Extended Photoionization Cross Section Calculations for C III

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This work provides high-accuracy atomic data and parameters of various model applications, such as for energy losses due to impurities in nuclear fusion, laser-based diagnostic methods, or for astrophysical plasma aimed at spectral analysis and diagnostics over a wide range of temperature and density.

Abstract

Spectral features of photoionization of various levels of C III are reported. These include characteristics of Rydberg and Seaton resonances, low and high excited levels, lifetimes, and total and partial cross sections. Calculations are performed in the relativistic Breit–Pauli R-matrix method with close-coupling approximation, including damping effects on the resonance structure associated with the core-excited states produced by the electron excitation of C IV and photoionization of C III. For bound channel contribution, the close-coupling wavefunction expansion for photoionization includes ground and 14 excited states of the target ion CIV and 105 states configurations of C III. Extensive sets of atomic data for bound fine-structure levels, resulting in 762 dipole-allowed transitions, radiative probabilities, and photoionization cross sections out of J^π = 0^± − 4^± fine-structure levels are obtained. The ground-level photoionization cross section smoothly decreases with increasing energy, showing a very narrow, strong Rydberg resonance converging to the CIV 1s²2p threshold. The work shows that prominent Seaton resonances for 2sns states with n ≥ 5, caused by photoexcitation of the core electron below the 2p threshold, visibly contribute to photoabsorption from excited states of C III. The present results provide highly accurate parameters of various model applications in plasma spectroscopy.

1. Introduction

The spectrum of the carbon atom is important for various applications, from the interstellar medium and the atmosphere of stars to the production of carbon clusters such as fullerenes, the study of energy losses due to impurities in nuclear fusion, or the development of a number of laser-based diagnostic methods. The theoretical models and numerical methods differ from magneto-hydrodynamic models (in the chromosphere [1,2]) to the modeling of the independent atom (in plasma of solar corona [3]). In the transition region the models become complex, including specific atomic processes. The emission and absorption lines of carbon ions are modeled according to the density and temperature parameters of the studied plasmas. For example, with increasing density, the dielectronic recombination role decreases [4,5]. In modeling the emission lines observed in the solar corona, this process is often ignored, considering that photoionization (PI) does not affect the diagnosis [6].

CIII consists of 70 LS-coupled levels ranging up to n = 9 and l = 2, with fine-structure levels being available from the web-based compilation table of the National Institute of Standards and Technology (NIST) [7]. The interaction of carbon ions with electrons and photons was modeled in non-relativistic and relativistic approaches [8,9,10,11]. Fourteen members, including C III, of the Be isoelectronic series [12] have been studied using the semi-relativistic Breit–Pauli R-matrix method [13]. Experimental and theoretical data were collected and critically evaluated by the Opacity Project team [14], Harris and Kramida [15], Wiese and Fuhr [16,17], and Li et al. [18]. Recently, the theoretical models and numerical methods used in the opacity calculation have been re-examined [19] along with the hierarchy of approximations adopted in the R-matrix methodology to check the accuracy of data. The ab initio R-matrix Floquet method (RMF) was also used to include, non-perturbatively, radiative damping effects of electron scattering on CIII [20,21,22,23]. Among the existing theoretical BPRM computations for electron excitation with C II and CIII, notable references exist in the literature [24,25,26,27,28]. Although a considerable amount of research has been conducted on carbon and its ions, there is still a need for extended sets of theoretical transition data.

The objective of this work is to complete the existing reported radiative and autoionization datasets with new photoionization (PI) and photoabsorption (PA) cross sections for CIII. The spectral features of the photoionization on the ground level in CIII at photon energy below the 2p_3/2 ionization threshold, with complex resonances, have been obtained, and associated resonances were delineated. This study entails fine-structure atomic data calculation for 488 levels, their radiative transition probabilities and weighted oscillator strengths, autoionizing resonances belonging to two Rydberg series, and their associated parameters. The photoionization cross sections for all 488 fine-structure levels were obtained in length and velocity gauges. Results show that the 2p4d ¹P level is the lowest autoionizing resonance as obtained from quantum defect calculation. After a careful survey of the existing literature, we found that none of the published articles report fine-structure photo-absorption or photorecombination calculations for C III out of the 2s5s ¹S excited state. The present work shows that the contributions from associated bound–bound excitation and the bound-free processes on the photorecombination energy profile in the vicinity of 2pnd ¹P^o₁ autoionizing resonances, as an example, are not comparable in magnitude, even for this simple system.

