Transition rates and radiative lifetimes of Ca I

Yanmei Yu; Andrei Derevianko

arXiv:1702.03473·physics.atom-ph·November 22, 2017

Transition rates and radiative lifetimes of Ca I

Yanmei Yu, Andrei Derevianko

PDF

TL;DR

This paper provides comprehensive ab initio calculations of spontaneous emission rates for all electric-dipole-allowed transitions among the lowest-energy states of neutral calcium, aiding various atomic physics applications.

Contribution

It presents the first complete tabulation of transition rates for 811 transitions in Ca I using relativistic configuration interaction and many-body perturbation theory.

Findings

01

Transition rates are consistent with existing literature where available.

02

The data can improve laser cooling and optical clock accuracy.

03

The results facilitate calculations of atomic polarizabilities and interaction coefficients.

Abstract

We tabulate spontaneous emission rates for all possible 811 electric-dipole-allowed transitions between the 75 lowest-energy states of Ca I. These involve the $4 s n s$ ( $n = 4 - 8$ ), $4 s n p$ ( $n = 4 - 7$ ), $4 s n d$ ( $n = 3 - 6$ ), $4 s n f$ ( $n = 4 - 6$ ), $4 p^{2}$ , and $3 d 4 p$ electronic configurations. We compile the transition rates by carrying out ab initio relativistic calculations using the combined method of configuration interaction and many-body perturbation theory. The results are compared to the available literature values. The tabulated rates can be useful in various applications, such as optimizing laser cooling in magneto-optical traps, estimating various systematic effects in optical clocks and evaluating static or dynamic polarizabilities and long-range atom-atom interaction coefficients and related atomic properties.

Tables7

Table 1. Table 1: Radiative electric-dipole decay rates A total subscript 𝐴 total A_{\mathrm{total}} and lifetimes τ 𝜏 \tau of Ca I.

State	Energy (cm^-1)		Diff.(%)	$A_{total}$ ( $10^{8}$ s^-1)	$τ$ (ns)
	This work	NIST			This work	Refs.
$4 s 4 p {}^{3}P_{0}$	15125.730	15157.900	0.2	0.0	$\infty$
$4 s 4 p {}^{3}P_{1}$	15179.500	15210.060	0.2	2.74 $\times 10^{- 5}$	3.65 $\times 10^{5}$	(3.4 $\pm 0.2$ ) $\times 10^{5}$ Exp. [21]
						4.25(10) $\times 10^{5}$ Exp. [2]
$4 s 4 p {}^{3}P_{2}$	15289.530	15315.940	0.2	0.0	$\infty$
$3 d 4 s {}^{3}D_{1}$	20822.630	20335.360	2.4	8.68 $\times 10^{- 3}$	1.15 $\times 10^{3}$
$3 d 4 s {}^{3}D_{2}$	20840.440	20349.260	2.4	8.50 $\times 10^{- 3}$	1.18 $\times 10^{3}$
$3 d 4 s {}^{3}D_{3}$	20868.160	20371.000	2.4	8.24 $\times 10^{- 3}$	1.21 $\times 10^{3}$
$3 d 4 s {}^{1}D_{2}$	22449.920	21849.630	2.7	4.88 $\times 10^{- 6}$	2.05 $\times 10^{6}$	2.3(5) $\times 10^{6}$ Exp. [24]
						1.71(3) $\times 10^{6}$ Exp. [25]
$4 s 4 p {}^{1}P_{1}$	23491.350	23652.300	0.7	2.17	4.61	4.535(28) Exp. [20]
$4 s 5 s {}^{3}S_{1}$	31729.740	31539.500	0.6	0.823	12.1	12.4 MPCI [9]
$4 s 5 s {}^{1}S_{0}$	33465.560	33317.260	0.4	0.229	43.6
$3 d 4 p {}^{3}F_{2}$	36235.100	35730.450	1.4	0.401	24.9
$3 d 4 p {}^{3}F_{3}$	36332.400	35818.710	1.4	0.381	26.2
$3 d 4 p {}^{1}D_{2}$	36350.570	35835.410	1.4	0.446	22.4
$3 d 4 p {}^{3}F_{4}$	36419.600	35896.890	1.5	0.385	26.0
$4 s 5 p {}^{3}P_{0}$	36513.680	36547.690	0.1	0.176	57.0
$4 s 5 p {}^{3}P_{1}$	36521.570	36554.750	0.1	0.176	56.9
$4 s 5 p {}^{3}P_{2}$	36543.800	36575.120	0.1	0.177	56.5
$4 s 5 p {}^{1}P_{1}$	36708.430	36731.620	0.1	0.163	61.5	57.6 MPCI [9]
$4 s 4 d {}^{1}D_{2}$	37660.590	37298.290	1.0	0.161	62.3	64.9 MPCI [9]
$4 s 4 d {}^{3}D_{1}$	38013.550	37748.200	0.7	0.786	12.7	13.0(5) Exp. [22]
$4 s 4 d {}^{3}D_{2}$	38017.720	37751.870	0.7	0.784	12.8	13.0(5) Exp. [22]
$4 s 4 d {}^{3}D_{3}$	38023.990	37757.450	0.7	0.781	12.8	13.0(5) Exp. [22]
$3 d 4 p {}^{3}D_{1}$	38787.640	38192.390	1.6	0.689	14.5
$3 d 4 p {}^{3}D_{2}$	38819.160	38219.120	1.6	0.690	14.5
$3 d 4 p {}^{3}D_{3}$	38866.410	38259.120	1.6	0.692	14.5
$4 p^{2} {}^{3}P_{0}$	38858.080	38417.540	1.1	1.83	5.48	6.9(4) Exp. [22]
$4 p^{2} {}^{3}P_{1}$	38908.680	38464.810	1.2	1.83	5.46	6.9(4) Exp. [22]
$4 p^{2} {}^{3}P_{2}$	39001.360	38551.560	1.2	1.83	5.45	6.9(4) Exp. [22]
$3 d 4 p {}^{3}P_{0}$	39871.870	39333.380	1.4	0.781	12.8
$3 d 4 p {}^{3}P_{1}$	39875.220	39335.320	1.4	0.781	12.8
$3 d 4 p {}^{3}P_{2}$	39883.770	39340.080	1.4	0.779	12.8
$4 s 6 s {}^{3}S_{1}$	40664.630	40474.240	0.5	0.327	30.6
$3 d 4 p {}^{1}F_{3}$	41100.840	40537.890	1.4	0.073	137
$4 s 6 s {}^{1}S_{0}$	40942.640	40690.440	0.6	0.070	142	113.0 MPCI [9]
$4 p^{2} {}^{1}D_{2}$	41182.450	40719.850	1.1	0.593	16.9	15.2 MPCI [9]
						16.3 Exp. [22]
$4 s 6 p {}^{1}P_{1}$	41787.870	41679.010	0.3	0.361	27.7
$4 p^{2} {}^{1}S_{0}$	42336.930	41786.280	1.3	0.792	12.6	12.5 MPCI [9]
						14.4(7) Exp. [22]
$4 s 4 f {}^{3}F_{2}$	42078.450	42170.210	0.2	0.261	38.4
$4 s 4 f {}^{3}F_{3}$	42078.850	42170.560	0.2	0.261	38.4
$4 s 4 f {}^{3}F_{4}$	42079.380	42171.030	0.2	0.261	38.3
$4 s 4 f {}^{1}F_{3}$	42392.680	42343.590	0.1	0.378	26.4	28.8 MPCI [9]
$4 s 6 p {}^{3}P_{0}$	42479.440	42514.850	0.1	0.005	0.020
$4 s 6 p {}^{3}P_{1}$	42483.640	42518.710	0.1	0.005	0.020
$4 s 6 p {}^{3}P_{2}$	42492.270	42526.590	0.1	0.005	0.019
$4 s 5 d {}^{3}D_{1}$	42979.530	42743.000	0.6	0.406	24.7
$4 s 5 d {}^{3}D_{2}$	42981.440	42744.720	0.6	0.405	24.7
$4 s 5 d {}^{3}D_{3}$	42984.390	42747.390	0.6	0.403	24.8
$4 s 5 d {}^{1}D_{2}$	43227.380	42919.050	0.7	0.511	19.6	22.8 MPCI [9]
$3 d^{2} {}^{3}F_{2}$	44231.820	43474.830	1.7	0.007	0.015
$3 d^{2} {}^{3}F_{3}$	44251.410	43489.120	1.8	0.007	0.015
$3 d^{2} {}^{3}F_{4}$	44277.650	43508.090	1.8	0.007	0.015
$4 s n p {}^{1}P_{1}$	44382.940	43933.480	1.0	0.757	13.2
$4 s 7 s {}^{3}S_{1}$	44707.350	43980.770	1.7	0.223	44.9
$4 s 7 s {}^{1}S_{0}$	45215.430	44276.540	2.1	0.248	40.4	73.2 MPCI [9]
						45.7 MCHF [5]
$4 s 5 f {}^{3}F_{2}$	44796.860	44762.620	0.1	0.170	58.8
$4 s 5 f {}^{3}F_{3}$	44797.140	44762.840	0.1	0.170	588
$4 s 5 f {}^{3}F_{4}$	44797.520	44763.120	0.1	0.171	58.6
$4 s 5 f {}^{1}F_{3}$	44870.500	44804.880	0.1	0.231	43.3	56.5 MPCI [9]
$4 s 5 g {}^{3}G_{5}$	45191.910	44874.860	0.7	0.005	195
$4 s 5 g {}^{1}G_{4}$	45191.510	44875.950	0.7	0.007	147
$4 s 7 p {}^{3}P_{0}$	45997.520	44955.670	2.3	0.002	550
$4 s 7 p {}^{3}P_{1}$	46001.620	44957.660	2.3	0.002	546
$4 s 7 p {}^{3}P_{2}$	46010.100	44961.760	2.3	0.002	539
$4 s 6 d {}^{1}D_{2}$	45815.480	44989.830	1.8	0.206	48.6	76.3 MPCI [9]
						58.9 Exp. [23]
$4 s 6 d {}^{3}D_{1}$	45890.620	45049.070	1.9	0.378	26.5
$4 s 6 d {}^{3}D_{2}$	45893.340	45050.420	1.9	0.377	26.5
$4 s 6 d {}^{3}D_{3}$	45897.080	45052.370	1.9	0.376	26.6
$4 s 7 p {}^{1}P_{1}$	46975.130	45425.360	3.4	0.407	24.5
$4 s 8 s {}^{3}S_{1}$	45738.680	45738.680	0.0	0.009	105	149 MPCI [9]
						118.3(6.3) Exp. [23]
$4 s 8 s {}^{1}S_{0}$	45887.200	45887.200	0.0	0.006	157
$4 s 6 f {}^{3}F_{2}$	47711.820	46164.640	3.4	0.227	112.7
$4 s 6 f {}^{3}F_{3}$	47712.420	46164.790	3.4	0.228	113.7
$4 s 6 f {}^{3}F_{4}$	47713.200	46164.970	3.4	0.228	121.9
$4 s 6 f {}^{1}F_{3}$	47768.330	46182.400	3.4	0.291	96.7

Table 2. Table 2: Spontaneous emission rates of transitions originating from the 4 s n s 4 𝑠 𝑛 𝑠 4sns ( n 𝑛 n =4-8) states of Ca I.

Transition		$λ$ (nm)	$A_{i f}$ ( $10^{8}$ s^-1)		Diff. (%)	BR.(%)
Initial	Final		$L$	$V$
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	610.441	9.246E-02	9.001E-02	2.65	11.23
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	612.391	2.759E-01	2.685E-01	2.67	33.51
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	616.388	4.549E-01	4.426E-01	2.71	55.26
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{1}P_{1}$	1267.877	5.911E-06	6.068E-06	-2.66	0.00
$4 s 5 s {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	552.267	1.694E-05	1.826E-05	-7.78	0.01
$4 s 5 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	1034.665	2.293E-01	2.217E-01	3.34	99.99
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}F_{2}$	2108.019	2.378E-05	2.360E-05	0.77	0.01
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{1}D_{2}$	2155.716	1.673E-04	1.664E-04	0.53	0.05
$4 s 6 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{0}$	2546.765	9.152E-03	9.132E-03	0.22	2.80
$4 s 6 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{1}$	2551.352	2.714E-02	2.708E-02	0.21	8.30
$4 s 6 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{2}$	2564.681	4.537E-02	4.528E-02	0.21	13.88
$4 s 6 s {}^{3}S_{1}$	$4 s 5 p {}^{1}P_{1}$	2671.925	2.703E-04	2.697E-04	0.24	0.08
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	395.002	2.621E-02	2.500E-02	4.60	8.01
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{1}$	4382.409	5.498E-07	4.698E-07	14.55	0.00
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{2}$	4434.354	1.660E-06	1.531E-06	7.76	0.00
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{0}$	8765.317	1.184E-04	1.166E-04	1.53	0.04
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	395.817	7.994E-02	7.638E-02	4.46	24.45
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{1}$	8780.248	3.539E-04	3.462E-04	2.19	0.11
$4 s 6 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{2}$	8817.098	5.849E-04	5.674E-04	2.99	0.18
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	397.483	1.377E-01	1.319E-01	4.20	42.10
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{1}P_{1}$	594.462	1.172E-06	1.231E-06	-5.01	0.00
$4 s 6 s {}^{1}S_{0}$	$4 s 5 p {}^{3}P_{1}$	2417.976	5.790E-04	5.636E-04	2.67	0.82
$4 s 6 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	2526.005	5.484E-02	5.299E-02	3.37	77.90
$4 s 6 s {}^{1}S_{0}$	$3 d 4 p {}^{3}D_{1}$	4003.122	8.321E-06	8.418E-06	-1.17	0.01
$4 s 6 s {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	392.459	7.678E-04	8.401E-04	-9.42	1.09
$4 s 6 s {}^{1}S_{0}$	$3 d 4 p {}^{3}P_{1}$	7379.420	1.071E-06	8.795E-07	17.85	0.00
$4 s 6 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	586.919	1.420E-02	2.181E-02	-53.58	20.17
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}F_{2}$	1212.074	9.204E-06	9.121E-06	0.90	0.00
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{1}D_{2}$	1227.693	6.343E-05	6.312E-05	0.48	0.03
$4 s 7 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{0}$	1345.337	4.039E-03	4.043E-03	-0.12	1.81
$4 s 7 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{1}$	1346.616	1.196E-02	1.197E-02	-0.13	5.37
$4 s 7 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{2}$	1350.320	1.990E-02	1.994E-02	-0.16	8.94
$4 s 7 s {}^{3}S_{1}$	$4 s 5 p {}^{1}P_{1}$	1379.472	1.143E-04	1.145E-04	-0.22	0.05
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	346.947	1.873E-02	1.773E-02	5.35	8.41
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{1}$	1727.599	2.534E-08	1.214E-08	52.10	0.00
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{2}$	1735.614	6.215E-08	4.375E-08	29.61	0.00
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{0}$	2151.745	6.592E-05	5.724E-05	13.17	0.03
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	347.576	5.630E-02	5.330E-02	5.32	25.27
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{1}$	2152.644	2.023E-04	1.771E-04	12.49	0.09
$4 s 7 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{2}$	2154.852	3.557E-04	3.143E-04	11.64	0.16
$4 s 7 s {}^{3}S_{1}$	$4 s 6 p {}^{1}P_{1}$	4344.502	3.555E-08	2.421E-08	31.91	0.00
$4 s 7 s {}^{3}S_{1}$	$4 s 4 f {}^{3}F_{2}$	5523.153	1.611E-13	1.419E-13	11.93	0.00
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	348.860	9.417E-02	8.923E-02	5.24	42.28
$4 s 7 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{0}$	6821.655	1.886E-03	1.631E-03	13.50	0.85
$4 s 7 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{1}$	6839.665	5.634E-03	4.869E-03	13.58	2.53
$4 s 7 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{2}$	6876.728	9.311E-03	8.031E-03	13.75	4.18
$4 s 7 s {}^{3}S_{1}$	$4 s n p {}^{1}P_{1}$	211461.197	6.064E-12	3.709E-10	-6016.54	0.00
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{1}P_{1}$	491.921	7.761E-07	8.123E-07	-4.67	0.00
$4 s 7 s {}^{1}S_{0}$	$4 s 5 p {}^{3}P_{1}$	1295.037	4.787E-04	4.881E-04	-1.97	0.19
$4 s 7 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	1325.395	4.599E-02	4.680E-02	-1.75	18.57
$4 s 7 s {}^{1}S_{0}$	$3 d 4 p {}^{3}D_{1}$	1643.615	1.933E-06	2.372E-06	-22.69	0.00
$4 s 7 s {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	344.039	3.318E-06	3.419E-06	-3.03	0.00
$4 s 7 s {}^{1}S_{0}$	$3 d 4 p {}^{3}P_{1}$	2023.792	2.553E-08	4.952E-08	-93.96	0.00
$4 s 7 s {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	3849.811	2.243E-02	1.991E-02	11.25	9.06
$4 s 7 s {}^{1}S_{0}$	$4 s 6 p {}^{3}P_{1}$	5688.832	3.489E-08	5.111E-08	-46.48	0.00
$4 s 7 s {}^{1}S_{0}$	$4 s n p {}^{1}P_{1}$	29149.420	3.074E-04	9.826E-05	68.03	0.12
$4 s 7 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	484.866	1.784E-01	1.834E-01	-2.79	72.05
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}F_{2}$	999.178	7.736E-09			0.00
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{1}D_{2}$	1009.767	7.664E-07			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{0}$	1088.022	1.542E-03			1.63
$4 s 8 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{1}$	1088.858	4.577E-03			4.83
$4 s 8 s {}^{3}S_{1}$	$4 s 5 p {}^{3}P_{2}$	1091.279	7.690E-03			8.11
$4 s 8 s {}^{3}S_{1}$	$4 s 5 p {}^{1}P_{1}$	1110.240	4.267E-05			0.05
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{1}$	1325.154	5.676E-08			0.00
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}D_{2}$	1329.865	2.426E-07			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	327.003	7.436E-03			7.85
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{0}$	1561.207	4.073E-05			0.04
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{1}$	1561.680	1.174E-04			0.12
$4 s 8 s {}^{3}S_{1}$	$3 d 4 p {}^{3}P_{2}$	1562.842	1.793E-04			0.19
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	327.561	2.225E-02			23.47
$4 s 8 s {}^{3}S_{1}$	$4 s 6 p {}^{1}P_{1}$	2463.254	2.019E-08			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 4 f {}^{3}F_{2}$	2802.321	8.155E-13			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	328.701	3.693E-02			38.96
$4 s 8 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{0}$	3101.901	8.286E-04			0.87
$4 s 8 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{1}$	3105.619	2.469E-03			2.61
$4 s 8 s {}^{3}S_{1}$	$4 s 6 p {}^{3}P_{2}$	3113.238	4.063E-03			4.29
$4 s 8 s {}^{3}S_{1}$	$4 s n p {}^{1}P_{1}$	5539.552	1.078E-08			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 5 f {}^{3}F_{2}$	10245.272	2.432E-13			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 7 p {}^{3}P_{0}$	12771.229	7.410E-04			0.78
$4 s 8 s {}^{3}S_{1}$	$4 s 7 p {}^{3}P_{1}$	12803.769	2.215E-03			2.34
$4 s 8 s {}^{3}S_{1}$	$4 s 7 p {}^{3}P_{2}$	12871.338	3.664E-03			3.87
$4 s 8 s {}^{3}S_{1}$	$4 s 7 p {}^{1}P_{1}$	31916.252	2.029E-08			0.00
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{1}P_{1}$	452.768	2.558E-07			0.00
$4 s 8 s {}^{1}S_{0}$	$4 s 5 p {}^{3}P_{1}$	1071.530	1.821E-04			0.29
$4 s 8 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	1092.230	1.964E-02			30.78
$4 s 8 s {}^{1}S_{0}$	$3 d 4 p {}^{3}D_{1}$	1299.577	9.657E-06			0.02
$4 s 8 s {}^{1}S_{0}$	$3 d 4 p {}^{3}P_{1}$	1526.279	7.658E-07			0.00
$4 s 8 s {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	325.976	6.115E-08			0.00
$4 s 8 s {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	2376.319	6.149E-03			9.63
$4 s 8 s {}^{1}S_{0}$	$4 s 6 p {}^{3}P_{1}$	2968.689	1.757E-07			0.00
$4 s 8 s {}^{1}S_{0}$	$4 s n p {}^{1}P_{1}$	5118.441	7.344E-05			0.12
$4 s 8 s {}^{1}S_{0}$	$4 s 7 p {}^{3}P_{1}$	10758.009	5.245E-07			0.00
$4 s 8 s {}^{1}S_{0}$	$4 s 7 p {}^{1}P_{1}$	21652.520	2.071E-03			3.25
$4 s 8 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	449.743	3.569E-02			55.93

