2\%)$ & $1.893907$ & $1.866664$ & $1.773134$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 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 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{3}\hspace*{-.5mm}F_{2}^{{\rm o}}~(94.0\%)$ & $1.972601$ & $1.953156$ & $1.861216$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 8 & $\rm 3s^{2}3p^{5}4s$ & $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(74.8\%)$ & $1.517409$ & $1.516872$ & $1.437439$ & 8 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{1}\hspace*{-.5mm}D_{2}^{{\rm o}}~(58.9\%)$ & $2.086507$ & $2.057880$ & $1.972081$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 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 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{3}\hspace*{-.5mm}D_{2}^{{\rm o}}~(54.0\%)$ & $2.095232$ & $2.072117$ & $1.984866$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 12 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{3}\hspace*{-.5mm}D_{3}^{{\rm o}}~(35.7\%)$ & $1.633040$ & $1.634775$ & $1.561671$ & 12 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{1}\hspace*{-.5mm}F_{3}^{{\rm o}}~(57.8\%)$ & $2.081461$ & $2.097941$ & $1.995780$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 13 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{1}\hspace*{-.5mm}D_{2}^{{\rm o}}~(41.6\%)$ & $1.639503$ & $1.634350$ & $1.560836$ & 13 & $\rm 3s^{2}3p^{5}4s$ & $\rm {}^{3}\hspace*{-.5mm}P_{2}^{{\rm o}}~(99.4\%)$ & $2.313063$ & $2.210253$ & $2.114045$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 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 & $\rm 3s^{2}3p^{5}4s$ & $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(87.6\%)$ & $2.369020$ & $2.257176$ & $2.160581$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 17 & $\rm 3s^{2}3p^{5}4p$ & $\rm {}^{3}\hspace*{-.5mm}S_{1}~(97.7\%)$ & $1.663215$ & $1.669479$ & $1.591351$ & 17 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(63.1\%)$\tablefootmark{\bigstar} & $2.545658$ & $2.545658$ & $2.492690$ \\ %\multicolumn{12}{c}{\vspace*{-2mm}} \\ 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 & $\rm 3s^{2}3p^{5}3d$ & $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(90.5\%)$\tablefootmark{\bigstar}& $1.840715$ & $1.840373$ & $1.817999$ & & & & & & \\ & $\rm 3s^{2}3p^{5}4d$ & $\rm {}^{1}\hspace*{-.5mm}P_{1}^{{\rm o}}~(90.0\%)$ & $2.033261$ & $2.033256$ & & & & & & & \\ \hline \end{tabular} \tablefoot{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 \ion{K}{ii} whose configuration is marked as questionable by \cite{Sugar:1985} and only recently properly identified by \cite{Pettersen:2007}. \tablefoottext{a}{present work: 51-level (${\rm K}^{+}$) and 69-level (${\rm Ca}^{2+}$) MCBP results;} \tablefoottext{b}{UV spark spectroscopy experimental data of \cite{Pettersen:2007};} \tablefoottext{c}{MCHF results of \cite{Irimia:2003};} \tablefoottext{d}{critically compiled experimental data of \cite{Sugar:1985};} \tablefoottext{\bigstar}{dominant excitation threshold -- see Table~\ref{Tab:tar-rad}.}}\vspace*{2mm} \end{table}