2. Computation Methods and Results

2.1. Atomic Structure Calculation

The present work is similar to the use of the R-matrix method for calculating photoionization cross sections of various atoms and ions. The calculation has been performed based on the well-known Breit–Pauli R-matrix numerical method (BPRM). Details of the theoretical background for the R-matrix method, photoionization, and the BPRM suite of codes can be found, for example, in refs. [29,30,31,32,33].

Two sets of theoretical calculations were performed to check the validity of our atomic structure model. The SUPERSTRUCTURE (SS) [30,31] has been used to calculate orbital parameters, λ_nl, variationally determined by optimizing the weighted sum of the term energies. The first model includes nine 1s² nl (n = 2–4, l = s, p, d, f) target states, represented in terms of ten orthonormal basis orbitals. At this stage we used the scaling parameters obtained by the Opacity Project team [34]. The (N + 1)–electron correlation for CIII includes all possible configurations with 2s²,2p²,3s²,3p²,3d² and 4s,4p,4d,4f. The second model calculation extends the first one to construct accurate wavefunctions of the N-electron target states belonging to C IV. Fifteen orthogonal, one-electron orbitals nl (n = 1–5, l = 0–4) were used. The values of the scaling parameters obtained following the minimization procedure are shown in

Table 1. Values of the adjustable parameters used in SUPERSTRUCTURE to compute the one-electron orbitals.

orb	1s	2s	3s	4s	5s	2p	3p	4p
λ	1.2898	0.9946	0.9842	0.9842	1.0000	0.8702	0.8667	8.1200
orb	5p	3d	4d	5d	4f	5f	5g
λ	1.0000	0.7898	48.120	1.0000	1.1600	1.0000	1.0000

.

Table 2. Models of calculation.

Bound Orbitals Included	N-electron Configuration Data Symmetries  Couplings	(N + 1)-electron configuration data Symmetries Couplings
10	4   9	22   173
15	5   14	30   488

presents the configuration data included in the two calculation models. The maximum total angular momentum L for the (N + 1)-electron LS-coupling Hamiltonian was set to 6 in the first model and at 8 in the second one. This enables the computation up to J = 5.

The R-matrix calculations were carried out in the intermediate coupling scheme by including the spin–orbit interaction terms of the Breit–Pauli Hamiltonian. The number of continuum basis orbitals used to express the wavefunction in the inner region of the R-matrix code was varied between 20 and 35, and the results were analyzed. We noticed that increasing the number of basic functions does not necessarily improve the results. It was decided to use 30 continuum basis orbitals in all calculations. The effect of varying the size of the R-matrix inner region radius has been investigated, and a value of 17.8 atomic units was chosen for numerical stability and convergence. The maximum LS-coupling Hamiltonian matrix size was about 400 in the first model calculation, and these LS-coupling symmetries give rise to J-resolved matrices of order 1470. The intermediate coupling calculations were carried out on recoupling the LS symmetries in a pair-coupling representation in stage RECUPD. The (e + ion) Hamiltonian matrix was diagonalized for each resulting J^π in STGH. The fine, structure-bound levels were sorted through the poles in the (e + ion) Hamiltonian with a fine mesh of effective quantum number ν. The mesh of 0.00002 has been used in the calculation. Figure 1 shows, for completeness, the percentage difference between calculated and experimental C IV target level energies. Both models indicate the 2p state energy of C IV at 0.59 Ryd above the ground with a relative discrepancy of ±1.05 percent with respect to the NIST value [35]. Comparing the present results with the observed values, despite the 1.05 percent difference found for 1s²2p levels, we found that overall, the average percent difference across the corresponding NIST J^π symmetries was up to 0.12 percent. We adopted these results for the scattering calculation. As a measure of the accuracy of the wavefunction and energy values, the transition probabilities have also been considered. The calculated and experimental A-values (in s⁻¹) were plotted in Figure 2 on a logarithmic versus logarithmic scale to incorporate the various magnitudes of results.

