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The Astrophysical Journal, 750:65 (7pp), 2012 May 1 C 2012.

doi:10.1088/0004-637X/750/1/65

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COLLISION STRENGTHS AND EFFECTIVE COLLISION STRENGTHS FOR TRANSITIONS WITHIN THE GROUND-STATE CONFIGURATION OF S iii C. E. Hudson, C. A. Ramsbottom, and M. P. Scott Department of Applied Maths and Theoretical Physics, The Queen’s University of Belfast, Belfast BT7 1NN, UK; [email protected], [email protected], [email protected] Received 2011 April 14; accepted 2012 February 20; published 2012 April 17

ABSTRACT We have carried out a 29-state R-matrix calculation in order to calculate collision strengths and effective collision strengths for the electron impact excitation of S iii. The recently developed parallel RMATRX II suite of codes have been used, which perform the calculation in intermediate coupling. Collision strengths have been generated over an electron energy range of 0–12 Ryd, and effective collision strength data have been calculated from these at electron temperatures in the range 1000–100,000 K. Results are here presented for the fine-structure transitions between the ground-state configurations of 3s2 3p2 3 P0,1,2 , 1 D2 , and 1 S0 , and the values given resolve a discrepancy between two previous R-matrix calculations. Key words: atomic data – atomic processes Online-only material: color figures, Supplemental data file (tar.gz)

effective collision strengths for transitions within the first five fine-structure levels of S iii, i.e., those arising from the groundstate configuration of 3s2 3p2 , and compare with the data given in Galav´ıs et al. (1995) and Tayal & Gupta (1999).

1. INTRODUCTION Observations have been reported recently by Rubin et al. (2008) for emission lines of several ions, including S iii, in a number of Galactic H ii regions using the Spitzer Space Telescope. From these, ionic abundance ratios have been determined and the Ne/S ratio estimated. Rubin et al. (2008) compare data from Spitzer observations from other groups (Lebouteiller et al. 2008; Wu et al. 2008) and determine that their derived ratios are somewhat higher than those obtained by the other groups. Rubin et al. (2008) attribute some of the variation to the use of differing atomic data in the form of effective collision strengths and note that between the two most recent sets of atomic data there exists a large discrepancy. In the infrared region where these Spitzer observations have been taken, the S iii emission line used as diagnostic is the 3s2 3p2 3 P1 −3s2 3p2 3 P2 transition at 18.71 μm, and at the temperature used for the diagnostic work (10,000 K) there exists a large discrepancy between the atomic data of Galav´ıs et al. (1995) and that of Tayal & Gupta (1999). The work of Galav´ıs et al. (1995) was performed as part of the IRON Project (Hummer et al. 1993) and was a 17-state R-matrix calculation. Tayal & Gupta (1999) also performed an R-matrix calculation and employed 27 states. Both of these calculations were performed in LS coupling with data for the fine-structure effective collision strengths created by transforming the LS-coupled K-matrices to an intermediate coupling scheme. Rubin et al (2008) also note that for all three of the infrared transitions between the fine-structure levels in the 3s2 3p2 3 P ground state the effective collision strengths of Galav´ıs et al. (1995) and those of Tayal & Gupta (1999) exhibit different behavior in shape, as well as differing in magnitude, and suggest that it would be worthwhile to resolve these differences. In the current work we have performed a new R-matrix calculation with 29 LS states, and utilized the parallel R-matrix package RMATRX II which has recently been extended to allow for the inclusion of relativistic effects. These codes have been exploited by Cassidy et al. (2010) and Wasson et al. (2010) for the electron impact excitation of the Fe-peak ions Ni ii and Cr ii. We present in this paper the collision strengths and

2. TARGET DESCRIPTION Configuration interaction wavefunctions for the 29 LS target states used in this calculation were constructed using the CIV3 code of Hibbert (1975). These are all the states arising from the six configurations of the form 3s2 3p2 , 3s3p3 , 3s2 3p3d, 3s2 3p4s, 3s2 3p4p, and 3s2 3p4d. Each target-state wavefunction Ψ is represented by a linear combination of single-configuration functions Φi , each of which has the same total LSπ symmetry as the target state: Ψ(LS) =

m

ai Φi (αi LS).