Table 3. Table 3: Spontaneous emission rates of transitions originating from the 4 s n p 4 𝑠 𝑛 𝑝 4snp ( n 𝑛 n =4-7) states of Ca I.

Transition		$λ$ (nm)	$A_{i f}$ ( $10^{8}$ s^-1)		Diff. (%)	BR.(%)
Initial	Final		$L$	$V$
$4 s 4 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	657.460	2.738E-05	3.531E-05	-28.98	100.00
$4 s 4 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	422.792	2.170E+00	2.327E+00	-7.20	100.00
$4 s 4 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{1}$	3014.827	3.767E-08	4.832E-08	-28.27	0.00
$4 s 4 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	3027.514	1.000E-07	3.825E-07	-282.52	0.00
$4 s 4 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	5547.327	5.341E-05	2.287E-06	95.72	0.00
$4 s 5 p {}^{3}P_{0}$	$4 s 5 s {}^{3}S_{1}$	1996.729	7.103E-02	7.143E-02	-0.55	40.46
$4 s 5 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	616.814	1.045E-01	1.102E-01	-5.38	59.54
$4 s 5 p {}^{3}P_{1}$	$4 s 5 s {}^{3}S_{1}$	1993.919	7.055E-02	7.096E-02	-0.58	40.15
$4 s 5 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	273.562	2.340E-06	4.425E-05	-1790.81	0.00
$4 s 5 p {}^{3}P_{1}$	$4 s 5 s {}^{1}S_{0}$	3088.813	2.055E-04	2.050E-04	0.24	0.12
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	616.546	2.532E-02	2.667E-02	-5.34	14.41
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	617.075	7.859E-02	8.296E-02	-5.55	44.73
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{1}D_{2}$	680.035	1.051E-03	1.177E-03	-11.99	0.60
$4 s 5 p {}^{3}P_{2}$	$4 s 5 s {}^{3}S_{1}$	1985.853	7.180E-02	7.223E-02	-0.60	40.59
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	615.773	6.273E-04	6.834E-04	-8.93	0.35
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	616.300	1.558E-02	1.638E-02	-5.14	8.81
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	617.127	8.710E-02	9.206E-02	-5.69	49.24
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{1}D_{2}$	679.095	1.792E-03	2.000E-03	-11.62	1.01
$4 s 5 p {}^{1}P_{1}$	$4 s 5 s {}^{3}S_{1}$	1925.996	7.950E-04	7.974E-04	-0.30	0.49
$4 s 5 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	272.245	7.505E-03	1.833E-02	-144.27	4.62
$4 s 5 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	2928.807	2.361E-02	2.339E-02	0.95	14.52
$4 s 5 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{1}$	609.895	3.978E-04	4.252E-04	-6.88	0.24
$4 s 5 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	610.413	2.354E-04	2.298E-04	2.38	0.14
$4 s 5 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	671.953	1.301E-01	1.446E-01	-11.19	79.98
$4 s 6 p {}^{1}P_{1}$	$4 s 5 s {}^{3}S_{1}$	986.241	5.599E-08	5.809E-08	-3.74	0.00
$4 s 6 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	239.929	9.182E-02	8.164E-02	11.09	25.41
$4 s 6 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	1195.922	1.516E-02	1.561E-02	-2.92	4.20
$4 s 6 p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	2282.730	1.407E-02	1.541E-02	-9.50	3.89
$4 s 6 p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{1}$	2544.005	2.339E-09	9.781E-09	-318.22	0.00
$4 s 6 p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{2}$	2546.382	1.725E-06	2.001E-06	-16.02	0.00
$4 s 6 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{0}$	3066.102	2.017E-06	1.819E-06	9.82	0.00
$4 s 6 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{1}$	3111.194	5.703E-09	4.304E-09	24.53	0.00
$4 s 6 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{2}$	3197.493	7.016E-06	6.775E-06	3.43	0.00
$4 s 6 p {}^{1}P_{1}$	$4 s 6 s {}^{3}S_{1}$	8300.339	1.476E-08	1.402E-08	5.02	0.00
$4 s 6 p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	10115.622	1.605E-03	1.577E-03	1.75	0.44
$4 s 6 p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	10425.789	7.877E-04	6.658E-04	15.47	0.22
$4 s 6 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{1}$	468.523	6.442E-07	1.470E-07	77.18	0.00
$4 s 6 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	468.829	2.073E-05	2.677E-05	-29.15	0.01
$4 s 6 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	504.302	2.379E-01	2.744E-01	-15.35	65.83
$4 s 6 p {}^{3}P_{0}$	$4 s 5 s {}^{3}S_{1}$	911.133	7.945E-03	8.043E-03	-1.23	15.61
$4 s 6 p {}^{3}P_{0}$	$4 s 4 d {}^{3}D_{1}$	2097.909	7.984E-03	7.472E-03	6.42	15.69
$4 s 6 p {}^{3}P_{0}$	$4 p^{2} {}^{3}P_{1}$	2469.111	4.647E-06	1.928E-06	58.52	0.01
$4 s 6 p {}^{3}P_{0}$	$4 s 6 s {}^{3}S_{1}$	4900.495	1.618E-02	1.650E-02	-1.97	31.79
$4 s 6 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	450.867	1.878E-02	2.995E-02	-59.42	36.90
$4 s 6 p {}^{3}P_{1}$	$4 s 5 s {}^{3}S_{1}$	910.812	8.107E-03	8.203E-03	-1.19	15.85
$4 s 6 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	235.191	1.122E-08	4.799E-08	-327.69	0.00
$4 s 6 p {}^{3}P_{1}$	$4 s 5 s {}^{1}S_{0}$	1086.785	1.281E-08	3.164E-08	-146.98	0.00
$4 s 6 p {}^{3}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1915.555	2.977E-07	2.213E-07	25.66	0.00
$4 s 6 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{1}$	2096.212	1.976E-03	1.848E-03	6.49	3.86
$4 s 6 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{2}$	2097.826	5.964E-03	5.579E-03	6.45	11.66
$4 s 6 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{0}$	2438.329	2.340E-08	6.862E-08	-193.25	0.00
$4 s 6 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{1}$	2466.760	6.170E-07	1.982E-07	67.88	0.00
$4 s 6 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{2}$	2520.701	1.270E-06	3.888E-07	69.38	0.00
$4 s 6 p {}^{3}P_{1}$	$4 s 6 s {}^{3}S_{1}$	4891.243	1.625E-02	1.657E-02	-1.96	31.78
$4 s 6 p {}^{3}P_{1}$	$4 s 6 s {}^{1}S_{0}$	5469.652	2.777E-08	3.211E-08	-15.61	0.00
$4 s 6 p {}^{3}P_{1}$	$4 p^{2} {}^{1}D_{2}$	5559.076	9.162E-09	5.895E-09	35.66	0.00
$4 s 6 p {}^{3}P_{1}$	$4 p^{2} {}^{1}S_{0}$	13653.182	5.670E-10	3.303E-10	41.75	0.00
$4 s 6 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	450.789	4.808E-03	7.627E-03	-58.62	9.40
$4 s 6 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	451.071	1.403E-02	2.241E-02	-59.70	27.43
$4 s 6 p {}^{3}P_{1}$	$3 d 4 s {}^{1}D_{2}$	483.814	2.442E-06	2.156E-06	11.73	0.00
$4 s 6 p {}^{3}P_{2}$	$4 s 5 s {}^{3}S_{1}$	910.159	8.442E-03	8.542E-03	-1.18	16.34
$4 s 6 p {}^{3}P_{2}$	$4 s 4 d {}^{1}D_{2}$	1912.668	1.141E-07	1.298E-07	-13.73	0.00
$4 s 6 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{1}$	2092.755	7.728E-05	7.217E-05	6.62	0.15
$4 s 6 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{2}$	2094.364	1.168E-03	1.091E-03	6.57	2.26
$4 s 6 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{3}$	2096.814	6.602E-03	6.170E-03	6.54	12.78
$4 s 6 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{1}$	2461.975	9.452E-07	1.747E-06	-84.89	0.00
$4 s 6 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{2}$	2515.704	1.001E-08	4.894E-07	-4791.12	0.00
$4 s 6 p {}^{3}P_{2}$	$4 s 6 s {}^{3}S_{1}$	4872.463	1.638E-02	1.671E-02	-1.99	31.71
$4 s 6 p {}^{3}P_{2}$	$4 p^{2} {}^{1}D_{2}$	5534.831	1.361E-08	1.069E-08	21.42	0.00
$4 s 6 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	450.628	2.012E-04	3.163E-04	-57.22	0.39
$4 s 6 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	450.911	2.942E-03	4.653E-03	-58.15	5.69
$4 s 6 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	451.353	1.585E-02	2.530E-02	-59.67	30.67
$4 s 6 p {}^{3}P_{2}$	$3 d 4 s {}^{1}D_{2}$	483.630	3.466E-06	4.781E-06	-37.96	0.01
$4 s n p {}^{1}P_{1}$	$4 s 5 s {}^{3}S_{1}$	806.843	1.985E-07	1.391E-07	29.94	0.00
$4 s n p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	227.617	3.246E-01	3.466E-01	-6.80	42.88
$4 s n p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	941.955	3.895E-02	4.001E-02	-2.71	5.15
$4 s n p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1507.116	1.273E-02	1.509E-02	-18.48	1.68
$4 s n p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{1}$	1616.742	6.691E-09	2.113E-08	-215.79	0.00
$4 s n p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{2}$	1617.702	1.500E-06	1.628E-06	-8.50	0.00
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{0}$	1812.928	5.659E-08	2.200E-08	61.12	0.00
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{1}$	1828.598	6.298E-09	1.871E-08	-197.07	0.00
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{2}$	1858.073	1.206E-06	1.524E-06	-26.37	0.00
$4 s n p {}^{1}P_{1}$	$4 s 6 s {}^{3}S_{1}$	2890.808	8.702E-08	1.053E-07	-21.02	0.00
$4 s n p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	3083.527	6.961E-03	7.698E-03	-10.59	0.92
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	3111.746	7.630E-04	8.518E-04	-11.63	0.10
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{1}S_{0}$	4657.228	3.175E-03	3.202E-03	-0.85	0.42
$4 s n p {}^{1}P_{1}$	$4 s 5 d {}^{3}D_{1}$	8399.973	1.344E-08	1.665E-08	-23.86	0.00
$4 s n p {}^{1}P_{1}$	$4 s 5 d {}^{3}D_{2}$	8412.127	2.373E-07	1.846E-07	22.23	0.00
$4 s n p {}^{1}P_{1}$	$4 s 5 d {}^{1}D_{2}$	9857.753	2.552E-03	2.015E-03	21.02	0.34
$4 s n p {}^{1}P_{1}$	$3 d^{2} {}^{3}F_{2}$	21803.118	2.171E-08	1.501E-08	30.87	0.00
$4 s n p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{1}$	423.763	7.516E-07	2.790E-07	62.87	0.00
$4 s n p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	424.012	5.665E-06	5.933E-06	-4.74	0.00
$4 s n p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	452.820	3.673E-01	4.427E-01	-20.53	48.52
$4 s 7 p {}^{3}P_{0}$	$4 s 5 s {}^{3}S_{1}$	745.369	1.781E-03	1.925E-03	-8.08	9.79
$4 s 7 p {}^{3}P_{0}$	$4 s 4 d {}^{3}D_{1}$	1387.449	5.557E-03	5.436E-03	2.17	30.55
$4 s 7 p {}^{3}P_{0}$	$4 p^{2} {}^{3}P_{1}$	1540.628	3.888E-06	3.340E-06	14.10	0.02
$4 s 7 p {}^{3}P_{0}$	$4 s 6 s {}^{3}S_{1}$	2231.431	2.027E-03	1.651E-03	18.56	11.14
$4 s 7 p {}^{3}P_{0}$	$4 s 5 d {}^{3}D_{1}$	4519.427	4.666E-03	2.823E-03	39.50	25.66
$4 s 7 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	406.169	1.349E-03	3.243E-03	-140.39	7.42
$4 s 7 p {}^{3}P_{0}$	$4 s 7 s {}^{3}S_{1}$	10257.462	2.804E-03	4.161E-03	-48.38	15.42
$4 s 7 p {}^{3}P_{1}$	$4 s 5 s {}^{3}S_{1}$	745.259	1.866E-03	2.014E-03	-7.91	10.19
$4 s 7 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	222.432	2.344E-07	3.119E-08	86.69	0.00
$4 s 7 p {}^{3}P_{1}$	$4 s 5 s {}^{1}S_{0}$	859.077	7.106E-08	3.350E-08	52.85	0.00
$4 s 7 p {}^{3}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1305.590	4.279E-07	3.715E-07	13.17	0.00
$4 s 7 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{1}$	1387.066	1.376E-03	1.346E-03	2.22	7.52
$4 s 7 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{2}$	1387.773	4.153E-03	4.062E-03	2.19	22.68
$4 s 7 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{0}$	1529.024	5.358E-08	2.853E-08	46.76	0.00
$4 s 7 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{1}$	1540.156	5.720E-07	4.865E-07	14.96	0.00
$4 s 7 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{2}$	1561.012	1.080E-06	8.977E-07	16.87	0.01
$4 s 7 p {}^{3}P_{1}$	$4 s 6 s {}^{3}S_{1}$	2230.440	2.065E-03	1.684E-03	18.47	11.28
$4 s 7 p {}^{3}P_{1}$	$4 s 6 s {}^{1}S_{0}$	2343.446	5.201E-09	7.345E-09	-41.23	0.00
$4 s 7 p {}^{3}P_{1}$	$4 p^{2} {}^{1}D_{2}$	2359.709	6.693E-09	1.793E-08	-167.98	0.00
$4 s 7 p {}^{3}P_{1}$	$4 p^{2} {}^{1}S_{0}$	3153.201	1.366E-07	1.495E-07	-9.47	0.00
$4 s 7 p {}^{3}P_{1}$	$4 s 5 d {}^{3}D_{1}$	4515.366	1.159E-03	7.005E-04	39.58	6.33
$4 s 7 p {}^{3}P_{1}$	$4 s 5 d {}^{3}D_{2}$	4518.875	3.489E-03	2.109E-03	39.57	19.05
$4 s 7 p {}^{3}P_{1}$	$4 s 5 d {}^{1}D_{2}$	4905.303	9.373E-08	7.250E-08	22.64	0.00
$4 s 7 p {}^{3}P_{1}$	$3 d^{2} {}^{3}F_{2}$	6743.861	1.526E-11	2.413E-13	98.42	0.00
$4 s 7 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	406.136	3.506E-04	8.310E-04	-137.01	1.91
$4 s 7 p {}^{3}P_{1}$	$4 s 7 s {}^{3}S_{1}$	10236.567	2.815E-03	4.179E-03	-48.48	15.37
$4 s 7 p {}^{3}P_{1}$	$4 s 7 s {}^{1}S_{0}$	14681.701	6.269E-08	8.214E-08	-31.03	0.00
$4 s 7 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	406.365	1.029E-03	2.465E-03	-139.62	5.62
$4 s 7 p {}^{3}P_{1}$	$3 d 4 s {}^{1}D_{2}$	432.750	4.981E-06	5.234E-06	-5.06	0.03
$4 s 7 p {}^{3}P_{2}$	$4 s 5 s {}^{3}S_{1}$	745.031	2.047E-03	2.203E-03	-7.63	11.03
$4 s 7 p {}^{3}P_{2}$	$4 s 4 d {}^{1}D_{2}$	1304.892	8.304E-08	9.558E-08	-15.10	0.00
$4 s 7 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{1}$	1386.278	5.391E-05	5.267E-05	2.30	0.29
$4 s 7 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{2}$	1386.984	8.143E-04	7.958E-04	2.27	4.39
$4 s 7 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{3}$	1388.058	4.603E-03	4.500E-03	2.24	24.81
$4 s 7 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{1}$	1539.184	4.980E-07	5.495E-07	-10.35	0.00
$4 s 7 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{2}$	1560.014	1.123E-08	4.110E-10	96.34	0.00
$4 s 7 p {}^{3}P_{2}$	$4 s 6 s {}^{3}S_{1}$	2228.402	2.145E-03	1.752E-03	18.29	11.56
$4 s 7 p {}^{3}P_{2}$	$4 p^{2} {}^{1}D_{2}$	2357.429	6.802E-09	7.577E-09	-11.39	0.00
$4 s 7 p {}^{3}P_{2}$	$4 s 5 d {}^{3}D_{1}$	4507.022	4.580E-05	2.759E-05	39.75	0.25
$4 s 7 p {}^{3}P_{2}$	$4 s 5 d {}^{3}D_{2}$	4510.519	6.890E-04	4.152E-04	39.74	3.71
$4 s 7 p {}^{3}P_{2}$	$4 s 5 d {}^{3}D_{3}$	4515.957	3.876E-03	2.337E-03	39.71	20.89
$4 s 7 p {}^{3}P_{2}$	$4 s 5 d {}^{1}D_{2}$	4895.458	1.470E-07	8.716E-08	40.69	0.00
$4 s 7 p {}^{3}P_{2}$	$3 d^{2} {}^{3}F_{2}$	6725.266	1.161E-13	2.007E-12	-1627.75	0.00
$4 s 7 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	406.068	1.509E-05	3.487E-05	-131.15	0.08
$4 s 7 p {}^{3}P_{2}$	$3 d^{2} {}^{3}F_{3}$	6790.526	3.141E-15	1.968E-11		0.00
$4 s 7 p {}^{3}P_{2}$	$4 s 7 s {}^{3}S_{1}$	10193.784	2.836E-03	4.219E-03	-48.74	15.29
$4 s 7 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	406.298	2.219E-04	5.176E-04	-133.28	1.20
$4 s 7 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	406.657	1.204E-03	2.852E-03	-136.81	6.49
$4 s 7 p {}^{3}P_{2}$	$3 d 4 s {}^{1}D_{2}$	432.673	7.948E-08	2.350E-07	-195.65	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 5 s {}^{3}S_{1}$	720.157	1.497E-06	1.062E-06	29.07	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	220.141	2.246E-01	2.898E-01	-29.01	55.13
$4 s 7 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	825.893	1.135E-02	1.209E-02	-6.49	2.79
$4 s 7 p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1230.456	4.083E-03	5.034E-03	-23.28	1.00
$4 s 7 p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{1}$	1302.565	1.678E-09	1.352E-08	-705.49	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 4 d {}^{3}D_{2}$	1303.188	2.058E-07	2.067E-07	-0.45	0.00
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{0}$	1426.977	5.766E-07	4.382E-07	24.01	0.00
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{1}$	1436.668	3.708E-08	1.279E-07	-245.02	0.00
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{3}P_{2}$	1454.799	2.469E-07	1.081E-06	-337.68	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 6 s {}^{3}S_{1}$	2019.745	7.975E-07	6.883E-07	13.69	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	2111.968	4.763E-03	4.261E-03	10.53	1.17
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	2125.168	1.349E-03	1.870E-03	-38.60	0.33
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{1}S_{0}$	2747.947	7.203E-07	5.423E-05	-7429.71	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 5 d {}^{3}D_{1}$	3728.060	5.631E-09	4.271E-10	92.42	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 5 d {}^{3}D_{2}$	3730.452	1.906E-10	3.758E-09	-1872.01	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 5 d {}^{1}D_{2}$	3989.929	7.689E-04	1.177E-04	84.70	0.19
$4 s 7 p {}^{1}P_{1}$	$3 d^{2} {}^{3}F_{2}$	5126.812	3.402E-07	1.639E-07	51.81	0.00
$4 s 7 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{1}$	398.565	1.918E-09	3.078E-08	-1504.30	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 7 s {}^{3}S_{1}$	6922.379	2.786E-07	5.027E-07	-80.46	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 7 s {}^{1}S_{0}$	8704.584	2.597E-03	4.065E-03	-56.57	0.64
$4 s 7 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	398.786	1.169E-05	1.428E-05	-22.12	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 6 d {}^{1}D_{2}$	22960.531	4.250E-04	1.325E-04	68.83	0.10
$4 s 7 p {}^{1}P_{1}$	$4 s 6 d {}^{3}D_{1}$	26575.248	6.286E-09	3.545E-09	43.61	0.00
$4 s 7 p {}^{1}P_{1}$	$4 s 6 d {}^{3}D_{2}$	26670.934	6.608E-07	1.930E-07	70.80	0.00
$4 s 7 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	424.165	1.575E-01	1.942E-01	-23.35	38.64