The intermediate coupling frame transformation approach entails transforming unphysical S- or K-matrices (within the framework of the multichannel quantum defect theory) to a jK-coupling scheme [36]. In the external R-matrix region, the code STGB is used to identify the J-resolved bound states of Be-like Carbon, which lie below the Li-like ground state.

Table 3. Energies of bound 1s²2snl and 1s²2pnl (n < 10) for J = 0^e and 1^o levels, in cm⁻¹ relative to the C IV 1s²2s ground state in the present BPRM calculation (the second column), to be compared with those obtained from the Breit–Pauli R-matrix plus pseudo-state (RMPS) close-coupling calculation [28] (the fourth column). The corresponding effective quantum numbers, n_eff, are indicated in the third and fifth columns, respectively. In the sixth and seventh columns are presented, respectively, the energies relative to the CIII 1s²2s² ground state, as output from the present BPRM calculation and the NIST values. The percentage difference relative to the NIST database [35] is shown in the 8th column.

J = 1o Levels	E (cm−1) Relative to 1s22s BPRM	neff	E (cm−1) Relative to 1s22s RMPS	neff	E (cm−1) Relative to 1s22s2 BPRM	E (cm−1) Relative to 1s22s2 NIST	% (cm−1)
$1{\mathrm{s}}^{2}2\mathrm{s}2\mathrm{p} {}^{3}P_1^o$	−332,894.8 894.8	1.7224	−333,688	1.7204	52,694	52,390.75	5.78−03
$2\mathrm{s}2\mathrm{p} {}^{1}P_1^o$	−281,386.5 386.5	1.8734	−283,424	1.8667	104,202.9	102,352.04	1.80−02
$2\mathrm{s}3\mathrm{p} {}^{1}P_1^o$	−126,926.2 926.2	2.7894	−127,216	2.7863	258,663.2	258,931.29	−1.03−03
$2\mathrm{s}3\mathrm{p} {}^{3}P_1^o$	−126,257.9 257.9	2.7944	−126,437	2.7944	259,331.5	259,711.22	−1.46−03
$2{\mathrm{p}}_{1/2}3\mathrm{s} {}^{3}P_1^o$	−77,205.0	2.6340	−75,905	2.6316	308,384.4	308,248.91	4.39−04
$2\mathrm{s}4\mathrm{p} {}^{1}P_1^o$	−75,682.4	3.6123	−75,905	3.6072	309,916.0	310,006.32	−2.91−04
$2\mathrm{s}4\mathrm{p} {}^{3}P_1^o$	−68,314.3	3.8021	−68,379	3.005	317,275.0	317,796.51	−1.64−03
$2{\mathrm{p}}_{2/3}3\mathrm{s} {}^{3}P_1^o$	−63,214.4	2.7727	−63,507	2.7693	322,375.0	322,404.20	−9.05−05
$2{\mathrm{p}}_{1/2}3\mathrm{d} {}^{3}D_1^o$	−47,789.8	2.9572	−47,947	2.9548	337,799.6	337,655.98	4.25−04
$2\mathrm{s}5\mathrm{p} {}^{1}P_1^o$	−42,679.1	4.8103	−42,781	4.8050	342,910.3	343,258.03	−1.01−03
$2\mathrm{s}5\mathrm{p} {}^{3}P_1^o$	−41,758.4	4.8631	−41,850	4.8581	343,831.4	344,236.29	−1.17−03
