2 Atomic data

The silicon model atom accounts for the most important levels and transitions of Si I and Si II and comprises 115 energy levels and 84 line transitions. For Si I (ionization limit at 8.15 eV) 75 energy levels up to 7.77 eV and 53 line transitions were included, for Si II (ionization limit at 16.35 eV) 40 energy levels up to 15.65 eV and 31 line transitions were taken into account. The atomic data are listed in Tables 1 and 2,

 

 

Table 1: Energy levels included in the model atom.

no.	config.	term	$E ({\rm eV})$	gi		no.	config.	term	$E ({\rm eV})$	gi
Si I 1	3s$^2\, 3$p$^2\,$	3P	0.0186	9		59	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	$^2\lbrack9/2\rbrack$	7.6394	20
2	3s$^2\, 3$p$^2\,$	1D	0.7810	5		60	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack9/2\rbrack^{\rm o}$	7.6398	20	*
3	3s$^2\, 3$p$^2\,$	1S	1.9087	1		61	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack7/2\rbrack^{\rm o}$	7.6411	16	*
4	3s$\, 3$p$^3\, (^4$P$)\,$	5S$^{\rm o}$	4.1319	5		62	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack11/2\rbrack^{\rm o}$	7.6429	24	*
5	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$s	3P$^{\rm o}$	4.9420	9		63	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	$^2\lbrack3/2\rbrack$	7.6434	8
6	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$s	1P$^{\rm o}$	5.0824	3		64	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack5/2\rbrack^{\rm o}$	7.6442	12	*
7	3s$\, 3$p$^3\,$	3D$^{\rm o}$	5.6169	15		65	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$s	$(3/2,1/2)^{\rm o}$	7.6679	8
8	3s$^2\, 3$p$\, 4$p	1P	5.8625	3		66	3s$^2\, 3$p$\,5$d	3P$^{\rm o}$	7.6730	9	*
9	3s$^2\, 3$p$\, 3$d	1D$^{\rm o}$	5.8708	5		67	3s$^2\, 3$p$\,6$d	1D$^{\rm o}$	7.7065	5
10	3s$^2\, 3$p$\, 4$p	3D	5.9713	15		68	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$p	(1/2,1/2)	7.7101	4
11	3s$^2\, 3$p$\, 4$p	3P	6.0911	9		69	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$p	(1/2,3/2)	7.7156	8
12	3s$^2\, 3$p$\, 4$p	3S	6.1248	3		70	3s$^2\, 3$p$\,6$d	3F$^{\rm o}$	7.7414	21
13	3s$^2\, 3$p$\, 3$d	3F$^{\rm o}$	6.1959	21		71	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$p	(3/2,3/2)	7.7491	16
14	3s$^2\, 3$p$\, 4$p	1D	6.2227	5		72	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$p	(3/2,1/2)	7.7527	8
15	3s$^2\, 3$p$\, 3$d	3P$^{\rm o}$	6.2653	9		73	3s$^2\, 3$p$\,6$d	1P$^{\rm o}$	7.7697	3
16	3s$^2\, 3$p$\, 4$p	1S	6.3990	1		74	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$f	$^2\lbrack7/2\rbrack$	7.7700	16
17	3s$^2\, 3$p$\, 3$d	1F$^{\rm o}$	6.6161	7		75	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$f	$^2\lbrack5/2\rbrack$	7.7701	12
18	3s$^2\, 3$p$\, 3$d	1P$^{\rm o}$	6.6192	3
19	3s$^2\, 3$p$\, 3$d	3D$^{\rm o}$	6.7232	15		Si II 76	3s $^2\, (^1$S$)\, 3$p	2P$^{\rm o}$	0.0237	6
20	3s$^2\, 3$p$\,5$s	3P$^{\rm o}$	6.7478	9		77	3s$\, 3$p$^2\,$	4P	5.3316	12	*
21	3s$^2\, 3$p$\,5$s	1P$^{\rm o}$	6.8031	3		78	3s$\, 3$p$^2\,$	2D	6.8587	10
22	3s$^2\, 3$p$\, 4$d	1D$^{\rm o}$	7.0055	5		79	3s $^2\, (^1$S$)\, 4$s	2S	8.1210	2
23	3s$^2\, 3$p$\, 4$d	3P$^{\rm o}$	7.0298	9		80	3s$\, 3$p$^2\,$	2S	9.5054	2
24	3s$^2\, 3$p$\,5$p	1P	7.0399	3		81	3s $^2\, (^1$S$)\, 3$d	2D	9.8380	10
25	3s$^2\, 3$p$\,5$p	3D	7.0787	15		82	3s $^2\, (^1$S$)\, 4$p	2P$^{\rm o}$	10.0715	6
26	3s$^2\, 3$p$\,5$p	3P	7.1170	9		83	3s$\, 3$p$^2\,$	2P	10.4069	6
27	3s$^2\, 3$p$\, 4$d	3F$^{\rm o}$	7.1277	21		84	3s $^2\, (^1$S$)\, 5$s	2S	12.1471	2
28	3s$^2\, 3$p$\,5$p	3S	7.1343	3		85	3s $^2\, (^1$S$)\, 4$d	2D	12.5255	10
29	3s$^2\, 3$p$\,5$p	1D	7.1660	5		86	3s $^2\, (^1$S$)\, 4$f	2F$^{\rm o}$	12.8394	14