Table 4. Table 4: Spontaneous emission rates of transitions originating from the 4 s n d 4 𝑠 𝑛 𝑑 4snd ( n 𝑛 n =3-6) states of Ca I.

Transition		$λ$ (nm)	$A_{i f}$ ( $10^{8}$ s^-1)		Diff. (%)	BR.(%)
Initial	Final		$L$	$V$
$3 d 4 s {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	1931.449	4.891E-03	4.940E-03	-0.99	56.36
$3 d 4 s {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	1951.105	3.564E-03	3.604E-03	-1.11	41.06
$3 d 4 s {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	1992.262	2.239E-04	2.271E-04	-1.46	2.58
$3 d 4 s {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	1945.828	6.467E-03	6.537E-03	-1.07	76.09
$3 d 4 s {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	1986.760	2.032E-03	2.060E-03	-1.37	23.91
$3 d 4 s {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	1978.216	8.240E-03	8.340E-03	-1.22	100.00
$3 d 4 s {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	1506.122	4.059E-06	3.854E-06	5.05	83.12
$3 d 4 s {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	1530.529	8.245E-07	4.298E-07	47.87	16.88
$4 s 4 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{2}$	6378.202	1.341E-05	4.334E-06	67.69	0.01
$4 s 4 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{3}$	6758.675	2.997E-12	9.405E-10		0.00
$4 s 4 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	6835.831	2.778E-05	7.399E-06	73.37	0.02
$4 s 4 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{1}$	13449.176	3.410E-06	3.878E-06	-13.75	0.00
$4 s 4 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{2}$	13828.007	3.794E-08	1.751E-08	53.85	0.00
$4 s 4 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	17646.955	1.270E-04	1.479E-04	-16.46	0.08
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	452.730	4.043E-06	2.354E-06	41.76	0.00
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	454.910	2.657E-04	2.853E-04	-7.37	0.17
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	732.816	1.601E-01	1.521E-01	5.04	99.73
$4 s 4 d {}^{3}D_{1}$	$3 d 4 p {}^{3}F_{2}$	4956.015	8.657E-05	3.087E-04	-256.62	0.01
$4 s 4 d {}^{3}D_{1}$	$3 d 4 p {}^{1}D_{2}$	5227.965	2.133E-05	9.554E-05	-347.94	0.00
$4 s 4 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{0}$	8329.793	8.753E-04	8.950E-04	-2.25	0.11
$4 s 4 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{1}$	8379.069	6.389E-04	6.531E-04	-2.23	0.08
$4 s 4 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{2}$	8524.568	4.144E-05	4.311E-05	-4.02	0.01
$4 s 4 d {}^{3}D_{1}$	$4 s 5 p {}^{1}P_{1}$	9836.904	4.067E-06	4.195E-06	-3.15	0.00
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	442.668	4.415E-01	4.444E-01	-0.66	56.18
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	443.692	3.223E-01	3.239E-01	-0.50	41.01
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	445.787	2.034E-02	2.038E-02	-0.19	2.59
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{1}P_{1}$	709.426	1.472E-05	1.545E-05	-4.93	0.00
$4 s 4 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{2}$	4947.017	4.947E-06	2.471E-05	-399.44	0.00
$4 s 4 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{3}$	5172.878	9.036E-05	3.505E-04	-287.87	0.01
$4 s 4 d {}^{3}D_{2}$	$3 d 4 p {}^{1}D_{2}$	5217.954	1.436E-05	3.049E-05	-112.32	0.00
$4 s 4 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{1}$	8353.381	1.159E-03	1.185E-03	-2.32	0.15
$4 s 4 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{2}$	8497.982	3.700E-04	3.778E-04	-2.11	0.05
$4 s 4 d {}^{3}D_{2}$	$4 s 5 p {}^{1}P_{1}$	9801.519	8.902E-06	9.008E-06	-1.20	0.00
$4 s 4 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	443.620	5.939E-01	5.979E-01	-0.66	75.78
$4 s 4 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	445.714	1.882E-01	1.889E-01	-0.38	24.01
$4 s 4 d {}^{3}D_{2}$	$4 s 4 p {}^{1}P_{1}$	709.241	5.037E-05	4.876E-05	3.20	0.01
$4 s 4 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{2}$	4933.399	4.148E-06	6.231E-06	-50.22	0.00
$4 s 4 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{3}$	5157.989	8.396E-06	3.183E-05	-279.06	0.00
$4 s 4 d {}^{3}D_{3}$	$3 d 4 p {}^{1}D_{2}$	5202.805	1.347E-05	1.265E-05	6.12	0.00
$4 s 4 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{4}$	5374.726	8.476E-05	3.470E-04	-309.41	0.01
$4 s 4 d {}^{3}D_{3}$	$4 s 5 p {}^{3}P_{2}$	8457.876	1.506E-03	1.542E-03	-2.44	0.19
$4 s 4 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	445.603	7.793E-01	7.841E-01	-0.62	99.79
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}F_{2}$	1426.015	5.674E-04	9.580E-04	-68.85	0.14
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{1}D_{2}$	1447.683	2.901E-04	4.608E-04	-58.87	0.07
$4 s 5 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{0}$	1614.124	2.721E-02	2.712E-02	0.35	6.71
$4 s 5 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{1}$	1615.966	2.024E-02	2.017E-02	0.34	4.99
$4 s 5 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{2}$	1621.303	1.351E-03	1.341E-03	0.71	0.33
$4 s 5 d {}^{3}D_{1}$	$4 s 5 p {}^{1}P_{1}$	1663.512	2.278E-04	2.272E-04	0.29	0.06
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	362.515	1.927E-01	1.949E-01	-1.17	47.50
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}D_{1}$	2197.508	3.832E-04	3.482E-04	9.15	0.09
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}D_{2}$	2210.492	1.230E-04	1.118E-04	9.10	0.03
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{0}$	2932.878	3.953E-03	4.409E-03	-11.52	0.97
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	363.201	1.452E-01	1.469E-01	-1.17	35.80
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{1}$	2934.548	2.947E-03	3.285E-03	-11.49	0.73
$4 s 5 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{2}$	2938.653	1.943E-04	2.166E-04	-11.48	0.05
$4 s 5 d {}^{3}D_{1}$	$4 s 6 p {}^{1}P_{1}$	9398.585	7.140E-09	1.133E-08	-58.67	0.00
$4 s 5 d {}^{3}D_{1}$	$4 s 4 f {}^{3}F_{2}$	17458.405	4.014E-04	3.943E-04	1.77	0.10
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	364.603	9.773E-03	9.890E-03	-1.20	2.41
$4 s 5 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{0}$	43830.813	2.419E-05	3.547E-05	-46.67	0.01
$4 s 5 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{1}$	44585.135	1.724E-05	2.545E-05	-47.63	0.00
$4 s 5 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{2}$	46208.586	1.033E-06	1.547E-06	-49.79	0.00
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{1}P_{1}$	523.815	4.670E-06	5.065E-06	-8.45	0.00
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{2}$	1425.665	1.123E-04	1.667E-04	-48.50	0.03
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{3}$	1443.833	7.112E-04	1.197E-03	-68.34	0.18
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{1}D_{2}$	1447.323	1.035E-06	3.266E-07	68.44	0.00
$4 s 5 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{1}$	1615.517	3.645E-02	3.632E-02	0.36	9.01
$4 s 5 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{2}$	1620.851	1.231E-02	1.227E-02	0.27	3.04
$4 s 5 d {}^{3}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1663.036	2.945E-04	2.945E-04	0.02	0.07
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{1}$	2196.677	4.749E-05	4.072E-05	14.27	0.01
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{2}$	2209.652	3.503E-04	3.173E-04	9.44	0.09
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{3}$	2229.356	7.036E-05	6.352E-05	9.73	0.02
$4 s 5 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	363.179	2.593E-01	2.624E-01	-1.18	64.09
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}P_{1}$	2933.067	5.367E-03	5.986E-03	-11.54	1.33
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{3}P_{2}$	2937.168	1.768E-03	1.971E-03	-11.51	0.44
$4 s 5 d {}^{3}D_{2}$	$3 d 4 p {}^{1}F_{3}$	4531.387	1.324E-07	1.016E-07	23.28	0.00
$4 s 5 d {}^{3}D_{2}$	$4 s 6 p {}^{1}P_{1}$	9383.416	3.239E-07	3.478E-07	-7.38	0.00
$4 s 5 d {}^{3}D_{2}$	$4 s 4 f {}^{3}F_{2}$	17406.137	4.516E-05	4.435E-05	1.79	0.01
$4 s 5 d {}^{3}D_{2}$	$4 s 4 f {}^{3}F_{3}$	17416.748	3.588E-04	3.525E-04	1.76	0.09
$4 s 5 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	364.581	8.734E-02	8.839E-02	-1.20	21.59
$4 s 5 d {}^{3}D_{2}$	$4 s 4 f {}^{1}F_{3}$	24929.574	1.528E-08	1.641E-08	-7.36	0.00
$4 s 5 d {}^{3}D_{2}$	$4 s 6 p {}^{3}P_{1}$	44245.830	3.176E-05	4.678E-05	-47.29	0.01
$4 s 5 d {}^{3}D_{2}$	$4 s 6 p {}^{3}P_{2}$	45844.221	9.520E-06	1.422E-05	-49.42	0.00
$4 s 5 d {}^{3}D_{2}$	$4 s 4 p {}^{1}P_{1}$	523.768	2.267E-05	2.414E-05	-6.45	0.01
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{2}$	1425.123	1.057E-05	8.168E-06	22.72	0.00
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{3}$	1443.276	6.712E-05	1.117E-04	-66.44	0.02
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{1}D_{2}$	1446.763	1.651E-04	1.682E-04	-1.83	0.04
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{4}$	1459.747	7.044E-04	1.199E-03	-70.24	0.17
$4 s 5 d {}^{3}D_{3}$	$4 s 5 p {}^{3}P_{2}$	1620.149	4.895E-02	4.878E-02	0.36	12.15
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}D_{2}$	2208.349	2.401E-05	1.934E-05	19.47	0.01
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}D_{3}$	2228.030	3.871E-04	3.443E-04	11.04	0.10
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{3}P_{2}$	2934.867	7.191E-03	8.024E-03	-11.59	1.78
$4 s 5 d {}^{3}D_{3}$	$3 d 4 p {}^{1}F_{3}$	4525.911	1.350E-08	1.565E-08	-15.96	0.00
$4 s 5 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{2}$	17325.618	9.287E-07	9.121E-07	1.79	0.00
$4 s 5 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{3}$	17336.130	3.247E-05	3.190E-05	1.77	0.01
$4 s 5 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	364.545	3.451E-01	3.494E-01	-1.23	85.62
$4 s 5 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{4}$	17350.267	3.751E-04	3.686E-04	1.74	0.09
$4 s 5 d {}^{3}D_{3}$	$4 s 4 f {}^{1}F_{3}$	24764.735	1.063E-11	4.116E-14	99.61	0.00
$4 s 5 d {}^{3}D_{3}$	$4 s 6 p {}^{3}P_{2}$	45289.855	3.953E-05	5.883E-05	-48.82	0.01
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{2}$	1391.091	3.178E-04	5.393E-04	-69.70	0.06
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{3}$	1408.383	1.842E-07	9.196E-08	50.07	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	1411.704	6.727E-04	1.171E-03	-74.00	0.13
$4 s 5 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{1}$	1571.265	2.494E-04	2.510E-04	-0.64	0.05
$4 s 5 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{2}$	1576.310	1.835E-07	7.977E-07	-334.59	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1616.180	3.302E-02	3.328E-02	-0.79	6.46
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{1}$	2115.659	6.374E-06	6.799E-06	-6.66	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{2}$	2127.691	2.942E-07	2.245E-07	23.69	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{3}$	2145.955	1.764E-08	5.117E-08	-190.06	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	360.894	4.989E-06	5.512E-06	-10.48	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{1}$	2790.389	2.158E-06	2.145E-06	0.61	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{2}$	2794.100	5.239E-07	7.264E-07	-38.65	0.00