$2{\mathrm{p}}_{3/2}3\mathrm{d} {}^{1}P_1^o$	−38,599.4	3.0839	−38,652	3.0827	346,990.0	346,712.73	7.99−04
$2\mathrm{s}6\mathrm{p} {}^{3}P_1^o$	−28,614.3	5.8748	−29,185	5.8175	356,975.0	357,050.17	−2.10−04
$2\mathrm{s}6\mathrm{p} {}^{1}P_1^o$	−21,305.56	5.9068	−29,122	5.8238	364,283.8	357,109.68
$2\mathrm{s}7\mathrm{p} {}^{1}P_1^o$	−21,882.3	6.8083	−21,346	6.8023	363,707.1	364,896.0	−3.25−03
$2\mathrm{s}7\mathrm{p} {}^{3}P_1^o$	−21,247.4	6.8176	−21,274	6.8138	364,342.0	-
$2\mathrm{s}8\mathrm{p} {}^{1}P_1^o$	−16,279.5	7.7887	−16,313	7.7814	369,309.9	369,926.0	−1.66−03
$2\mathrm{s}8\mathrm{p} {}^{3}P_1^o$	−16,167.2	7.8157	−16,187	7.8115	369,422.2	-
$2\mathrm{s}9\mathrm{p} {}^{1}P_1^o$	−12,863.9	8.7619	−12,893	8.7526	372,725.5	-	-
$2\mathrm{s}9\mathrm{p} {}^{3}P_1^o$	−12,712.8	8.8138	−12,728	8.8087	372,876.6	-	-
$2{\mathrm{p}}_{1/2}4\mathrm{s} {}^{3}P_1^o$	−9200.3	3.6448	−9258	3.6426	376,389.4	376,299.2	2.39−04
$\mathrm{Last} \mathrm{bound} 2{\mathrm{p}}_{3/2}4\mathrm{s} {}^{1}P_1^o$	−66,240	3.7070	−7566	3.6821	319,349.4	-
$2{\mathrm{s}}^2 {}^{1}S_0^e$	−385,589.4	1.6003	−386,147	1.5993	0.000000	0.00000
$2{\mathrm{p}}^2 {}^{3}P_0^e$	−246,470.8	1.7802	−248,378	1.7748	139,118.6	137,454.40	1.21−02
$2{\mathrm{p}}^2 {}^{1}S_0^e$	−198,825.0	1.9342	−202,090	1.9223	186,764.4	182,519.88	2.32−02
$2\mathrm{s}3\mathrm{s} {}^{1}S_0^e$	−138,703.8	2.6683	−139,069	2.6649	246,885.6	247,170.26	−1.15−03
$2\mathrm{s}4\mathrm{s} {}^{1}S_0^e$	−74,453.1	3.6420	−74,495	3.6411	311,136.3	311,721.51	−1.87−03
$2{\mathrm{p}}_{1/2}3\mathrm{p} {}^{3}P_0^e$	−55,379	2.8626	−55,982	2.8551	330,209.6	329,685.38	1.59−03
$2\mathrm{s}5\mathrm{s} {}^{1}S_0^e$	−47,302.3	4.5692	−47,396	4.5649	338,287.1	338,514.33	−6.71−04
$2{\mathrm{p}}_{3/2}3\mathrm{p} {}^{1}S_0^e$	−39,774.1	3.0666	−40,492	3.0557	345,815.3	345,095.43	2.08−03
$2\mathrm{s}6\mathrm{s} {}^{1}S_0^e$	−30,404.6	5.6992	−30,523	5.6884	355,184.8	-
$2\mathrm{s}7\mathrm{s} {}^{1}S_0^e$	−22,187.3	6.6716	−22,232	6.6653	363,402.1	-
$2\mathrm{s}8\mathrm{s} {}^{1}S_0^e$	−17,045.1	7.6611	−16,852	7.6557	368,544.3	-
$2\mathrm{s}9\mathrm{s} {}^{1}S_0^e$	−13,185.5	8.6544	−13,203	8.6494	372,403.9	-
$2\mathrm{s}10\mathrm{s} {}^{1}S_0^e$	−10,606.7	9.6444	−10,619	9.6444	374,982.7
$$\begin{gathered} \mathrm{Last} \mathrm{bound} \\ 2{\mathrm{p}}_{1/2}4\mathrm{p} {}^{3}P_0^e \end{gathered}$$	−1206.1	3.8582	−1165	3.8584	384,383.3	384,345.00	9.96−05
2s1/2	0	∞	0	∞	385,589.4	386,241.0	1.68−03