30	3s$^2\, 3$p$\,5$p	1S	7.2297	1		87	3s $^2\, (^1$S$)\, 5$p	2P$^{\rm o}$	12.8792	6
31	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	$^2\lbrack5/2\rbrack$	7.2872	12		88	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 3$d	2D$^{\rm o}$	13.4901	10
32	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	3F	7.2888	16		89	3s $^2\, (^1$S$)\, 6$s	2S	13.7852	2
33	3s$^2\, 3$p$\, 4$d	1P$^{\rm o}$	7.2905	3		90	3s $^2\, (^1$S$)\, 5$d	2D	13.9353	10
34	3s$^2\, 3$p$\, 4$d	1F$^{\rm o}$	7.3019	7		91	3s $^2\, (^1$S$)\, 5$f	2F$^{\rm o}$	14.1046	14
35	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	3G	7.3196	16		92	3s $^2\, (^1$S$)\, 6$p	2P$^{\rm o}$	14.1308	6
36	3s$^2\, 3$p$\, 4$d	3D$^{\rm o}$	7.3247	15		93	3s $^2\, (^1$S$)\, 5$g	2G	14.1563	18
37	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	$^2\lbrack5/2\rbrack$	7.3288	12		94	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 3$d	4F$^{\rm o}$	14.1858	28	*
38	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	$^2\lbrack9/2\rbrack$	7.3312	20		95	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 4$s	4P$^{\rm o}$	14.5136	12	*
39	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\, 4$f	$^2\lbrack3/2\rbrack$	7.3388	8		96	3s$^2\, (^1$S$)\,7$s	2S	14.6196	2
40	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$s	3P$^{\rm o}$	7.3474	4		97	3s$^2\, (^1$S$)\, 6$d	2D	14.6951	10
41	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$s	$(3/2,1/2)^{\rm o}$	7.3840	8		98	3s$^2\, (^1$S$)\,7$p	2P$^{\rm o}$	14.7870	6
42	3s$^2\, 3$p$\,$nd	3P$^{\rm o}$	7.4344	9		99	3s$^2\, (^1$S$)\, 6$f	2F$^{\rm o}$	14.7928	14
43	3s$^2\, 3$p$\,5$d	1D$^{\rm o}$	7.4764	5		100	3s$^2\, (^1$S$)\, 6$g	2G	14.8258	18
44	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$p	(1/2,1/2)	7.4938	4		101	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 4$s	2P$^{\rm o}$	15.0693	6
45	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$p	(1/2,3/2)	7.5002	8		102	3s$^2\, (^1$S$)\, 8$s	2S	15.1031	2
46	3s$^2\, 3$p$\,5$d	3F$^{\rm o}$	7.5324	21		103	3s$^2\, (^1$S$)\,7$d	2D	15.1463	10
47	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$p	(3/2,3/2)	7.5403	16		104	3s$^2\, (^1$S$)\,7$f	2F$^{\rm o}$	15.2073	14
48	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,6$p	(3/2,1/2)	7.5422	8		105	3s$^2\, (^1$S$)\,7$g	2G	15.2296	18
49	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	$^2\lbrack5/2\rbrack$	7.6008	12		106	3p$^3\,$	4S$^{\rm o}$	15.2542	4	*
50	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	3F	7.6010	16		107	3s $^2\, (^1$S$)\, 8$p	2P$^{\rm o}$	15.2656	6
51	3s$^2\, 3$p$\,5$d	1P$^{\rm o}$	7.6011	3		108	3s $^2\, (^1$S$)\, 9$s	2S	15.4084	2
52	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack7/2\rbrack^{\rm o}$	7.6060	16		109	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 3$d	4D$^{\rm o}$	15.4204	20	*
53	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$g	$^2\lbrack9/2\rbrack^{\rm o}$	7.6061	20		110	3s $^2\, (^1$S$)\, 8$d	2D	15.4355	10
54	3s$^2\, 3$p$\,5$d	1F$^{\rm o}$	7.6156	7		111	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 3$d	4P$^{\rm o}$	15.4479	12	*
55	3s$^2\, 3$p$\,5$d	3D$^{\rm o}$	7.6276	15		112	3s $^2\, (^1$S$)\, 8$f	2F$^{\rm o}$	15.4760	14
56	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	3G	7.6329	16		113	3s $^2\, (^1$S$)\, 8$g	2G	15.4916	18
57	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,7$s	3P$^{\rm o}$	7.6351	4		114	3s $^2\, (^1$S$)\, 9$p	2P$^{\rm o}$	15.5018	6
58	3s$^2\, 3$p$\,(^2$P $^{\rm o} )\,5$f	3D	7.6372	12		115	3s$\, 3$p$\, (^3$P $^{\rm o} )\, 3$d	2P$^{\rm o}$	15.6531	6