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	4199.634	1.274E-03	9.537E-04	25.14	0.25
$4 s 5 d {}^{1}D_{2}$	$4 s 6 p {}^{1}P_{1}$	8064.256	4.324E-03	4.715E-03	-9.06	0.85
$4 s 5 d {}^{1}D_{2}$	$4 s 4 f {}^{3}F_{2}$	13353.988	1.317E-08	1.371E-08	-4.12	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 4 f {}^{3}F_{3}$	13360.232	7.626E-08	7.525E-08	1.33	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	362.278	9.190E-06	1.055E-05	-14.76	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 4 f {}^{1}F_{3}$	17377.402	3.433E-04	3.685E-04	-7.32	0.07
$4 s 5 d {}^{1}D_{2}$	$4 s 6 p {}^{3}P_{1}$	24978.768	2.028E-08	2.336E-08	-15.19	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 6 p {}^{3}P_{2}$	25480.304	8.673E-09	9.809E-09	-13.10	0.00
$4 s 5 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	519.029	4.710E-01	4.953E-01	-5.16	92.13
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{2}$	1079.986	6.757E-06	8.174E-05	-1109.68	0.00
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{3}$	1090.379	1.109E-05	1.180E-05	-6.38	0.01
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	1092.368	5.667E-05	3.284E-04	-479.57	0.03
$4 s 6 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{1}$	1185.525	9.629E-04	9.650E-04	-0.22	0.47
$4 s 6 d {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{2}$	1188.395	2.516E-05	3.142E-05	-24.89	0.01
$4 s 6 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1210.916	5.046E-02	5.069E-02	-0.45	24.53
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{1}$	1471.142	2.112E-06	2.190E-06	-3.69	0.00
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{2}$	1476.950	6.605E-06	6.655E-06	-0.75	0.00
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{3}$	1485.727	6.257E-06	7.255E-06	-15.94	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	335.798	4.997E-04	5.146E-04	-2.98	0.24
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{1}$	1768.500	6.652E-08	9.571E-08	-43.88	0.00
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{2}$	1769.990	3.555E-08	2.483E-08	30.16	0.00
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	2246.212	1.202E-03	1.889E-03	-57.15	0.58
$4 s 6 d {}^{1}D_{2}$	$4 s 6 p {}^{1}P_{1}$	3020.400	7.402E-03	9.236E-03	-24.76	3.60
$4 s 6 d {}^{1}D_{2}$	$4 s 4 f {}^{3}F_{2}$	3546.577	2.016E-09	1.129E-11	99.44	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 4 f {}^{3}F_{3}$	3547.017	2.270E-08	1.627E-09	92.83	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	336.997	1.545E-04	1.594E-04	-3.17	0.08
$4 s 6 d {}^{1}D_{2}$	$4 s 4 f {}^{1}F_{3}$	3778.947	3.857E-06	2.326E-05	-502.93	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 6 p {}^{3}P_{1}$	4046.748	1.297E-05	1.768E-05	-36.33	0.01
$4 s 6 d {}^{1}D_{2}$	$4 s 6 p {}^{3}P_{2}$	4059.694	4.392E-06	5.752E-06	-30.98	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s n p {}^{1}P_{1}$	9466.559	2.409E-03	4.866E-03	-102.02	1.17
$4 s 6 d {}^{1}D_{2}$	$4 s 5 f {}^{3}F_{2}$	44012.147	1.136E-08	5.438E-09	52.12	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 5 f {}^{3}F_{3}$	44054.804	9.300E-08	4.405E-08	52.63	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 5 f {}^{1}F_{3}$	54068.667	3.250E-05	1.512E-05	53.47	0.02
$4 s 6 d {}^{1}D_{2}$	$4 s 7 p {}^{3}P_{1}$	310848.617	2.924E-10	1.492E-11	94.90	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 7 p {}^{3}P_{2}$	356252.227	4.427E-11	1.051E-12	97.63	0.00
$4 s 6 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	468.658	1.425E-01	1.510E-01	-6.00	69.25
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}F_{2}$	1073.120	3.603E-03	4.349E-03	-20.72	0.95
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{1}D_{2}$	1085.345	1.577E-03	1.884E-03	-19.46	0.42
$4 s 6 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{0}$	1176.280	2.879E-02	2.872E-02	0.24	7.62
$4 s 6 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{1}$	1177.257	2.135E-02	2.131E-02	0.22	5.65
$4 s 6 d {}^{3}D_{1}$	$4 s 5 p {}^{3}P_{2}$	1180.087	1.379E-03	1.372E-03	0.53	0.36
$4 s 6 d {}^{3}D_{1}$	$4 s 5 p {}^{1}P_{1}$	1202.292	2.353E-04	2.346E-04	0.26	0.06
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	334.547	1.707E-01	1.759E-01	-3.04	45.16
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}D_{1}$	1458.432	2.695E-03	2.616E-03	2.94	0.71
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}D_{2}$	1464.140	9.003E-04	8.734E-04	2.99	0.24
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{0}$	1749.570	7.835E-05	1.128E-04	-44.03	0.02
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	335.132	1.280E-01	1.319E-01	-3.03	33.86
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{1}$	1750.164	4.797E-05	7.106E-05	-48.13	0.01
$4 s 6 d {}^{3}D_{1}$	$3 d 4 p {}^{3}P_{2}$	1751.623	1.974E-06	3.170E-06	-60.57	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 6 p {}^{1}P_{1}$	2967.306	3.408E-09	2.205E-10	93.53	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 4 f {}^{3}F_{2}$	3473.597	4.555E-07	5.349E-06	-1074.42	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	336.325	8.498E-03	8.754E-03	-3.01	2.25
$4 s 6 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{0}$	3945.987	5.568E-03	7.494E-03	-34.58	1.47
$4 s 6 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{1}$	3952.007	4.186E-03	5.630E-03	-34.50	1.11
$4 s 6 d {}^{3}D_{1}$	$4 s 6 p {}^{3}P_{2}$	3964.353	2.794E-04	3.753E-04	-34.34	0.07
$4 s 6 d {}^{3}D_{1}$	$4 s n p {}^{1}P_{1}$	8963.867	3.648E-08	6.193E-08	-69.79	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 5 f {}^{3}F_{2}$	34910.106	1.213E-04	6.145E-05	49.33	0.03
$4 s 6 d {}^{3}D_{1}$	$4 s 7 p {}^{3}P_{0}$	107066.381	2.278E-06	4.384E-07	80.75	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 7 p {}^{3}P_{1}$	109397.221	1.601E-06	2.851E-07	82.18	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 7 p {}^{3}P_{2}$	114534.418	9.254E-08	1.398E-08	84.89	0.00
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{1}P_{1}$	467.360	3.252E-06	3.641E-06	-11.96	0.00
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{2}$	1072.965	5.600E-04	6.729E-04	-20.16	0.15
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}F_{3}$	1083.223	4.395E-03	5.317E-03	-20.97	1.17
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{1}D_{2}$	1085.186	2.603E-05	3.473E-05	-33.42	0.01
$4 s 6 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{1}$	1177.070	3.799E-02	3.790E-02	0.26	10.08
$4 s 6 d {}^{3}D_{2}$	$4 s 5 p {}^{3}P_{2}$	1179.899	1.291E-02	1.289E-02	0.21	3.43
$4 s 6 d {}^{3}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1202.096	8.279E-04	8.295E-04	-0.19	0.22
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{1}$	1458.145	4.962E-04	4.780E-04	3.67	0.13
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{2}$	1463.850	2.428E-03	2.353E-03	3.08	0.64
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}D_{3}$	1472.472	5.408E-04	5.232E-04	3.26	0.14
$4 s 6 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	335.117	2.294E-01	2.365E-01	-3.06	60.89
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}P_{1}$	1749.751	1.170E-04	1.661E-04	-41.91	0.03
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{3}P_{2}$	1751.209	2.603E-05	3.915E-05	-50.36	0.01
$4 s 6 d {}^{3}D_{2}$	$3 d 4 p {}^{1}F_{3}$	2216.052	1.595E-06	2.762E-06	-73.16	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 6 p {}^{1}P_{1}$	2966.118	1.247E-05	1.536E-05	-23.22	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 4 f {}^{3}F_{2}$	3471.969	3.633E-08	6.501E-07	-1689.24	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 4 f {}^{3}F_{3}$	3472.391	2.941E-07	5.183E-06	-1662.09	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	336.310	7.651E-02	7.884E-02	-3.04	20.31
$4 s 6 d {}^{3}D_{2}$	$4 s 4 f {}^{1}F_{3}$	3694.358	1.691E-11	8.874E-08		0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 6 p {}^{3}P_{1}$	3949.899	7.509E-03	1.011E-02	-34.60	1.99
$4 s 6 d {}^{3}D_{2}$	$4 s 6 p {}^{3}P_{2}$	3962.232	2.517E-03	3.383E-03	-34.43	0.67
$4 s 6 d {}^{3}D_{2}$	$4 s n p {}^{1}P_{1}$	8953.032	5.585E-06	1.077E-05	-92.89	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 5 f {}^{3}F_{2}$	34746.352	1.366E-05	6.933E-06	49.23	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 5 f {}^{3}F_{3}$	34772.933	1.088E-04	5.521E-05	49.23	0.03
$4 s 6 d {}^{3}D_{2}$	$4 s 5 f {}^{1}F_{3}$	40726.562	1.239E-07	6.247E-08	49.57	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 7 p {}^{3}P_{1}$	107805.088	3.007E-06	5.644E-07	81.23	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 7 p {}^{3}P_{2}$	112790.435	8.756E-07	1.398E-07	84.03	0.00
$4 s 6 d {}^{3}D_{2}$	$4 s 4 p {}^{1}P_{1}$	467.331	3.448E-04	3.640E-04	-5.57	0.09
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{2}$	1072.740	3.034E-06	1.988E-06	34.49	0.00
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{3}$	1082.994	4.090E-04	4.943E-04	-20.86	0.11
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{1}D_{2}$	1084.956	2.059E-04	2.089E-04	-1.46	0.05
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}F_{4}$	1092.242	4.385E-03	5.331E-03	-21.58	1.17
$4 s 6 d {}^{3}D_{3}$	$4 s 5 p {}^{3}P_{2}$	1179.628	5.147E-02	5.134E-02	0.25	13.70
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}D_{2}$	1463.432	3.365E-04	3.216E-04	4.42	0.09
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}D_{3}$	1472.049	2.951E-03	2.848E-03	3.46	0.79
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{3}P_{2}$	1750.611	1.644E-04	2.315E-04	-40.83	0.04
$4 s 6 d {}^{3}D_{3}$	$3 d 4 p {}^{1}F_{3}$	2215.095	1.731E-07	1.819E-07	-5.07	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{2}$	3469.620	4.376E-10	1.488E-08	-3300.03	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{3}$	3470.041	1.504E-08	5.199E-07	-3357.32	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	336.288	3.055E-01	3.149E-01	-3.10	81.33
$4 s 6 d {}^{3}D_{3}$	$4 s 4 f {}^{3}F_{4}$	3470.607	1.790E-07	6.017E-06	-3261.02	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 4 f {}^{1}F_{3}$	3691.699	5.711E-09	6.355E-09	-11.27	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 6 p {}^{3}P_{2}$	3959.173	1.005E-02	1.353E-02	-34.57	2.68
$4 s 6 d {}^{3}D_{3}$	$4 s 5 f {}^{3}F_{2}$	34512.511	2.834E-07	1.443E-07	49.09	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 5 f {}^{3}F_{3}$	34538.735	9.918E-06	5.048E-06	49.10	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 5 f {}^{3}F_{4}$	34572.169	1.145E-04	5.826E-05	49.11	0.03
$4 s 6 d {}^{3}D_{3}$	$4 s 5 f {}^{1}F_{3}$	40405.673	1.512E-12	1.608E-13	89.36	0.00
$4 s 6 d {}^{3}D_{3}$	$4 s 7 p {}^{3}P_{2}$	110363.095	3.748E-06	6.449E-07	82.79	0.00