shows the comparison with other theoretical calculation results on some bound states 1s²2snl and 1s²2pnl (n < 10) for J = 0^e and 1^o levels, in cm⁻¹. Results are provided relative to the C IV 1s²2s ground states when compared with the Breit–Pauli R-matrix plus pseudo-state close-coupling calculation (RMPS) [28], and relative to the C III 1s²2s² ground state when compared to NIST listing [35]. Compared to previous theoretical works and to the NIST listing, it can be seen that the present theoretical results determined via the Breit–Pauli R-matrix method show very good agreement. Uncertainty in the energy determination in the present work has been reduced by almost an order of magnitude with the use of suitable correlated target and scattering wavefunctions.

2.2. Photoionization and Photoabsorption Cross Sections

The numerical evaluation of photoionization and photoabsorption cross sections has been performed, accounting for the modifications suggested in refs. [37,38,39,40] to include the type I damping case. According to this, we considered the inner-region damping involving radiative decay to a bound state for which all orbitals are completely contained within the R-matrix box. The damping effect is responsible for the separation between photoionization and photoabsorption cross sections. Detailed spectral features in photoionization of the ground and excited bound fine structure levels, 488 in total, were obtained. Photoionization features included Rydberg resonances formed by the 1s²2pns (¹P₁^o) and 1s²2pnd (¹P₁^o) quasi-bound autoionizing states, Seaton resonances formed at dipole allowed excitation energies of the core ion, the impact of the channel couplings in fine structure, background cross section, and interference effects among them in photoionization cross sections. Convergence of resonances is illustrated as a further indication of weakening of resonances with increasing core ion excitation energy, and their merging on the background cross section indicates that the wave function expansion has been achieved. The code uses a multi-channel quantum defect theory approach within the asymptotic R-matrix codes STGF and STGBF. The photoionization cross section on the ground level 1s²2s² is presented in Figure 3.

The feature in Figure 3 is typical for a ground state with a strong background cross section and 1s²2pnp (n ≤ 10) J = 0^e resonance structures converging to CIV 1s²2p thresholds. Target representations listed in Table 1 were used. The compressed set of resonances at the ionization threshold of about 0.58 Ry is formed through the coupling of fine structure channels. Resonances are delineated and resolved as follows. Figure 4 represents the 2pnp Rydberg series of resonances in the photoionization of the CIII 1s²2s² ground state.

The length and velocity results, including the 2s and 2p open channels, are presented as a further indication of the accuracy of the calculation. Figure 5 shows the partial photoionization cross sections (in length and velocity gauge) out of the (a) 1s²2s2p ³P₁^o and (b) 1s²2s2p¹P₁^o levels, respectively, as a function of the photon energy above the ground state of C III.

Figure 6 presents the photoionization spectra from 2s5s (¹S^e) and 2p3p (¹S^e) of CIII, the dominant contribution of 2pnd ¹P₁^o configurations, and the clearly visible 2pns (¹P^o) autoionizing series. The cross section of the 2p_3/25s (¹P^o₁) resonances is substantially reduced in the 2p_3/23p ¹S^e photoionization spectrum, while other 2pnd (¹P^o₁) and 2pns (¹P^o₁) remain strong. The ratios of the 2p_3/2n (n ≥ 5) d (¹P^o₁) peak photoionization cross sections between 2p3p (¹S^e) and 2s5s(¹S^e) spectra are approximately 2.36, which is close to the ratio of 2.6 between the 2p3p components in the 2p3p ¹S and 2s5s ¹S initial state [41]. Looking at the cross section ratios as functions of photon energy, we note that, due to the interchannel coupling which falls off with increasing energy, the features of all np and nd photoionization cross sections are independent of l for l > 0 and σ_nl (ω) ~1/ω^9/2, in agreement with ref. [42].