 

 

Table 2: Line transitions used in the model atom.

no.	mult.	i	k	$\lambda$ (Å)	$\log gf$			no.	mult.	i	k	$\lambda$ (Å)	$\log gf$
Si I-1	0.01F	1	2	16263.251	-9.126	F		Si I-43	31	8	22	10846.829	+0.150	F
Si I-2	1F	1	3	6567.708	-9.634	F		Si I-44	32.02	8	33	8680.080	-3.191	F
Si I-3	0.01	1	4	3014.243	-4.522	F		Si I-45	34	8	41	8093.231	-1.354	F
Si I-4	UV 1	1	5	2517.485	+0.173	F		Si I-46	36	8	43	7680.265	-0.691	F
Si I-5	UV 2	1	6	2448.510	-2.264	F		Si I-47	38	8	67	6721.840	-0.938	F
Si I-6	UV 3	1	7	2213.972	-0.217	F		Si I-48	42.21	10	20	15964.678	+0.456	F
Si I-7	UV 7	1	15	1984.967	-0.314	V		Si I-49	53	10	27	10720.959	+0.672	F
Si I-8	UV 8	1	17	1881.854	-1.922	V		Si I-50	57	10	46	7939.870	+0.061	F
Si I-9	UV 10	1	19	1849.336	+0.387	V		Si I-51	60	10	70	7002.660	-0.380	F
Si I-10	UV 11	1	20	1842.489	-0.663	V		Si I-52		11	21	17205.800	-1.450	L
Si I-11	2F	2	3	10991.400	-7.839	F		Si I-53		12	20	20343.900	-0.810	L
Si I-12	1	2	5	2979.674	-2.045	F		Si II-1	UV 0.01	76	77	2325.848	-4.193	F
Si I-13	UV 43	2	6	2881.577	-0.151	F		Si II-2	UV 1	76	78	1813.980	-1.474	F
Si I-14	UV 45	2	9	2435.154	-0.680	V		Si II-3	UV 2	76	79	1531.183	-0.108	F
Si I-15	UV 48	2	17	2124.111	+0.533	V		Si II-4	UV 3	76	80	1307.636	-0.249	F
Si I-16	UV 49	2	18	2122.990	-0.915	V		Si II-5	UV 4	76	81	1263.313	+0.759	F
Si I-17	UV 50	2	19	2084.462	-1.573	V		Si II-6	UV 5	76	83	1194.096	+0.742	F
Si I-18	UV 51	2	20	2082.021	-2.229	V		Si II-7	UV 5.01	76	84	1022.698	-0.902	F
Si I-19	UV 52	2	21	2058.133	-1.030	V		Si II-8	UV 6	76	85	991.745	+0.072	F
Si I-20	UV 53	2	22	1991.853	-2.189	V		Si II-9		77	82	2618.212	-4.135	F
Si I-21	2	3	5	4102.935	-2.916	F		Si II-10		77	86	1652.411	-3.759	F
Si I-22	3	3	6	3905.521	-1.092	F		Si II-11		77	106	1249.510	+0.551	F
Si I-23	UV 82	3	15	2842.333	-3.274	V		Si II-12	1	78	82	3858.050	-0.426	F
Si I-24	UV 83	3	18	2631.282	-0.520	V		Si II-13	UV 9	78	86	2072.430	-0.045	F
Si I-25	UV 86	3	21	2532.381	-1.200	V		Si II-14	2	79	82	6355.200	+0.406	F
Si I-26	4	5	10	12045.959	+0.744	F		Si II-15	3	81	86	4129.760	+0.706	F
Si I-27	5	5	11	10789.570	+0.539	F		Si II-16	UV 17	81	91	2905.130	+0.100	F
Si I-28	6	5	12	10482.452	+0.074	F		Si II-17	UV 18	81	99	2501.570	-0.269	F
Si I-29		5	14	9768.400	-2.300	L		Si II-18	4	82	84	5971.800	+0.109	F
Si I-30	9	5	25	5800.880	-0.866	F		Si II-19	5	82	85	5051.010	+0.662	F
Si I-31	10	5	26	5698.800	-0.867	F		Si II-20	6	82	89	3337.590	-0.823	F
Si I-32	11	5	28	5653.900	-1.170	F		Si II-21	7	82	90	3207.970	-0.149	F
Si I-33	11.04	5	45	4846.646	-1.527	F		Si II-22	UV 19	82	96	2725.220	-1.272	F
Si I-34	11.06	5	48	4768.462	-1.155	F		Si II-23		83	86	5113.168	-3.514	F
Si I-35	11.12	6	8	15892.767	-0.036	F		Si II-24	7.02	85	91	7849.400	+0.735	F
Si I-36		6	11	12390.200	-1.710	L		Si II-25	7.03	85	99	5466.720	+0.213	F
Si I-37		6	12	11890.500	-2.090	L		Si II-26	7.05	85	104	4621.600	-0.144	F
Si I-38	13	6	14	10872.520	+0.309	F		Si II-27	7.12	86	97	6679.650	-1.028	F
Si I-39	14	6	16	9413.506	-0.445	F		Si II-28	7.19	87	96	7121.700	-0.642	F
Si I-40	14.01	6	24	6331.957	-3.744	F		Si II-29	7.20	87	97	6826.000	-0.042	F
Si I-41	16	6	29	5948.540	-1.234	F		Si II-30	7.21	87	102	5573.430	-1.096	F
Si I-42	17	6	30	5772.145	-1.745	F		Si II-31	7.23	87	108	4900.700	-1.418	F
F = Fuhr & Wiese (1998), L = Lambert & Luck (1978), V = VALD (Piskunov et al. 1995 ; Kurucz 1993).