Table 5. Table 5: Spontaneous emission rates of transitions originating from the 4 s n f 4 𝑠 𝑛 𝑓 4snf ( n 𝑛 n =4-6) states of Ca I.

Transition		$λ$ (nm)	$A_{i f}$ ( $10^{8}$ s^-1)		Diff. (%)	BR.(%)
Initial	Final		$L$	$V$
$4 s 4 f {}^{3}F_{2}$	$4 s 5 s {}^{3}S_{1}$	940.671	2.802E-13	1.357E-13	51.58	0.00
$4 s 4 f {}^{3}F_{2}$	$4 s 4 d {}^{1}D_{2}$	2052.579	1.385E-06	1.352E-06	2.37	0.00
$4 s 4 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{1}$	2261.415	8.393E-02	8.413E-02	-0.23	32.22
$4 s 4 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{2}$	2263.293	1.559E-02	1.562E-02	-0.21	5.98
$4 s 4 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{3}$	2266.155	4.422E-04	4.429E-04	-0.18	0.17
$4 s 4 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{1}$	2698.764	2.194E-06	2.208E-06	-0.60	0.00
$4 s 4 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{2}$	2763.462	6.099E-07	6.172E-07	-1.21	0.00
$4 s 4 f {}^{3}F_{2}$	$4 s 6 s {}^{3}S_{1}$	5896.331	2.241E-13	2.165E-13	3.39	0.00
$4 s 4 f {}^{3}F_{2}$	$4 p^{2} {}^{1}D_{2}$	6894.840	3.576E-09	4.377E-09	-22.40	0.00
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	457.983	1.348E-01	1.346E-01	0.12	51.72
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	458.275	2.508E-02	2.506E-02	0.11	9.63
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	458.732	7.142E-04	7.134E-04	0.11	0.27
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{1}D_{2}$	492.112	9.191E-06	9.248E-06	-0.62	0.00
$4 s 4 f {}^{3}F_{3}$	$4 s 4 d {}^{1}D_{2}$	2052.431	1.173E-05	1.187E-05	-1.17	0.00
$4 s 4 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{2}$	2263.114	8.863E-02	8.885E-02	-0.24	34.02
$4 s 4 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{3}$	2265.976	1.106E-02	1.108E-02	-0.22	4.24
$4 s 4 f {}^{3}F_{3}$	$4 p^{2} {}^{3}P_{2}$	2763.194	3.435E-06	3.449E-06	-0.39	0.00
$4 s 4 f {}^{3}F_{3}$	$4 p^{2} {}^{1}D_{2}$	6893.176	4.241E-09	3.877E-09	8.59	0.00
$4 s 4 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	458.268	1.429E-01	1.427E-01	0.12	54.84
$4 s 4 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	458.725	1.791E-02	1.789E-02	0.11	6.87
$4 s 4 f {}^{3}F_{3}$	$3 d 4 s {}^{1}D_{2}$	492.103	3.396E-05	3.360E-05	1.07	0.01
$4 s 4 f {}^{3}F_{4}$	$4 s 4 d {}^{3}D_{3}$	2265.734	9.963E-02	9.990E-02	-0.26	38.13
$4 s 4 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	458.715	1.617E-01	1.615E-01	0.13	61.87
$4 s 4 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1982.043	6.368E-02	6.694E-02	-5.12	16.83
$4 s 4 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{2}$	2177.833	4.902E-06	5.192E-06	-5.92	0.00
$4 s 4 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{3}$	2180.483	6.505E-08	5.181E-08	20.35	0.00
$4 s 4 f {}^{1}F_{3}$	$4 p^{2} {}^{3}P_{2}$	2637.110	2.345E-05	2.319E-05	1.10	0.01
$4 s 4 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	6158.621	2.920E-03	2.690E-03	7.88	0.77
$4 s 4 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{2}$	454.663	5.336E-05	4.883E-05	8.49	0.01
$4 s 4 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{3}$	455.112	1.616E-05	1.754E-05	-8.50	0.00
$4 s 4 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	487.949	3.116E-01	2.919E-01	6.32	82.37
$4 s 5 f {}^{3}F_{2}$	$4 s 5 s {}^{3}S_{1}$	756.251	4.042E-13	2.396E-13	40.73	0.00
$4 s 5 f {}^{3}F_{2}$	$4 s 4 d {}^{1}D_{2}$	1339.705	2.099E-07	1.973E-07	6.00	0.00
$4 s 5 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{1}$	1425.635	1.131E-02	1.132E-02	-0.08	6.65
$4 s 5 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{2}$	1426.381	2.086E-03	2.087E-03	-0.03	1.23
$4 s 5 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{3}$	1427.517	5.888E-05	5.885E-05	0.06	0.03
$4 s 5 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{1}$	1587.854	4.242E-08	4.323E-08	-1.91	0.00
$4 s 5 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{2}$	1610.031	7.211E-09	7.895E-09	-9.48	0.00
$4 s 5 f {}^{3}F_{2}$	$4 s 6 s {}^{3}S_{1}$	2331.883	1.295E-12	1.288E-12	0.51	0.00
$4 s 5 f {}^{3}F_{2}$	$4 p^{2} {}^{1}D_{2}$	2473.552	1.699E-08	1.574E-08	7.38	0.00
$4 s 5 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{1}$	4951.427	2.095E-02	2.217E-02	-5.80	12.31
$4 s 5 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{2}$	4955.647	3.886E-03	4.110E-03	-5.78	2.28
$4 s 5 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{3}$	4962.213	1.106E-04	1.170E-04	-5.78	0.06
$4 s 5 f {}^{3}F_{2}$	$4 s 5 d {}^{1}D_{2}$	5424.258	5.316E-07	5.810E-07	-9.30	0.00
$4 s 5 f {}^{3}F_{2}$	$3 d^{2} {}^{3}F_{2}$	7765.241	3.178E-08	5.672E-07	-1684.76	0.00
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	409.379	1.106E-01	1.122E-01	-1.51	64.99
$4 s 5 f {}^{3}F_{2}$	$3 d^{2} {}^{3}F_{3}$	7852.375	4.424E-09	7.138E-08	-1513.46	0.00
$4 s 5 f {}^{3}F_{2}$	$4 s 7 s {}^{3}S_{1}$	12790.177	2.412E-14	3.985E-14	-65.24	0.00
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	409.612	2.057E-02	2.088E-02	-1.51	12.09
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	409.977	5.884E-04	5.973E-04	-1.50	0.35
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{1}D_{2}$	436.434	6.474E-06	6.582E-06	-1.66	0.00
$4 s 5 f {}^{3}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1339.665	1.773E-06	1.806E-06	-1.85	0.00
$4 s 5 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{2}$	1426.336	1.192E-02	1.193E-02	-0.12	7.00
$4 s 5 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{3}$	1427.472	1.475E-03	1.476E-03	-0.03	0.87
$4 s 5 f {}^{3}F_{3}$	$4 p^{2} {}^{3}P_{2}$	1609.974	4.163E-08	4.164E-08	-0.03	0.00
$4 s 5 f {}^{3}F_{3}$	$4 p^{2} {}^{1}D_{2}$	2473.417	5.270E-08	5.376E-08	-2.01	0.00
$4 s 5 f {}^{3}F_{3}$	$4 s 5 d {}^{3}D_{2}$	4955.107	2.214E-02	2.342E-02	-5.80	13.01
$4 s 5 f {}^{3}F_{3}$	$4 s 5 d {}^{3}D_{3}$	4961.671	2.764E-03	2.925E-03	-5.80	1.62
$4 s 5 f {}^{3}F_{3}$	$4 s 5 d {}^{1}D_{2}$	5423.611	2.734E-06	2.905E-06	-6.27	0.00
$4 s 5 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{2}$	7763.915	3.583E-09	4.521E-08	-1161.85	0.00
$4 s 5 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{3}$	7851.019	2.904E-08	5.463E-07	-1781.01	0.00
$4 s 5 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{4}$	7969.715	3.279E-09	5.241E-08	-1498.50	0.00
$4 s 5 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	409.608	1.172E-01	1.189E-01	-1.50	68.84
$4 s 5 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	409.973	1.471E-02	1.493E-02	-1.50	8.64
$4 s 5 f {}^{3}F_{3}$	$3 d 4 s {}^{1}D_{2}$	436.429	3.280E-05	3.278E-05	0.06	0.02
$4 s 5 f {}^{3}F_{4}$	$4 s 4 d {}^{3}D_{3}$	1427.415	1.333E-02	1.335E-02	-0.14	7.82
$4 s 5 f {}^{3}F_{4}$	$4 s 5 d {}^{3}D_{3}$	4960.982	2.489E-02	2.634E-02	-5.82	14.59
$4 s 5 f {}^{3}F_{4}$	$3 d^{2} {}^{3}F_{3}$	7849.294	3.028E-09	3.428E-08	-1031.94	0.00
$4 s 5 f {}^{3}F_{4}$	$3 d^{2} {}^{3}F_{4}$	7967.937	3.248E-08	6.179E-07	-1802.55	0.00
$4 s 5 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	409.968	1.323E-01	1.343E-01	-1.51	77.59
$4 s 5 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1332.163	1.783E-02	1.829E-02	-2.58	7.72
$4 s 5 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{2}$	1417.834	7.599E-07	7.848E-07	-3.28	0.00
$4 s 5 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{3}$	1418.957	2.190E-10	9.774E-11	55.36	0.00
$4 s 5 f {}^{1}F_{3}$	$4 p^{2} {}^{3}P_{2}$	1599.151	9.537E-07	9.462E-07	0.78	0.00
$4 s 5 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	2447.962	5.935E-03	6.158E-03	-3.76	2.57
$4 s 5 f {}^{1}F_{3}$	$4 s 5 d {}^{3}D_{2}$	4853.992	2.822E-06	3.029E-06	-7.36	0.00
$4 s 5 f {}^{1}F_{3}$	$4 s 5 d {}^{3}D_{3}$	4860.291	1.191E-09	8.065E-10	32.30	0.00
$4 s 5 f {}^{1}F_{3}$	$4 s 5 d {}^{1}D_{2}$	5302.705	1.878E-02	2.032E-02	-8.20	8.13
$4 s 5 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{2}$	7518.514	4.818E-07	5.906E-07	-22.59	0.00
$4 s 5 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{3}$	7600.170	1.378E-10	1.242E-09	-801.12	0.00
$4 s 5 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{4}$	7711.349	1.617E-10	7.512E-10	-364.55	0.00
$4 s 5 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{2}$	408.904	3.547E-05	3.541E-05	0.17	0.02
$4 s 5 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{3}$	409.268	3.427E-07	3.977E-07	-16.05	0.00
$4 s 5 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	435.630	1.884E-01	1.866E-01	0.95	81.57
$4 s 6 f {}^{3}F_{2}$	$4 s 5 s {}^{3}S_{1}$	23476.383	3.096E-11			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 4 d {}^{1}D_{2}$	683.754	7.751E-09			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{1}$	1127.860	2.663E-03			3.00
$4 s 6 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{2}$	1188.151	4.872E-04			0.55
$4 s 6 f {}^{3}F_{2}$	$4 s 4 d {}^{3}D_{3}$	1188.669	1.364E-05			0.02
$4 s 6 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{1}$	1189.458	1.919E-07			0.00
$4 s 6 f {}^{3}F_{2}$	$4 p^{2} {}^{3}P_{2}$	1298.730	2.903E-08			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 6 s {}^{3}S_{1}$	1313.529	6.059E-13			0.00
$4 s 6 f {}^{3}F_{2}$	$4 p^{2} {}^{1}D_{2}$	1757.346	1.426E-08			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{1}$	1836.618	6.585E-03			7.42
$4 s 6 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{2}$	2922.575	1.215E-03			1.37
$4 s 6 f {}^{3}F_{2}$	$4 s 5 d {}^{3}D_{3}$	2924.045	3.456E-05			0.04
$4 s 6 f {}^{3}F_{2}$	$4 s 5 d {}^{1}D_{2}$	2926.330	4.574E-07			0.00
$4 s 6 f {}^{3}F_{2}$	$3 d^{2} {}^{3}F_{2}$	3081.104	5.369E-07			0.00
$4 s 6 f {}^{3}F_{2}$	$3 d^{2} {}^{3}F_{3}$	3717.735	6.821E-08			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 7 s {}^{3}S_{1}$	387.158	5.704E-14			0.00
$4 s 6 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	3737.591	5.931E-02			66.82
$4 s 6 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	4579.027	1.101E-02			12.40
$4 s 6 f {}^{3}F_{2}$	$4 s 6 d {}^{1}D_{2}$	387.366	1.013E-06			0.00
$4 s 6 f {}^{3}F_{2}$	$4 s 6 d {}^{3}D_{1}$	8512.015	5.860E-03			6.60
$4 s 6 f {}^{3}F_{2}$	$4 s 6 d {}^{3}D_{2}$	8964.027	1.089E-03			1.23
$4 s 6 f {}^{3}F_{2}$	$4 s 6 d {}^{3}D_{3}$	8974.888	1.648E-04			0.19
$4 s 6 f {}^{3}F_{2}$	$4 s 8 s {}^{3}S_{1}$	8990.623	1.511E-12			0.00
$4 s 6 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	387.692	3.166E-04			0.36
$4 s 6 f {}^{3}F_{2}$	$3 d 4 s {}^{1}D_{2}$	411.269	1.067E-05			0.01
$4 s 6 f {}^{3}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1127.841	7.618E-08			0.00
$4 s 6 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{2}$	1188.648	2.806E-03			3.19
$4 s 6 f {}^{3}F_{3}$	$4 s 4 d {}^{3}D_{3}$	1189.437	3.444E-04			0.39
$4 s 6 f {}^{3}F_{3}$	$4 p^{2} {}^{3}P_{2}$	1313.503	1.671E-07			0.00
$4 s 6 f {}^{3}F_{3}$	$4 p^{2} {}^{1}D_{2}$	1836.568	1.285E-07			0.00
$4 s 6 f {}^{3}F_{3}$	$4 s 5 d {}^{3}D_{2}$	2923.917	6.950E-03			7.90
$4 s 6 f {}^{3}F_{3}$	$4 s 5 d {}^{3}D_{3}$	2926.201	8.652E-04			0.98
$4 s 6 f {}^{3}F_{3}$	$4 s 5 d {}^{1}D_{2}$	3080.962	4.168E-06			0.00
$4 s 6 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{2}$	3717.527	1.031E-08			0.00
$4 s 6 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{3}$	3737.382	4.362E-07			0.00
$4 s 6 f {}^{3}F_{3}$	$3 d^{2} {}^{3}F_{4}$	3764.068	4.538E-08			0.00
$4 s 6 f {}^{3}F_{3}$	$4 s 5 g {}^{1}G_{4}$	387.364	5.031E-10			0.00
$4 s 6 f {}^{3}F_{3}$	$4 s 6 d {}^{1}D_{2}$	7758.915	4.900E-06			0.01
$4 s 6 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	8510.928	6.277E-02			71.37
$4 s 6 f {}^{3}F_{3}$	$4 s 6 d {}^{3}D_{2}$	8973.680	6.224E-03			7.08
$4 s 6 f {}^{3}F_{3}$	$4 s 6 d {}^{3}D_{3}$	8989.410	1.029E-05			0.01
$4 s 6 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	387.690	7.898E-03			8.98
$4 s 6 f {}^{3}F_{3}$	$3 d 4 s {}^{1}D_{2}$	411.266	7.556E-05			0.09
$4 s 6 f {}^{3}F_{4}$	$4 s 4 d {}^{3}D_{3}$	1189.411	3.132E-03			3.82
$4 s 6 f {}^{3}F_{4}$	$4 s 5 d {}^{3}D_{3}$	2926.047	7.799E-03			9.50
$4 s 6 f {}^{3}F_{4}$	$3 d^{2} {}^{3}F_{3}$	3737.130	3.533E-08			0.00
$4 s 6 f {}^{3}F_{4}$	$3 d^{2} {}^{3}F_{4}$	3763.813	4.728E-07			0.00
$4 s 6 f {}^{3}F_{4}$	$4 s 5 g {}^{3}G_{5}$	7751.277	2.433E-04			0.30
$4 s 6 f {}^{3}F_{4}$	$4 s 5 g {}^{1}G_{4}$	7757.832	6.584E-12			0.00
$4 s 6 f {}^{3}F_{4}$	$4 s 6 d {}^{3}D_{3}$	8987.956	1.238E-07			0.00
$4 s 6 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	387.688	7.088E-02			86.38
$4 s 6 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1125.605	5.391E-03			5.21
$4 s 6 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{2}$	1186.165	1.504E-11			0.00
$4 s 6 f {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{3}$	1186.951	1.325E-08			0.00
$4 s 6 f {}^{1}F_{3}$	$4 p^{2} {}^{3}P_{2}$	1310.472	3.967E-07			0.00
$4 s 6 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	1830.647	2.969E-03			2.87
$4 s 6 f {}^{1}F_{3}$	$4 s 5 d {}^{3}D_{2}$	2908.939	5.057E-06			0.00
$4 s 6 f {}^{1}F_{3}$	$4 s 5 d {}^{3}D_{3}$	2911.200	7.052E-09			0.00
$4 s 6 f {}^{1}F_{3}$	$4 s 5 d {}^{1}D_{2}$	3064.336	5.037E-03			4.87
$4 s 6 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{2}$	3693.349	2.889E-05			0.03
$4 s 6 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{3}$	3712.945	3.051E-10			0.00
$4 s 6 f {}^{1}F_{3}$	$3 d^{2} {}^{3}F_{4}$	3739.282	1.498E-09			0.00
$4 s 6 f {}^{1}F_{3}$	$4 s 5 g {}^{1}G_{4}$	387.100	7.996E-05			0.08
$4 s 6 f {}^{1}F_{3}$	$4 s 6 d {}^{1}D_{2}$	7654.330	5.901E-03			5.71
$4 s 6 f {}^{1}F_{3}$	$4 s 6 d {}^{3}D_{2}$	8385.252	6.309E-06			0.01
$4 s 6 f {}^{1}F_{3}$	$4 s 6 d {}^{3}D_{3}$	8834.078	6.540E-11			0.00
$4 s 6 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{2}$	8849.323	9.069E-05			0.09
$4 s 6 f {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{3}$	387.426	7.248E-08			0.00
$4 s 6 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	410.968	8.390E-02			81.13

Table 6. Table 6: Spontaneous emission rates of transitions originating from the 3 d 2 3 superscript 𝑑 2 3d^{2} , 4 p 2 4 superscript 𝑝 2 4p^{2} , 3 d 4 p 3 𝑑 4 𝑝 3d4p , and 4 s 5 g 4 𝑠 5 𝑔 4s5g states of Ca I.