Compared to the ns, the σ_nl/σ_{(n − 1) l} ratios remain constant with energy, while σ_ns/σ_{(n − 1) s} ratios decrease with energy and become constant with higher energy. For higher 2sns ¹S bound excited states with small 2pnp mixing, the photoionization is dominated by 2s-2p core excitation, followed by the shake-up of the outer ns electron, similar to the two-electron excitation of the core. Photorecombination cross sections of 2sns levels have been detailed in our earlier work [23], together with resonance quantum defects.

Figure 7 represents (on a semi-logarithmic scale) the photoionization and the photo-absorption cross section (in Mb) versus photon energy (in Ry) out of the 2s5s ¹S level. The calculation has been performed based on the Hickman–Robicheaux theory [42,43] and computed by STGBF0DAMP.

2.3. Resonant Widths and Lifetime of Resonant Transitions

Various experimental methods [44,45,46] have been developed for the measurement of radiative lifetimes in atoms. On the theoretical side, large scale calculations based on the configuration interaction (CIV3) [47], multiconfiguration Hartree–Fock (MCHF) [48], and multiconfiguration Dirac–Fock (MCDF) [49] methods, or the relativistic many-body theory [50] have shown that the agreement between the lengths and velocity gauges cannot be uniquely used for the accuracy assessment.

The strong cancellations (up to three orders of magnitude) in the relativistic transition amplitudes between the 2s − 2p_1/2 and 2s − 2p_3/2 matrix elements in the LS-coupling limit ([51] and references therein]) justify the difficulty of the transition rate calculations for the 2s²(¹S) − 1s²2s2p³P₁^o. For CIII, due to the fact that the 1s²2s2p¹P₁^o state decays rapidly to the ground state C III 2s²(¹S), in contrast to the long lifetime of the C III 2s2p ³P₁^o, the 1s²2s2p¹P₁^o resonance lifetime is defined by its line strength. In R-matrix approaches, in the absence of measured values for physical quantities, one normally shifts the ab initio energies to the experimental or observed energy levels in the diagonalization of the Hamiltonian. This procedure provides a better positioning of resonance features in the corresponding cross sections.

Table 4. Electric-dipole weighted oscillator strength in length gauge, gf^l, for the 2s²(¹S)-, 1s²2s2p¹P₁^o-, 2s²(¹S)-, and 1s²2s3p ¹P₁^o-allowed transitions and lifetime (ns). Comparison with experiments and other theoretical calculations.

2s2(1S) − 1s22s2p1P1o Source     gfl	2s2(1S) − 1s22s3p 1P1o Source     gfl
Experiment	Experiment
Reistad et al. [46]     0.754	NIST       0.232
Jönsson et al. [52]       0.760	Curtis et al. [53]    0.1979
Reistad and Martison [54]   0.753
Theory	Theory
Present         0.767	Present         0.231
Glass [47]         0.796	Sofronova et. al. [50]    0.267
Mitnik et al. [55]      0.787	Froese-Fischer [48]     0.241
Jönsson and F Fischer [49]   0.757	Tachiev, Fischer [27]     0.240
Source       lifetime(ns)	Source       lifetime(ns)
Experiment	Experiment
Reistad et al. [46]     0.57 ± 0.02	Curtis and Ellis [56]     0.28
Chang M.-W. [55]     0.50
Others        0.66
Curtis and Ellis [56]     0.572
Wisse et.al. [57]     0.53
Theory	Theory
Present          0.5399	Present           0.290
Glass [47]         0.559	Tachiev, Fischer [27]       0.251
Tachiev, G.; F-C. Fischer [27]  0.5651	K. M. Aggarwal, F. P. Keenan [58]  0.265
K. M. Aggarwal, F. P. Keenan [58] 0.4648

presents a comparison of experimental and theoretical values of the weighted oscillator strengths in length gauge (gf^l) and a lifetime calculation for the 2s^{2 1}S^e − 1s²2s2p ¹P₁^o- and 2s^{2 1}S^e − 1s²2s3p ¹P₁^o-allowed transitions.

Table 5. Comparison of calculated resonant widths (Γ in Ry) of 2pns ¹P^o and 2pnd ¹P^o autoionizing states of C III (a^b reads a × 10^b).