while Fig. 1 shows the corresponding Grotrian diagrams.

The data for the energy levels were adopted from a compilation of Martin & Zalubas (1983) which is available from the internet server of the National Institute of Standards and Technology (NIST, http://physics.nist.gov). This source also includes some unpublished measurements. It should be mentioned that apart from LS coupling, other schemes ( $Jl(j_{\rm c} \lbrack K \rbrack ^\pi_J$), $Jj((j,J)^\pi$) were found for Si I. For consistency and practical reasons the concerned energy levels were designated to LS coupling if possible (Table 1).

Data for the line transitions used in the model atom (Table 2) were obtained from the NIST server, the Vienna Atomic Line Data Base (Piskunov et al. 1995; Kurucz 1993) and Lambert & Luck (1978). The NIST data refer to the compilation of Wiese et al. (1969) and the newer version by Fuhr & Wiese (1998). The latter provides improved transition probabilities for some line transitions.
Photoionization cross-sections were taken from the Opacity Project (Seaton et al. 1992, 1994) for almost all energy levels with the exception of eleven mostly high excited ones (marked with ^* in Table 1). In these cases the Kramers Gaunt aproximation for hydrogen-like atoms as given by Allen (1973) was used.

Figure 1: Grotrian diagrams of the silicon model atom including Si I with 75 energy levels and 53 line transitions and Si II with 40 levels and 31 transitions.

The majority of the more important electron collisional cross-sections of Si I were calculated using the tables given by Sobelman et al. (1981). Transistions not covered by the Sobelman tables were treated with the formulas compiled by Drawin (1967) but additionally needed to be scaled to the corresponding maximum cross-sections. For optically allowed transitions, the maximum cross-sections were calculated with the approximation of Van Regemorter (1962) using all available oscillator strengths and additional values from the Opacity Project. In all other cases, especially for optically forbidden transitions, the cross-sections were scaled with the collision strength formula described by Allen (1973).
Drawin (1967) also provides an estimate for collisional ionization by electrons, which was applied here, and for inelastic collisions with neutral hydrogen atoms. Cross-sections for the latter were calculated with the more generalized formula given by Steenbock & Holweger (1984). Due to a complete lack of data, the collisional parameter Q (maximum cross-section in units of $\pi\,a_0^2\,$) in this formula was set equal to the value of the respective electron collision (derived via the different approximations for optically allowed and forbidden bound-bound and bound-free collisions described above) and was additionally scaled with an empirical factor $S_{\rm H}=0.1$ (Holweger 1996).