Transition		$λ$ (nm)	$A_{i f}$ ( $10^{8}$ s^-1)		Diff. (%)	BR.(%)
Initial	Final		$L$	$V$
$3 d 4 p {}^{3}F_{2}$	$4 s 5 s {}^{3}S_{1}$	2386.094	1.489E-05	1.490E-05	-0.06	0.00
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	649.558	2.250E-01	2.062E-01	8.37	56.13
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	650.145	4.840E-02	4.514E-02	6.74	12.07
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	651.065	7.591E-04	6.482E-04	14.60	0.19
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{1}D_{2}$	720.419	1.267E-01	1.435E-01	-13.25	31.61
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	646.435	3.367E-01	3.086E-01	8.36	88.32
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	647.345	4.447E-02	4.113E-02	7.51	11.67
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{1}D_{2}$	715.867	5.039E-05	4.493E-05	10.83	0.01
$3 d 4 p {}^{1}D_{2}$	$4 s 5 s {}^{3}S_{1}$	2327.796	1.115E-04	1.118E-04	-0.28	0.02
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{1}$	645.159	9.127E-02	8.382E-02	8.16	20.46
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{2}$	645.738	1.210E-02	1.073E-02	11.31	2.71
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{3}$	646.646	1.798E-03	1.857E-03	-3.30	0.40
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{1}D_{2}$	715.012	3.408E-01	3.840E-01	-12.67	76.40
$3 d 4 p {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	644.085	3.850E-01	3.530E-01	8.30	100.00
$3 d 4 p {}^{3}D_{1}$	$4 s 5 s {}^{3}S_{1}$	1503.106	2.929E-06	2.599E-06	11.27	0.00
$3 d 4 p {}^{3}D_{1}$	$4 s^{2} {}^{1}S_{0}$	261.832	7.250E-05	9.235E-05	-27.38	0.01
$3 d 4 p {}^{3}D_{1}$	$4 s 5 s {}^{1}S_{0}$	2051.227	8.697E-06	9.073E-06	-4.33	0.00
$3 d 4 p {}^{3}D_{1}$	$4 s 4 d {}^{1}D_{2}$	11184.431	1.313E-07	1.517E-07	-15.48	0.00
$3 d 4 p {}^{3}D_{1}$	$4 s 4 d {}^{3}D_{1}$	22512.889	4.675E-07	8.653E-07	-85.10	0.00
$3 d 4 p {}^{3}D_{1}$	$4 s 4 d {}^{3}D_{2}$	22700.445	2.167E-07	3.977E-07	-83.57	0.00
$3 d 4 p {}^{3}D_{1}$	$3 d 4 s {}^{3}D_{1}$	560.004	5.100E-01	5.685E-01	-11.48	74.03
$3 d 4 p {}^{3}D_{1}$	$3 d 4 s {}^{3}D_{2}$	560.440	1.788E-01	2.002E-01	-12.00	25.95
$3 d 4 p {}^{3}D_{1}$	$3 d 4 s {}^{1}D_{2}$	611.892	1.973E-05	1.650E-05	16.35	0.00
$3 d 4 p {}^{3}D_{2}$	$4 s 5 s {}^{3}S_{1}$	1497.091	5.606E-06	5.337E-06	4.80	0.00
$3 d 4 p {}^{3}D_{2}$	$4 s 4 d {}^{1}D_{2}$	10859.768	9.848E-11	6.034E-10	-512.78	0.00
$3 d 4 p {}^{3}D_{2}$	$4 s 4 d {}^{3}D_{1}$	21235.029	1.139E-07	2.015E-07	-76.85	0.00
$3 d 4 p {}^{3}D_{2}$	$4 s 4 d {}^{3}D_{2}$	21401.819	4.939E-07	9.157E-07	-85.39	0.00
$3 d 4 p {}^{3}D_{2}$	$4 s 4 d {}^{3}D_{3}$	21660.493	1.881E-07	3.420E-07	-81.77	0.00
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{1}$	559.167	1.062E-01	1.181E-01	-11.22	15.39
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{2}$	559.601	4.691E-01	5.232E-01	-11.51	67.98
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{3}$	560.283	1.146E-01	1.288E-01	-12.37	16.61
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{1}D_{2}$	610.893	1.438E-04	1.689E-04	-17.46	0.02
$3 d 4 p {}^{3}D_{3}$	$4 s 4 d {}^{1}D_{2}$	10407.668	3.897E-08	2.840E-08	27.12	0.00
$3 d 4 p {}^{3}D_{3}$	$4 s 4 d {}^{3}D_{2}$	19714.145	1.103E-07	1.898E-07	-72.05	0.00
$3 d 4 p {}^{3}D_{3}$	$4 s 4 d {}^{3}D_{3}$	19933.422	8.589E-07	1.569E-06	-82.62	0.00
$3 d 4 p {}^{3}D_{3}$	$3 d 4 s {}^{3}D_{2}$	558.352	8.072E-02	8.971E-02	-11.14	11.66
$3 d 4 p {}^{3}D_{3}$	$3 d 4 s {}^{3}D_{3}$	559.030	6.113E-01	6.825E-01	-11.65	88.33
$3 d 4 p {}^{3}D_{3}$	$3 d 4 s {}^{1}D_{2}$	609.403	1.765E-07	8.340E-07	-372.51	0.00
$4 p^{2} {}^{3}P_{0}$	$4 s 5 p {}^{3}P_{1}$	5368.292	6.316E-07	3.988E-06	-531.44	0.00
$4 p^{2} {}^{3}P_{0}$	$4 s 5 p {}^{1}P_{1}$	5931.480	6.195E-07	5.585E-07	9.85	0.00
$4 p^{2} {}^{3}P_{0}$	$3 d 4 p {}^{3}D_{1}$	44414.835	3.804E-07	1.233E-06	-224.19	0.00
$4 p^{2} {}^{3}P_{0}$	$4 s 4 p {}^{3}P_{1}$	430.896	1.826E+00	2.020E+00	-10.65	99.98
$4 p^{2} {}^{3}P_{0}$	$4 s 4 p {}^{1}P_{1}$	677.266	2.992E-04	3.512E-04	-17.40	0.02
$4 p^{2} {}^{3}P_{1}$	$3 d 4 p {}^{3}F_{2}$	3657.163	1.577E-08	8.457E-09	46.38	0.00
$4 p^{2} {}^{3}P_{1}$	$3 d 4 p {}^{1}D_{2}$	3803.149	6.818E-09	2.776E-09	59.28	0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 5 p {}^{3}P_{0}$	5216.158	1.346E-06	3.461E-06	-157.02	0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 5 p {}^{3}P_{1}$	5235.438	2.798E-07	1.248E-06	-345.96	0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 5 p {}^{3}P_{2}$	5291.873	1.654E-09	6.758E-07		0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 5 p {}^{1}P_{1}$	5769.708	1.410E-09	6.768E-10	51.99	0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{0}$	429.057	6.116E-01	6.765E-01	-10.62	33.42
$4 p^{2} {}^{3}P_{1}$	$3 d 4 p {}^{3}D_{1}$	36708.024	1.646E-07	7.103E-07	-331.44	0.00
$4 p^{2} {}^{3}P_{1}$	$3 d 4 p {}^{3}D_{2}$	40701.697	3.709E-07	1.379E-06	-271.81	0.00
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{1}$	430.020	4.633E-01	5.123E-01	-10.56	25.32
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{2}$	431.987	7.551E-01	8.358E-01	-10.69	41.26
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{1}P_{1}$	675.105	4.708E-06	6.010E-06	-27.64	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{3}F_{2}$	3544.704	2.188E-08	7.096E-08	-224.26	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{3}F_{3}$	3659.184	4.339E-08	1.008E-08	76.78	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{1}D_{2}$	3681.682	1.422E-07	2.910E-07	-104.66	0.00
$4 p^{2} {}^{3}P_{2}$	$4 s 5 p {}^{3}P_{1}$	5007.988	9.858E-07	2.596E-06	-163.32	0.00
$4 p^{2} {}^{3}P_{2}$	$4 s 5 p {}^{3}P_{2}$	5059.602	3.420E-07	2.677E-06	-682.95	0.00
$4 p^{2} {}^{3}P_{2}$	$4 s 5 p {}^{1}P_{1}$	5494.687	2.137E-06	2.192E-06	-2.59	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{3}D_{1}$	27841.969	1.472E-08	1.770E-07	-1102.26	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{3}D_{2}$	30080.616	1.749E-07	1.156E-06	-560.76	0.00
$4 p^{2} {}^{3}P_{2}$	$3 d 4 p {}^{3}D_{3}$	34195.049	6.898E-07	3.349E-06	-385.57	0.00
$4 p^{2} {}^{3}P_{2}$	$4 s 4 p {}^{3}P_{1}$	428.421	4.571E-01	5.055E-01	-10.59	24.93
$4 p^{2} {}^{3}P_{2}$	$4 s 4 p {}^{3}P_{2}$	430.374	1.376E+00	1.522E+00	-10.59	75.05
$4 p^{2} {}^{3}P_{2}$	$4 s 4 p {}^{1}P_{1}$	671.174	3.911E-04	4.160E-04	-6.39	0.02
$3 d 4 p {}^{3}P_{0}$	$4 s 5 s {}^{3}S_{1}$	1283.058	5.926E-03	5.734E-03	3.24	0.76
$3 d 4 p {}^{3}P_{0}$	$4 s 4 d {}^{3}D_{1}$	6308.432	7.123E-04	9.429E-04	-32.38	0.09
$3 d 4 p {}^{3}P_{0}$	$4 p^{2} {}^{3}P_{1}$	11513.177	1.430E-07	1.807E-06	-1163.46	0.00
$3 d 4 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	526.371	7.748E-01	9.561E-01	-23.40	99.15
$3 d 4 p {}^{3}P_{1}$	$4 s 5 s {}^{3}S_{1}$	1282.739	5.936E-03	5.734E-03	3.41	0.76
$3 d 4 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	254.224	8.447E-05	9.012E-05	-6.69	0.01
$3 d 4 p {}^{3}P_{1}$	$4 s 5 s {}^{1}S_{0}$	1661.665	8.536E-06	8.572E-06	-0.42	0.00
$3 d 4 p {}^{3}P_{1}$	$4 s 4 d {}^{1}D_{2}$	4909.108	1.481E-06	1.789E-06	-20.79	0.00
$3 d 4 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{1}$	6300.721	1.806E-04	2.392E-04	-32.43	0.02
$3 d 4 p {}^{3}P_{1}$	$4 s 4 d {}^{3}D_{2}$	6315.324	5.308E-04	7.037E-04	-32.58	0.07
$3 d 4 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{0}$	10895.857	9.717E-08	4.750E-07	-388.82	0.00
$3 d 4 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{1}$	11487.519	4.307E-08	3.780E-07	-777.57	0.00
$3 d 4 p {}^{3}P_{1}$	$4 p^{2} {}^{3}P_{2}$	12759.008	5.176E-08	6.460E-07	-1148.16	0.00
$3 d 4 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	526.317	2.025E-01	2.493E-01	-23.08	25.95
$3 d 4 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	526.702	5.712E-01	7.062E-01	-23.63	73.18
$3 d 4 p {}^{3}P_{1}$	$3 d 4 s {}^{1}D_{2}$	571.896	3.207E-05	3.961E-05	-23.51	0.00
$3 d 4 p {}^{3}P_{2}$	$4 s 5 s {}^{3}S_{1}$	1281.956	5.961E-03	5.754E-03	3.48	0.77
$3 d 4 p {}^{3}P_{2}$	$4 s 4 d {}^{1}D_{2}$	4897.663	2.486E-10	2.697E-09	-984.62	0.00
$3 d 4 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{1}$	6281.881	7.430E-06	9.849E-06	-32.55	0.00
$3 d 4 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{2}$	6296.397	1.095E-04	1.451E-04	-32.59	0.01
$3 d 4 p {}^{3}P_{2}$	$4 s 4 d {}^{3}D_{3}$	6318.596	5.950E-04	7.906E-04	-32.87	0.08
$3 d 4 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{1}$	11425.046	1.004E-07	2.588E-07	-157.78	0.00
$3 d 4 p {}^{3}P_{2}$	$4 p^{2} {}^{3}P_{2}$	12681.987	1.437E-07	8.985E-07	-525.27	0.00
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	526.185	8.820E-03	1.081E-02	-22.54	1.13
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	526.570	1.248E-01	1.535E-01	-23.03	16.02
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	527.174	6.382E-01	7.903E-01	-23.84	81.96
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{1}D_{2}$	571.741	2.357E-04	2.689E-04	-14.10	0.03
$3 d 4 p {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	3086.801	1.565E-02	1.370E-02	12.50	21.49
$3 d 4 p {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{2}$	3589.350	1.096E-06	9.243E-07	15.64	0.00
$3 d 4 p {}^{1}F_{3}$	$4 s 4 d {}^{3}D_{3}$	3596.553	9.869E-09	9.761E-09	1.09	0.00
$3 d 4 p {}^{1}F_{3}$	$4 p^{2} {}^{3}P_{2}$	5034.410	9.118E-07	9.848E-07	-8.00	0.00
$3 d 4 p {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{2}$	495.328	8.657E-06	5.114E-06	40.93	0.01
$3 d 4 p {}^{1}F_{3}$	$3 d 4 s {}^{3}D_{3}$	495.862	1.253E-04	1.353E-04	-7.92	0.17
$3 d 4 p {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	535.095	5.705E-02	4.314E-02	24.38	78.32
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{2}$	2004.249	1.011E-03	1.219E-03	-20.49	0.17
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}F_{3}$	2040.342	1.507E-07	1.511E-07	-0.27	0.00
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	2047.318	2.401E-03	2.903E-03	-20.89	0.40
$4 p^{2} {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{1}$	2400.903	1.333E-04	1.276E-04	4.31	0.02
$4 p^{2} {}^{1}D_{2}$	$4 s 5 p {}^{3}P_{2}$	2412.702	8.136E-06	9.871E-06	-21.32	0.00
$4 p^{2} {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	2507.378	1.308E-02	1.248E-02	4.60	2.20
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{1}$	3956.541	1.206E-06	1.147E-06	4.90	0.00
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{2}$	3998.832	3.892E-08	3.281E-08	15.68	0.00
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}D_{3}$	4063.835	4.311E-08	1.269E-08	70.57	0.00
$4 p^{2} {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	392.006	4.591E-05	5.303E-05	-15.51	0.01
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{1}$	7222.668	1.387E-07	1.401E-07	-1.04	0.00
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{3}P_{2}$	7247.585	2.099E-08	7.039E-08	-235.33	0.00
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	54957.133	2.891E-07	3.722E-06	-1187.40	0.00
$4 p^{2} {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	393.640	7.852E-04	8.614E-04	-9.70	0.13
$4 p^{2} {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	585.907	5.760E-01	6.310E-01	-9.55	97.06
$4 p^{2} {}^{1}S_{0}$	$4 s 5 p {}^{3}P_{1}$	1911.487	1.158E-04	1.302E-04	-12.38	0.01
$4 p^{2} {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	1978.372	1.276E-02	1.436E-02	-12.54	1.61
$4 p^{2} {}^{1}S_{0}$	$3 d 4 p {}^{3}D_{1}$	2782.500	1.236E-06	1.489E-06	-20.55	0.00
$4 p^{2} {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	376.276	1.085E-03	1.177E-03	-8.45	0.14
$4 p^{2} {}^{1}S_{0}$	$3 d 4 p {}^{3}P_{1}$	4080.034	2.225E-06	2.502E-06	-12.47	0.00
$4 p^{2} {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	93222.709	2.055E-06	8.250E-07	59.85	0.00
$4 p^{2} {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	551.451	7.780E-01	8.682E-01	-11.59	98.24
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}F_{2}$	1291.259	2.826E-02	3.549E-02	-25.58	41.20
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}F_{3}$	1306.145	4.691E-03	5.912E-03	-26.03	6.84
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{1}D_{2}$	1309.000	1.043E-02	1.312E-02	-25.81	15.20
$3 d^{2} {}^{3}F_{2}$	$4 s 5 p {}^{3}P_{1}$	1445.070	2.803E-07	2.438E-07	13.00	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 5 p {}^{3}P_{2}$	1449.336	2.329E-06	3.080E-06	-32.22	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 5 p {}^{1}P_{1}$	1482.973	3.879E-06	3.621E-06	6.66	0.01
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}D_{1}$	1893.065	2.132E-02	2.025E-02	5.02	31.08
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}D_{2}$	1902.693	3.754E-03	3.547E-03	5.51	5.47
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}D_{3}$	1917.285	9.916E-05	9.262E-05	6.59	0.14
$3 d^{2} {}^{3}F_{2}$	$4 s 4 p {}^{3}P_{1}$	353.797	9.691E-08	3.045E-08	68.57	0.00
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}P_{1}$	2415.745	2.031E-06	2.003E-06	1.36	0.00
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{3}P_{2}$	2418.526	6.890E-07	6.922E-07	-0.46	0.00
$3 d^{2} {}^{3}F_{2}$	$3 d 4 p {}^{1}F_{3}$	3404.904	2.474E-07	3.775E-07	-52.57	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 6 p {}^{1}P_{1}$	5568.487	2.282E-07	2.658E-07	-16.47	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 4 f {}^{3}F_{2}$	7665.067	1.019E-07	6.964E-07	-583.68	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 4 f {}^{3}F_{3}$	7667.124	1.199E-08	8.371E-08	-597.88	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 4 p {}^{3}P_{2}$	355.128	2.801E-09	1.007E-10	96.41	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 4 f {}^{1}F_{3}$	8839.857	3.297E-08	2.348E-08	28.79	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 6 p {}^{3}P_{1}$	10458.938	1.945E-10	1.992E-10	-2.41	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 6 p {}^{3}P_{2}$	10545.853	5.590E-11	6.354E-11	-13.65	0.00
$3 d^{2} {}^{3}F_{2}$	$4 s 4 p {}^{1}P_{1}$	504.476	3.937E-05	4.524E-05	-14.90	0.06
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}F_{2}$	1288.881	2.306E-03	2.934E-03	-27.24	3.41
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}F_{3}$	1303.711	3.596E-02	4.524E-02	-25.80	53.17
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{1}D_{2}$	1306.556	9.782E-04	1.232E-03	-25.90	1.45
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}F_{4}$	1317.136	3.292E-03	4.159E-03	-26.33	4.87
$3 d^{2} {}^{3}F_{3}$	$4 s 5 p {}^{3}P_{2}$	1446.341	1.068E-06	1.125E-06	-5.35	0.00
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}D_{2}$	1897.533	2.249E-02	2.136E-02	5.02	33.25
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}D_{3}$	1912.046	2.605E-03	2.454E-03	5.80	3.85
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{3}P_{2}$	2410.196	3.913E-06	3.858E-06	1.40	0.01
$3 d^{2} {}^{3}F_{3}$	$3 d 4 p {}^{1}F_{3}$	3388.418	1.948E-07	1.508E-07	22.57	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 4 f {}^{3}F_{2}$	7582.018	1.001E-08	6.587E-08	-558.24	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 4 f {}^{3}F_{3}$	7584.031	1.028E-07	6.809E-07	-562.43	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 4 p {}^{3}P_{2}$	354.948	1.583E-07	6.037E-08	61.86	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 4 f {}^{3}F_{4}$	7586.735	9.143E-09	6.170E-08	-574.86	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 4 f {}^{1}F_{3}$	8729.584	1.863E-09	4.751E-10	74.50	0.00
$3 d^{2} {}^{3}F_{3}$	$4 s 6 p {}^{3}P_{2}$	10389.287	3.400E-10	3.393E-10	0.19	0.00
$3 d^{2} {}^{3}F_{4}$	$3 d 4 p {}^{3}F_{3}$	1300.495	2.489E-03	3.174E-03	-27.54	3.75
$3 d^{2} {}^{3}F_{4}$	$3 d 4 p {}^{3}F_{4}$	1313.853	3.893E-02	4.913E-02	-26.20	58.62
$3 d^{2} {}^{3}F_{4}$	$3 d 4 p {}^{3}D_{3}$	1905.136	2.499E-02	2.372E-02	5.08	37.63
$3 d^{2} {}^{3}F_{4}$	$3 d 4 p {}^{1}F_{3}$	3366.777	7.887E-08	8.891E-08	-12.74	0.00
$3 d^{2} {}^{3}F_{4}$	$4 s 4 f {}^{3}F_{3}$	7476.468	8.641E-09	5.454E-08	-531.16	0.00
$3 d^{2} {}^{3}F_{4}$	$4 s 4 f {}^{3}F_{4}$	7479.096	1.246E-07	7.938E-07	-537.00	0.00
$3 d^{2} {}^{3}F_{4}$	$4 s 4 f {}^{1}F_{3}$	8587.377	1.090E-10	4.795E-10	-339.84	0.00
$4 s 5 g {}^{3}G_{5}$	$3 d 4 p {}^{3}F_{4}$	1113.838	5.774E-04	5.741E-04	0.57	1.13
$4 s 5 g {}^{3}G_{5}$	$4 s 4 f {}^{3}F_{4}$	3698.457	5.062E-02	4.824E-02	4.70	98.86
$4 s 5 g {}^{3}G_{5}$	$4 s 5 f {}^{3}F_{4}$	89493.467	4.431E-06	4.434E-06	-0.07	0.01
$4 s 5 g {}^{1}G_{4}$	$3 d 4 p {}^{3}F_{3}$	1104.089	4.806E-05	4.773E-05	0.69	0.07
$4 s 5 g {}^{1}G_{4}$	$3 d 4 p {}^{3}F_{4}$	1113.702	2.859E-06	2.823E-06	1.24	0.00
$4 s 5 g {}^{1}G_{4}$	$3 d 4 p {}^{3}D_{3}$	1511.298	7.408E-07	7.175E-07	3.14	0.00
$4 s 5 g {}^{1}G_{4}$	$3 d 4 p {}^{1}F_{3}$	2305.178	2.755E-02	2.658E-02	3.53	40.61
$4 s 5 g {}^{1}G_{4}$	$4 s 4 f {}^{3}F_{3}$	3696.325	3.928E-03	3.743E-03	4.69	5.79
$4 s 5 g {}^{1}G_{4}$	$4 s 4 f {}^{3}F_{4}$	3696.967	2.649E-04	2.523E-04	4.77	0.39
$4 s 5 g {}^{1}G_{4}$	$4 s 4 f {}^{1}F_{3}$	3948.886	3.606E-02	3.409E-02	5.45	53.14
$4 s 5 g {}^{1}G_{4}$	$4 s 5 f {}^{3}F_{3}$	88409.513	3.588E-07	3.594E-07	-0.17	0.00
$4 s 5 g {}^{1}G_{4}$	$4 s 5 f {}^{3}F_{4}$	88628.911	2.384E-08	2.424E-08	-1.68	0.00
$4 s 5 g {}^{1}G_{4}$	$4 s 5 f {}^{1}F_{3}$	140706.346	9.701E-07	2.417E-05	-2391.78	0.00

Table 7. Table 7: Comparison of transition probabilities with literature values.