State 2p3/2 ns (1Po)	Γ(Ry) Ref. [54]	Γ(Ry) Ref. [28]	Γ(Ry) Present	State 2p3/2 nd (1Po)	Γ(Ry) Ref. [55]	Γ(Ry) Ref. [29]	Γ(Ry) Present
5	9.57−03	1.04−02	1.028−02	4	3.07−03	3.82−03	3.56−03
6	5.09−03	5.43−03	5.95−03	5	1.63−03	2.13−03	1.69−03
7	3.07−03	3.23−03	3.60−03	6	9.52−04	1.32−03	1.11−03
8	1.99−03	2.057−03	1.98−03	7	6.05−04	8.08−04	6.94−04
9	1.36−03	1.39−03	1.60−03	8	4.06−04	5.878−04	4.607−04

presents the comparison of calculated resonant widths of a few selected doubly excited 2pns ¹P₁^o and 2pnd ¹P₁^o autoionizing states of C III below the ²P_3/2 threshold. The energies for the 2pns ¹P^o, 2pnd ¹P^o, and 2pnp ¹S^e Rydberg states, as output from combining the quantum defect theory and the R-matrix code, were previously reported in ref. [22]. In the present report, we adopt an approach described by Sakimoto et al. [59], which entails fitting the dipole matrix elements obtained from the scattering calculation.

3. Discussion

We report an extensive and elaborate theoretical study of atomic properties for CIII. We have applied systematic methods to the computation of transition data and photoionization cross sections. This study implies the electron-impact excitation of C IV and photoionization of CIII. For the electron impact excitation, we concentrated on 105 transitions from 15 target levels, finding 5929 collision strengths. The photoionization calculation of CIII has been computed for ground and excited states, accounting for radiative and Auger damping. We find good agreement in the calculated weighted oscillator strengths with the experiment. The unified approach of the R-matrix method in intermediate coupling, with and without damping, allowed us to examine in detail not only the individual structure of the autoionizing doubly excited states, but also collectively in the autoionization series. The resonances appearing for photoionization of C III 2s^{2 1}S ground states at 3.51 Ry, below the photoionization threshold of metastable states at 3.62 Ry, shown in Figure 3, are associated with the photoionization of 1s²2s2p ¹P^o metastable state. The resonances appearing within the 3.62 Ry and 4.1Ry photon energy range are caused by the photoionization of the C III 2s^{2 1}S ground state. Two autoionizing series, 2pns¹P^o and 2pnd ¹P^o, are discernible. The relative contribution of the strong 2pnd ¹P^o autoionizing resonances and the highly excited Rydberg states, such as 2sns ¹S^e and 2p_3/2 np ¹S^e has been presented in Figure 5. These results show very strong 2p5s ¹P^o₁ −2s5s ¹S^e photoionization, compared to the less accurate results obtained in the earlier calculation [22]. This cross section is substantially reduced in the photoionization spectrum given in Figure 5b. The calculated resonant widths and lifetimes of resonant transitions are very close to the other theoretical results. Figure 7 confirms atomic data calculation with respect to the 2p4d ¹P level, which appears as the lowest autoionizing resonance level.

The energy dependence profile of the photoabsorption cross section in the vicinity of 2pnd ¹P^o₁ autoionizing resonances shown in Figure 7 indicates that the contribution from associated bound–bound excitation and the bound–continuum processes are not comparable in magnitude. Present lifetime calculated values come closest to the experimental ones for 2s²(¹S) − 1s²2s2p¹P₁^o and 2s^{2 1}S − 1s²2s3p ¹P₁^o, 0.5399 compared to 0.53 [52], and 0.2902 compared to 0.28 [54], respectively. The position of these resonances is completely consistent with a previous well-known description of a strongly coupled two-level system [21,22].

This study provides accurate atomic data based on the BPRM methodology. The present results for CIII and other ions [60] provide a model [61] for atomic spectroscopy aimed at spectral analysis and population transfer in atoms or ions in an external radiation field. With the advance of laser technologies, population transfer due to quantum interference studied in closed systems [62,63,64,65] becomes possible for open systems, such as CIII [66].