Final state	Initial state	This work ( $L$ , $10^{8}$ s^-1)	Other theory ( $10^{8}$ s^-1)	Diff.	NIST	Diff. (%)
$4 s 4 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	2.170E+00	2.171E+00 MPCI [9]	-0.02	2.18E+00	-0.44
			2.15E+00 CI+MBPT [11]	0.9
$4 s 4 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	2.738E-05	2.75E-05 CI+MBPT [11]	0.43	2.6E-05	5.30
			2.098E-05 MCHF [10]	23.37
$4 s 4 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	5.341E-05	5.274E-05 MPCI [9]	1.26
			5.70E-05 CI+MBPT [11]	6.72
$4 s 6 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	8.390E-02	8.570E-02 MPCI [9]	-2.10	9.0E-01	-90.68
$4 s 5 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	7.505E-03	5.850E-03 MPCI [9]	28.30	2.7E-03	177.96
$4 s 5 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	1.301E-01	1.440E-01 MPCI [9]	-9.71	1.2E-01	8.38
$4 p^{2} {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	5.760E-01	6.393E-01 MPCI [9]	-9.90	6.6E-01	-12.73
$4 s 6 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	9.182E-02	1.398E-01 MPCI [9]	-34.33	1.67E-01	-45.02
$4 s 6 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	2.379E-01	2.871E-01 MPCI [9]	-17.14	3.3E-01	-27.91
$4 p^{2} {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	7.780E-01	7.605E-01 MPCI [9]	2.31	1.1E+00	-29.27
$4 s 4 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	3.116E-01	2.622E-01 MPCI [9]	18.82	1.88E-01	65.73
$4 s 5 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	4.710E-01	3.930E-01 MPCI [9]	19.83	4.0E-01	17.75
$4 s n p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	3.246E-01	2.772E-01 MPCI [9]	17.08	3.01E-01	7.84
$4 s n p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	3.673E-01	2.801E-01 MPCI [9]	31.13	4.1E-01	-10.42
$4 s 5 f {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	1.884E-01	1.398E-01 MPCI [9]	34.74	1.9E-01	-0.83
$4 s 6 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	1.425E-01	8.248E-02 MPCI [9]	72.76	8.0E-02	78.12
$4 s 7 p {}^{1}P_{1}$	$4 s^{2} {}^{1}S_{0}$	2.246E-01	1.546E-01 MPCI [9]	45.29	1.53E-01	46.82
$4 s 5 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	2.293E-01	2.401E-01 MPCI [9]	-4.48
$4 s 6 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	5.391E-03	3.926E-03 MPCI [9]	37.31
$4 s 6 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	2.969E-03	3.131E-03 MPCI [9]	-5.16
$4 s 6 f {}^{1}F_{3}$	$4 s 5 d {}^{1}D_{2}$	5.037E-03	4.493E-03 MPCI [9]	12.09
$4 s 6 f {}^{1}F_{3}$	$4 s 5 g {}^{1}G_{4}$	5.901E-03	7.346E-03 MPCI [9]	-19.66
$4 s 5 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	2.361E-02	2.354E-02 MPCI [9]	0.30
$4 s 4 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	2.778E-05	4.910E-05 MPCI [9]	-43.43
$4 s 4 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1.270E-04	1.395E-04 MPCI [9]	-8.97
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{1}P_{1}$	1.601E-01	1.537E-01 MPCI [9]	4.18
$3 d 4 p {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1.565E-02	9.734E-03 MPCI [9]	60.83
$3 d 4 p {}^{1}F_{3}$	$3 d 4 s {}^{1}D_{2}$	5.705E-02	1.189E-01 MPCI [9]	-52.01
$4 s 6 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	5.484E-02	4.506E-02 MPCI [9]	21.72
$4 s 6 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	1.420E-02	4.357E-02 MPCI [9]	-67.41
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	2.401E-03	4.125E-03 MPCI [9]	-41.78
$4 p^{2} {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	1.308E-02	1.228E-02 MPCI [9]	6.55
$4 p^{2} {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	2.891E-07	2.208E-08 MPCI [9]	92.39
$4 s 6 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	1.516E-02	2.310E-02 MPCI [9]	-34.36
$4 s 6 p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1.407E-02	1.583E-02 MPCI [9]	-11.12
$4 s 6 p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	1.605E-03	1.313E-03 MPCI [9]	22.30
$4 s 6 p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	7.877E-04	6.613E-04 MPCI [9]	19.11
$4 p^{2} {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	1.276E-02	2.607E-02 MPCI [9]	-51.07
$4 p^{2} {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	2.055E-06	3.607E-07 MPCI [9]	469.66
$4 s 4 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	6.368E-02	7.943E-02 MPCI [9]	-19.83
$4 s 4 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	2.920E-03	2.743E-03 MPCI [9]	6.46
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	6.727E-04	8.300E-04 MPCI [9]	-18.96
$4 s 5 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	3.302E-02	3.850E-02 MPCI [9]	-14.25
$4 s 5 d {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	1.274E-03	1.029E-04 MPCI [9]	91.92
$4 s 5 d {}^{1}D_{2}$	$4 s 6 p {}^{1}P_{1}$	4.324E-03	3.961E-03 MPCI [9]	9.15
$4 s 5 d {}^{1}D_{2}$	$4 s 4 f {}^{1}F_{3}$	3.433E-04	3.752E-04 MPCI [9]	-8.48
$4 s n p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	3.895E-02	3.431E-02 MPCI [9]	13.55
$4 s n p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	1.273E-02	1.103E-02 MPCI [9]	15.43
$4 s n p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	6.961E-03	8.416E-03 MPCI [9]	-17.29
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	7.630E-04	5.603E-04 MPCI [9]	36.19
$4 s n p {}^{1}P_{1}$	$4 p^{2} {}^{1}S_{0}$	3.175E-03	3.970E-03 MPCI [9]	-20.04
$4 s n p {}^{1}P_{1}$	$4 s 5 d {}^{1}D_{2}$	2.552E-03	3.253E-03 MPCI [9]	-21.56
$4 s 7 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	4.599E-02	3.338E-02 MPCI [9]	37.80
$4 s 7 s {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	2.243E-02	1.532E-02 MPCI [9]	46.47
$4 s 7 s {}^{1}S_{0}$	$4 s n p {}^{1}P_{1}$	3.074E-04	4.353E-04 MPCI [9]	-29.39
$4 s 7 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	1.784E-01	8.625E-02 MPCI [9]	106.86
$4 s 5 f {}^{1}F_{3}$	$4 s 4 d {}^{1}D_{2}$	1.783E-02	1.474E-02 MPCI [9]	20.91
$4 s 5 f {}^{1}F_{3}$	$4 p^{2} {}^{1}D_{2}$	5.935E-03	3.063E-03 MPCI [9]	93.77
$4 s 5 f {}^{1}F_{3}$	$4 s 5 d {}^{1}D_{2}$	1.878E-02	1.853E-02 MPCI [9]	1.35
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{1}D_{2}$	5.667E-05	3.354E-05 MPCI [9]	68.96
$4 s 6 d {}^{1}D_{2}$	$4 s 5 p {}^{1}P_{1}$	5.046E-02	3.690E-02 MPCI [9]	36.75
$4 s 6 d {}^{1}D_{2}$	$3 d 4 p {}^{1}F_{3}$	1.202E-03	1.296E-03 MPCI [9]	-7.21
$4 s 6 d {}^{1}D_{2}$	$4 s 6 p {}^{1}P_{1}$	7.402E-03	5.143E-03 MPCI [9]	43.93
$4 s 6 d {}^{1}D_{2}$	$4 s 4 f {}^{1}F_{3}$	3.857E-06	5.605E-06 MPCI [9]	-31.18
$4 s 6 d {}^{1}D_{2}$	$4 s n p {}^{1}P_{1}$	2.409E-03	4.352E-03 MPCI [9]	-44.65
$4 s 6 d {}^{1}D_{2}$	$4 s 5 f {}^{1}F_{3}$	3.250E-05	5.590E-05 MPCI [9]	-41.87
$4 s 7 p {}^{1}P_{1}$	$4 s 5 s {}^{1}S_{0}$	1.135E-02	1.304E-02 MPCI [9]	-12.95
$4 s 7 p {}^{1}P_{1}$	$4 s 4 d {}^{1}D_{2}$	4.083E-03	4.259E-03 MPCI [9]	-4.12
$4 s 7 p {}^{1}P_{1}$	$4 s 6 s {}^{1}S_{0}$	4.763E-03	5.618E-03 MPCI [9]	-15.22
$4 s 7 p {}^{1}P_{1}$	$4 p^{2} {}^{1}D_{2}$	1.349E-03	1.127E-03 MPCI [9]	19.66
$4 s 7 p {}^{1}P_{1}$	$4 s 5 d {}^{1}D_{2}$	7.689E-04	5.028E-05 MPCI [9]	93.46
$4 s 7 p {}^{1}P_{1}$	$4 s 7 s {}^{1}S_{0}$	2.597E-03	5.038E-03 MPCI [9]	-48.46
$4 s 7 p {}^{1}P_{1}$	$4 s 6 d {}^{1}D_{2}$	4.250E-04	8.985E-04 MPCI [9]	-52.70
$4 s 7 p {}^{1}P_{1}$	$3 d 4 s {}^{1}D_{2}$	1.575E-01	1.118E-01 MPCI [9]	40.78
$4 s 8 s {}^{1}S_{0}$	$4 s 5 p {}^{1}P_{1}$	1.964E-02	1.834E-02 MPCI [9]	7.10
$4 s 8 s {}^{1}S_{0}$	$4 s 6 p {}^{1}P_{1}$	6.149E-03	8.316E-03 MPCI [9]	-26.06
$4 s 8 s {}^{1}S_{0}$	$4 s n p {}^{1}P_{1}$	7.344E-05	7.689E-04 MPCI [9]	-90.45
$4 s 8 s {}^{1}S_{0}$	$4 s 7 p {}^{1}P_{1}$	2.071E-03	2.235E-03 MPCI [9]	-7.31
$4 s 8 s {}^{1}S_{0}$	$4 s 4 p {}^{1}P_{1}$	3.569E-02	3.693E-02 MPCI [9]	-3.36
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{1}$	9.127E-02	6.680E-02 MCHF [10]	36.63	9.0E-02	1.41
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{2}$	1.210E-02	9.061E-03 MCHF [10]	33.56	1.4E-02	-13.56
$4 s 5 s {}^{1}S_{0}$	$4 s 4 p {}^{3}P_{1}$	1.694E-05	5.201E-06 MCHF [10]	225.74
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{1}D_{2}$	1.267E-01	8.431E-02 MCHF [10]	50.30
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{1}D_{2}$	5.039E-05	7.257E-05 MCHF [10]	-30.57
$3 d 4 p {}^{1}D_{2}$	$3 d 4 s {}^{3}D_{3}$	1.798E-03	7.160E-04 MCHF [10]	151.07
$4 s 5 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	2.340E-06	4.098E-05 MCHF [10]	-94.28
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{1}D_{2}$	1.051E-03	6.208E-04 MCHF [10]	69.35
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{1}D_{2}$	1.792E-03	1.454E-04 MCHF [10]	91.88
$4 s 5 p {}^{1}P_{1}$	$3 d 4 s {}^{3}D_{2}$	2.354E-04	2.884E-04 MCHF [10]	-18.38
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{1}$	4.043E-06	1.222E-05 MCHF [10]	-66.92
$4 s 4 d {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	2.657E-04	1.709E-04 MCHF [10]	55.50
$3 d 4 s {}^{1}D_{2}$	$4 s 4 p {}^{3}P_{2}$	8.245E-07	8.86E-07 CI+MBPT [11]	6.94
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{1}P_{1}$	5.911E-06	6.13E-06 CI+MBPT [11]	3.59
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	1.707E-01			1.51E-01	13.05
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	1.280E-01			1.11E-01	15.32
$4 s 6 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	8.498E-03			5.9E-03	44.03
$4 s 6 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	2.294E-01			1.78E-01	28.89
$4 s 6 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	7.651E-02			6.5E-02	17.71
$4 s 6 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	3.055E-01			2.23E-01	36.98
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	4.415E-01			4.98E-01	-11.35
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	3.223E-01			3.42E-01	-5.76
$4 s 4 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	2.034E-02			2.45E-02	-16.96
$4 s 4 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	5.939E-01			6.7E-01	-11.35
$4 s 4 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	1.882E-01			2.0E-01	-5.92
$4 s 4 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	7.793E-01			8.7E-01	-10.43
$3 d 4 p {}^{3}D_{1}$	$4 s^{2} {}^{1}S_{0}$	7.250E-05			1.6E-04	-54.69
$3 d 4 p {}^{3}D_{1}$	$3 d 4 s {}^{3}D_{1}$	5.100E-01			4.3E-01	18.59
$3 d 4 p {}^{3}D_{1}$	$3 d 4 s {}^{3}D_{2}$	1.788E-01			1.4E-01	27.70
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{1}$	1.062E-01			8.3E-02	27.93
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{2}$	4.691E-01			3.8E-01	23.46
$3 d 4 p {}^{3}D_{2}$	$3 d 4 s {}^{3}D_{3}$	1.146E-01			8.6E-02	33.26
$3 d 4 p {}^{3}D_{3}$	$3 d 4 s {}^{3}D_{2}$	8.072E-02			6.0E-02	34.53
$3 d 4 p {}^{3}D_{3}$	$3 d 4 s {}^{3}D_{3}$	6.113E-01			4.9E-01	24.75
$4 p^{2} {}^{3}P_{0}$	$4 s 4 p {}^{3}P_{1}$	1.826E+00			1.99E+00	-8.24
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{0}$	6.116E-01			6.0E-01	1.93
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{1}$	4.633E-01			4.66E-01	-0.57
$4 p^{2} {}^{3}P_{1}$	$4 s 4 p {}^{3}P_{2}$	7.551E-01			7.4E-01	2.04
$4 p^{2} {}^{3}P_{2}$	$4 s 4 p {}^{3}P_{1}$	4.571E-01			4.34E-01	5.33
$4 p^{2} {}^{3}P_{2}$	$4 s 4 p {}^{3}P_{2}$	1.376E+00			1.36E+00	1.18
$3 d 4 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	7.748E-01			6.0E-01	29.13
$3 d 4 p {}^{3}P_{1}$	$4 s^{2} {}^{1}S_{0}$	8.447E-05			1.7E-04	-50.31
$3 d 4 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	2.025E-01			1.5E-01	35.03
$3 d 4 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	5.712E-01			4.4E-01	29.82
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	8.820E-03			6.1E-03	44.59
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	1.248E-01			9.1E-02	37.10
$3 d 4 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	6.382E-01			5.0E-01	27.63
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	2.621E-02			3.34E-02	-21.53
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	7.994E-02			9.8E-02	-18.43
$4 s 6 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	1.377E-01			1.75E-01	-21.34
$4 s 6 f {}^{3}F_{2}$	$3 d^{2} {}^{3}F_{3}$	5.931E-02			7.2E-02	-17.63
$4 s 6 f {}^{3}F_{2}$	$4 s 7 s {}^{3}S_{1}$	1.101E-02			9.8E-03	12.34
$4 s 6 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	3.166E-04			3.5E-04	-9.56
$4 s 6 f {}^{3}F_{3}$	$4 s 6 d {}^{1}D_{2}$	6.277E-02			5.4E-02	16.23
$4 s 6 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	7.898E-03			8.9E-03	-11.26
$4 s 6 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	7.088E-02			7.9E-02	-10.28
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	7.436E-03			9.4E-03	-20.90
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	2.225E-02			3.0E-02	-25.83
$4 s 8 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	3.693E-02			5.3E-02	-30.33
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	1.106E-01			1.1E-01	0.52
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	2.057E-02			2.1E-02	-2.05
$4 s 5 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	5.884E-04			5.8E-04	1.45
$4 s 5 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	1.172E-01			1.2E-01	-2.36
$4 s 5 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	1.471E-02			1.5E-02	-1.97
$4 s 5 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	1.323E-01			1.3E-01	1.79
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	1.873E-02			1.3E-02	44.07
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	5.630E-02			4.6E-02	22.38
$4 s 7 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	9.417E-02			7.8E-02	20.73
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{0}$	1.927E-01			2.12E-01	-9.12
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{1}$	1.452E-01			1.53E-01	-5.10
$4 s 5 d {}^{3}D_{1}$	$4 s 4 p {}^{3}P_{2}$	9.773E-03			9.5E-03	2.87
$4 s 5 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{1}$	2.593E-01			2.97E-01	-12.69
$4 s 5 d {}^{3}D_{2}$	$4 s 4 p {}^{3}P_{2}$	8.734E-02			9.4E-02	-7.08
$4 s 5 d {}^{3}D_{3}$	$4 s 4 p {}^{3}P_{2}$	3.451E-01			3.55E-01	-2.78
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	1.348E-01			1.76E-01	-23.43
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	2.508E-02			3.5E-02	-28.33
$4 s 4 f {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	7.142E-04			9.8E-04	-27.13
$4 s 4 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	1.429E-01			2.09E-01	-31.63
$4 s 4 f {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	1.791E-02			2.5E-02	-28.38
$4 s 4 f {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	1.617E-01			2.29E-01	-29.40
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{1}$	6.273E-04			2.3E-03	-72.72
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{2}$	1.558E-02			3.3E-02	-52.79
$4 s 5 p {}^{3}P_{2}$	$3 d 4 s {}^{3}D_{3}$	8.710E-02			1.9E-01	-54.16
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{1}$	2.532E-02			5.6E-02	-54.79
$4 s 5 p {}^{3}P_{1}$	$3 d 4 s {}^{3}D_{2}$	7.859E-02			1.7E-01	-53.77
$3 d 4 p {}^{3}F_{4}$	$3 d 4 s {}^{3}D_{3}$	3.850E-01			5.3E-01	-27.36
$4 s 5 p {}^{3}P_{0}$	$3 d 4 s {}^{3}D_{1}$	1.045E-01			2.2E-01	-52.48
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{2}$	3.367E-01			4.7E-01	-28.36
$3 d 4 p {}^{3}F_{3}$	$3 d 4 s {}^{3}D_{3}$	4.447E-02			5.9E-02	-24.62
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{1}$	2.250E-01			4.4E-01	-48.86
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{2}$	4.840E-02			8.1E-02	-40.25
$3 d 4 p {}^{3}F_{2}$	$3 d 4 s {}^{3}D_{3}$	7.591E-04			2.4E-03	-68.37
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{0}$	9.246E-02			9.6E-02	-3.69
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{1}$	2.759E-01			2.87E-01	-3.88
$4 s 5 s {}^{3}S_{1}$	$4 s 4 p {}^{3}P_{2}$	4.549E-01			4.77E-01	-4.63

Equations4

A_{i f} = 2.02613 \times 1 0^{18} \frac{∣ ⟨ i ∣∣ D ∣∣ f ⟩ ∣ ^{2}}{( 2 J _{i} + 1 ) λ ^{3}} s^{- 1},

A_{i f} = 2.02613 \times 1 0^{18} \frac{∣ ⟨ i ∣∣ D ∣∣ f ⟩ ∣ ^{2}}{( 2 J _{i} + 1 ) λ ^{3}} s^{- 1},

g f = (2 J_{f} + 1) f_{f i} = - (2 J_{i} + 1) f_{i f} = 1.499 \times 1 0^{- 16} A_{i f} λ^{2} (2 J_{i} + 1),

g f = (2 J_{f} + 1) f_{f i} = - (2 J_{i} + 1) f_{i f} = 1.499 \times 1 0^{- 16} A_{i f} λ^{2} (2 J_{i} + 1),

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Full text

Transition rates and radiative lifetimes of Ca I

Yanmei YU

[email protected]

Andrei Derevianko

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190,China

Department of Physics, University of Nevada, Reno, Nevada 89557, USA

We tabulate spontaneous emission rates for all possible 811 electric-dipole-allowed transitions between the 75 lowest-energy states of Ca I. These involve the $4sns$ ( $n=4-8$ ), $4snp$ ( $n=4-7$ ), $4snd$ ( $n=3-6$ ), $4snf$ ( $n=4-6$ ), $3d^{2}$ , $4p^{2}$ , $3d4p$ , and $4s5g$ electronic configurations. We compile the transition rates by carrying out ab initio relativistic calculations using the combined method of configuration interaction and many-body perturbation theory. The results are compared to the available literature values. The tabulated rates can be useful in various applications, such as optimizing laser cooling in magneto-optical traps, estimating various systematic effects in optical clocks and evaluating static or dynamic polarizabilities and long-range atom-atom interaction coefficients and related atomic properties.

Contents@starttoctoc

@starttoc

ldt

@starttoc

ldf

1 Introduction

Alkaline-earth atoms and divalent-like atoms (such as Yb and Hg) became a subject of interest to the cold atom community in the past decade. These atoms possess two valence electrons outside a tightly bound core and in the LS coupling scheme, the atomic states can be classified by being either singlet or triplet states. The availability of relatively wide spin-allowed and narrow spin-forbidden electric-dipole (E1) transitions enables stacking laser cooling on both types of transitions, with the spin-allowed transitions used for the initial rapid cooling and spin-forbidden transitions - for reaching much lower Doppler-limit temperatures. Moreover, the narrow inter-combination transitions, such as the $4s^{2}\,{}^{1}\!S_{0}-4s4p~{}^{3}\!P_{1}$ transition, can be used as an optical frequency reference [1, 2]. The highly-forbidden $4s^{2}\,{}^{1}\!S_{0}-4s4p~{}^{3}\!P_{0}$ transition can be potentially used for an optical lattice clock scheme [3]. However, due to peculiarities of its electronic structure, Ca, unlike other alkaline-earth atoms, has a relatively short lifetime in conventional magneto-optical traps (MOT). To improve the MOT efficiency, several re-pumping schemes were proposed and demonstrated [4]. That work required reliable electric-dipole transition data for many transitions between the 75 lowest energy states of neutral Ca. Here, we compile the results of our computational work that served as a basis of the MOT performance analysis [4]. We anticipate that the tabulated data will be useful in multiple other contexts, such as estimating various systematic effects in optical clocks and computing static or dynamic polarizabilities and long-range inter-atomic interaction coefficients.

There have been a number of atomic-structure calculations for neutral calcium. The earlier work includes multi-configuration Hartree-Fock (MCHF) calculation [5] and semi-empirical model-potential calculations[6, 7, 8, 9]. These computations provide oscillator strengths for spin-allowed transitions for levels up to $4s10s$ , $4s9p$ and $4s6d$ . Most of them are non-relativistic with very limited numbers of low-lying levels treated with ab initio relativistic methods. In particular, Fisher and Tachiev [10] reported energies and E1 transition rates for levels below $3d4p~{}^{1}F_{3}$ . Porsev et al. [11] and Savukov and Johnson [12] computed the $4s^{2}-4s4p$ , $4s4p-3d4s$ , and $4s4p-4s5s$ transition rates using a combination of configuration-interaction (CI) and many-body perturbation theory (MBPT) (referred to as the CI+MBPT method). The CI+MBPT method results were in excellent agreement with high-precision experimental values. This fact partially motivated our use of the relativistic CI+MBPT method for the present work.

2 Computational details

The CI+MBPT method employs a systematic formalism that combines advantages of both configuration interaction (CI) method and many-body perturbation theory (MBPT) [13]. This method has been used extensively for evaluation of atomic properties (see, e.g., review [14] for optical lattice clock applications and references therein). Relativistic effects are included exactly as the formalism starts from the Dirac equation and employs relativistic bi-spinor wave functions throughout the entire calculation. In our treatment, the CI model space is limited to excitations of the two valence electrons. Contributions involving virtual excitations of core orbitals are treated within the MBPT. In this approach, we first solve for the valence electron orbitals and energies in the field of core electrons. The one-electron effective potential includes both the frozen-cored Dirac-Hartree-Fock (DHF $V^{N-2}$ ) and self-energy (core-polarization) potentials. The self-energy correction is computed using second-order MBPT diagrams involving virtual core excitations. At the next step, the computed one-electron valence orbitals are used to diagonalize the atomic Hamiltonian in the model space of two valence electrons within the CI method. The CI model-space Hamiltonian includes the residual (beyond DHF) Coulomb interaction between the valence electrons and also their core-polarization-mediated interaction. The latter was computed in the second-order MBPT. This step yields two-electron wave-functions and energies. Finally, with the obtained wave-functions we calculated the required electric-dipole matrix elements. In calculations of transition rates we used experimental energy intervals and the computed CI+MBPT matrix elements.

We used two independent CI+MBPT implementations: (i) by the Reno group (see the decription of the earlier version in Ref. [15]) and (ii) the recently published package [16]. The practical goal of the calculations was not reaching the best possible accuracy, but rather the generation of massive amounts of reliable data for the transition array involving 75 lowest-energy levels. The Reno code was run on a large basis set but without including core-polarization-mediated interaction in the CI Hamiltonian due to considerable computational costs. The production runs with package [16] employed a smaller basis set (due to code limitations) but treated the correlation problem more fully.

While using the package [16] we employed the one-electron basis set that included the $1s-17s$ , $2p-17p$ , $3d-17d$ , $4f-17f$ , and $5g-17g$ orbitals, where the core and $4s,\cdots,6f$ orbitals are DHF ones, while the remaining orbitals were represented by a B-spline basis set. The Reno code used the dual-kinetic-balance basis set generated in the DHF $V^{N-2}$ potential using spherical cavity of 75 bohr radius [17]. The basis included orbitals with orbital angular momentum $\ell$ up to 6. The total number of positive-energy (in the Dirac sense) orbitals per partial wave was 40 with the 35 lowest-energy orbitals used in the calculations.

For most states, the values of transition rates obtained with package [16] were in closer agreement with the NIST recommended values due to more complete treatment of the correlation problem. The level of agreement was degraded for states with the $4s6f$ electron configuration which was traced to our use of small basis set due to package [16] limitations. For these $4s6f$ states, the values of transition rates obtained with the Reno code displayed a better agreement with the NIST data because of the larger basis set. In addition, due to the restriction on the number of eigenvalues in the package [16], we were not able to compute the states arising from the $4s8s$ configuration. Our final values combine the outputs of the two codes. While the bulk of the results comes from the package [16], rates for states involving the $4s6f$ and $4s8s$ configurations are taken from the Reno code output in our tabulation.

The spontaneous emission rate $A_{if}$ from the upper (initial) state $i$ to the lower (final) state $f$ was calculated as

[TABLE]

where $\langle i||D||f\rangle$ is the reduced matrix element of the electric-dipole operator in atomic units, the transition wavelength $\lambda$ is expressed in $\AA$ , and $J_{i}$ is the total angular momentum of the upper (initial) state. The emission rate can be converted into the weighted oscillator strength using [18]

[TABLE]

where $gf$ is weighted oscillator strength, $f_{if}$ is the emission oscillator strength (usually taken to be negative), $f_{fi}$ is the adsorption oscillator strength, and $J_{f}$ is the total angular momentum of the lower (final) state. We determined $\lambda$ from the NIST recommended energy values [19]. Finally, the total transition rate $A_{\mathrm{total}}$ from a given initial state is a sum of $A_{if}$ over all E1-allowed final states, with the resulting initial state lifetime $\tau=1/A_{\mathrm{total}}$ .

3 Results and discussion

We summarize the lifetime of the 75 states in Table 1 and compare with the available theoretical and experimental values. Our data show better agreement with the experimental values, as compared with the other theoretical data. The computed spontaneous emission rates are compiled in Tables 2-6. For completeness, we list values obtained with the electric dipole operator in both the length and velocity forms (gauges) in columns marked $L$ and $V$ , respectively. Generally, the length and velocity gauges agree at a few percent level, except for some occasional large discrepancies for weak transitions. The length form values are in better overall agreement with the available literature data and therefore we recommend using the length-form values.

We further assessed the quality of our calculation by comparing our values with other theoretical data [9, 10, 11] and with the NIST recommended values [19] in Table 7. The other theoretical data are taken primarily from three sources. The first source is the non-relativistic semi-empirical calculation by Hansen et al. [9]. They used the model potential and CI (MPCI) method to determine rates for the LS allowed E1 transitions for levels up to $4s10s$ . From a comparison with other semi-empirical work [6, 7], Hansen et al. concluded that their data are more accurate because they have used larger basis size, larger cut-off radius, and more accurate model potential. In Table 7 we compare 80 transition rates with Hansen’s results [9]. For comparison, their weighted oscillator strength $gf$ values are converted to $A_{if}$ (in 1/s) as $A_{if}=6.67\times 10^{15}gf/[(2J_{i}+1)\lambda^{2}]$ , where $\lambda$ is in Å. The difference between our and the Hansen’s results is better than 1% for the $4s4p~{}^{1}P_{1}-4s^{2}~{}^{1}S_{0}$ and $4s4p~{}^{3}P_{1}-4s^{2}~{}^{1}S_{0}$ transitions and better than 50% for majority of other transitions. There are a few cases where the discrepancy between our and Hansen’s data is worse than 50% for some specific transitions decaying from highly excited states like $4sns$ with $n=6-8$ , $4s7p$ , $4s6d$ , and $4s5d$ . The second source is the ab initio relativistic MCHF calculations by Fischer, et al. [10]. They report the transition rates between levels below $3d4p~{}^{1}F_{3}$ , both allowed and spin forbidden. In Table 7, we compared 13 spin forbidden singlet-triplet transition rates with their results. Our values are in better agreement with the NIST data than the MCHF results, for example, for the $4s4p~{}^{3}P_{1}-4s^{2}~{}^{1}S_{0}$ , $3d4p~{}^{1}D_{2}-3d4s~{}^{3}D_{1}$ , $3d4p~{}^{1}D_{2}-3d4s~{}^{3}D_{2}$ transitions. The third source is the CI+MBPT calculation [11]. These authors reported rates for the spin-allowed $4s^{2}-4s4p$ , $4s4p-3d4s$ transitions, and for the spin-forbidden $4s4p~{}^{1}P_{1}-4s5s~{}^{3}S_{1}$ and $4s4p~{}^{3}P_{1,2}-3d4s~{}^{1}D_{2}$ transitions. We find excellent agreement with their CI+MBPT results [11]. Finally, we compared 99 transition rates with the NIST Atomic Spectra Database [19] in Table 7. In most cases, the discrepancy is better than 50%. There are some instances when the discrepancy is worse than 50%. In particular, for the $4s6f~{}^{1}F_{0}-3d4s~{}^{1}D_{2}$ , $4s5p~{}^{1}P_{1}-4s^{2}~{}^{1}S_{0}$ , and $4s4f~{}^{1}F_{3}-3d4s~{}^{1}D_{2}$ transitions, our data show good agreement with the MPCI theoretical data, but display large differences with the NIST recommended values.

Acknowledgments

We would like to thank Eric Hudson for motivating this work and Mikhail Kozlov for a valuable assistance with the code [16]. Y.Y. thanks the University of Nevada, Reno for hospitality during her visit. Y.Y. was supported by the National Natural Science Foundation of China under Grant No. 91536106, the NKRD Program of China (2016YFA0302104) and the CAS XDB21030300. A.D. was supported in part by the US National Science Foundation grant PHY-1607396.

Explanation of Tables

In Table I, we compile radiative E1 lifetimes of the 74 lowest-energy excited states of Ca I. In Tables 2-6, we tabulate our theoretical data for spontaneous emission rates of all possible 811 E1-allowed transitions between the 75 lowest-energy states of Ca I. A comparison with other literature values is presented in Table 7.

Table 1. Radiative electric-dipole decay rates $A_{\mathrm{total}}$ and lifetimes $\tau$ of Ca I.

[TABLE]

Table 2. Spontaneous emission rates of transitions originating from the $4sns$ ( $n$ =4-8) states of Ca I.

[TABLE]

Table 3. Spontaneous emission rates of transitions originating from the $4snp$ ( $n$ =4-7) states of Ca I.

[TABLE]

Table 4. Spontaneous emission rates of transitions originating from the $4snd$ ( $n$ =3-6) states of Ca I.

[TABLE]

Table 5. Spontaneous emission rates of transitions originating from the $4snf$ ( $n$ =4-6) states of Ca I.

[TABLE]

Table 6. Spontaneous emission rates of transitions originating from the $3d^{2}$ , $4p^{2}$ , $3d4p$ , and $4s5g$ states of Ca I.

[TABLE]

Table 7. Comparison of transition probabilities with literature values.

[TABLE]

Bibliography25

The reference list from the paper itself. Each links out to its DOI / PubMed record.

1[1] C. W. Oates, E. A. Curtis, and L. Hollberg, Opt. Lett. 25 (2000) 1603.
2[2] C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, Phys. Rev. A 72 (2005) 062111.
3[3] A. Derevianko and H. Katori, Rev. Mod. Phys. 83 (2011) 331.
4[4] M. Mills, P. Puri, Y.-M. Yu, A. Derevianko, C. Schneider, and E. R. Hudson, arxiv:1701.04948 (2017).
5[5] N. Vaeck, M. Godefroidtn, and J. E. Hansent, J. Phys. B 24 (1991) 361.
6[6] J. Mitroy, J. Phys. B 26 (1993) 3703.
7[7] T. Brage, C. F. Fischer, Phys. Rev. A 50 (1994) 2937.
8[8] C. Laughlin, J. E. Hansen, J. Phys B 29 (1996) L 441.

TL;DR

Contribution

Findings

Abstract

Peer Reviews

Videos

Transition rates and radiative lifetimes of Ca I

1 Introduction

2 Computational details

3 Results and discussion

Acknowledgments

Explanation of Tables

Table 1. Radiative electric-dipole decay rates AtotalA_{\mathrm{total}}Atotal​ and lifetimes τ\tauτ of Ca I.

Table 2. Spontaneous emission rates of transitions originating from the 4sns4sns4sns (nnn=4-8) states of Ca I.

Table 3. Spontaneous emission rates of transitions originating from the 4snp4snp4snp (nnn=4-7) states of Ca I.

Table 4. Spontaneous emission rates of transitions originating from the 4snd4snd4snd (nnn=3-6) states of Ca I.

Table 5. Spontaneous emission rates of transitions originating from the 4snf4snf4snf (nnn=4-6) states of Ca I.

Table 6. Spontaneous emission rates of transitions originating from the 3d23d^{2}3d2, 4p24p^{2}4p2, 3d4p3d4p3d4p, and 4s5g4s5g4s5g states of Ca I.

Table 7. Comparison of transition probabilities with literature values.

Table 1. Radiative electric-dipole decay rates $A_{\mathrm{total}}$ and lifetimes $\tau$ of Ca I.

Table 2. Spontaneous emission rates of transitions originating from the $4sns$ ( $n$ =4-8) states of Ca I.

Table 3. Spontaneous emission rates of transitions originating from the $4snp$ ( $n$ =4-7) states of Ca I.

Table 4. Spontaneous emission rates of transitions originating from the $4snd$ ( $n$ =3-6) states of Ca I.

Table 5. Spontaneous emission rates of transitions originating from the $4snf$ ( $n$ =4-6) states of Ca I.

Table 6. Spontaneous emission rates of transitions originating from the $3d^{2}$ , $4p^{2}$ , $3d4p$ , and $4s5g$ states of Ca I.