(1)

i=1

The Φi in Equation (1) are constructed from a set of one-electron orbitals. The αi represent the coupling of the angular momenta associated with these one-electron spin orbitals to form the total L and S. The mixing coefficients ai are determined by the CIV3 code and are eigenvector components of the Hamiltonian matrix having particular LSπ symmetry. The Hamiltonian matrix elements are defined as Hij = Φi | H | Φj ,

(2)

where H denotes the Hamiltonian operator. The one-electron orbitals used to construct the Φi each consists of a radial function, a spherical harmonic, and a spin function: unlml ms (r, σ ) =

1 Pnl (r)Ylml (θ, φ)χms (σ ). r

(3)

These orbitals are chosen to be analytic, with the radial part being expressed as Pnl (r) = cj nl r Ij nl exp(−ζj nl r)., (4) j

1

The Astrophysical Journal, 750:65 (7pp), 2012 May 1

Hudson, Ramsbottom, & Scott

have been generated by allowing a one-electron replacement on the target states, as well as adding the pseudostate 3s2 3p5d. The energy levels obtained for the 29 LS target states are given in Table 3 and are compared to the values in the NIST database (Ralchenko et al. 2008). The LS energies given by Galav´ıs et al. (1995) are also displayed in Table 3, and we show the difference between the NIST values and the two calculations in parentheses. We find that the energies of Galav´ıs et al. (1995) are slightly better for the first few excited levels, but from level 7 onward, the current work exhibits an improvement.

Table 1 Orbital Parameters nl

cjnl

Ijnl

3d

5.75028 2.36474 1.32063

3 3 3

0.02926 0.28535 0.76009

4s

12.75127 5.31881 2.40583 1.23858

1 2 3 4

0.05828 −0.22358 0.62896 −1.12691

4p

6.32733 2.02135 1.11067

2 3 4

0.14361 −0.60405 1.15001

4d

1.77895 0.77232

3 4

0.48414 −1.03968

5d

1.59350 1.07245 1.04504

3 4 5

1.59057 −4.85498 3.79767

ζj nl

3. SCATTERING CALCULATION Using the orbital parameters derived, the scattering calculation was carried out using the RMATRX II suite of codes in the internal region (see Burke et al. 1994 and references within). These codes comprise three main stages: RAD computes the radial integrals, ANG computes the angular integrals, and these are combined in HAM to form the Hamiltonian matrix elements. Up to this point the calculation is performed in LS coupling, and via the code FINE (V. M. Burke 2010, private communication) the relativistic fine-structure effects are included. In FINE the R-matrix in LS coupling at energy E is transformed into an R-matrix in pair coupling. However, rather than performing this transformation for each energy, the energy-independent surface amplitudes are transformed at the R-matrix boundary. Thus, the re-coupling is carried out only once for each LSπ and J π symmetry instead of at each energy. FINE also takes account of the term splitting in the target by employing the term coupling coefficients which are the mixing coefficients for the individual Li Si πi states forming a Ji π state. Compared to other transformation methods, the advantage of this method allows us to include some fine-structure channels in the external region since the transformation occurs earlier on the R-matrix boundary as opposed to the asymptotic boundary. This method also allows the complex configuration–interaction wavefunctions representing the target model to be included in the internal region where LS coupling is used. In the external region, the parallel PSTGF program (Ballance & Griffin 2004) was used. In the current work, we have incorporated 29 LS states which give rise to 53 fine-structure levels. The energies of these levels are adjusted to the observed values from the NIST database to ensure that all the target-state thresholds lie in their correct positions. Table 4 displays these values and assigns a “J-index” which orders the levels according to their fine-structure energies. The 53 jj-level calculation includes all (N + 1) partial waves with angular momentum 2J 15 for all even and odd parities. For all the transitions, the contributions coming from each partial

In this expression, for each orbital the powers of r (Ijnl ) are kept fixed and the coefficients cjnl and exponents ζj nl are treated as variational parameters which are optimized by the CIV3 code. In describing the target states (Ψ) arising from our set of six configurations, nine “1real” one-electron orbitals are required—1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d. To these, a 5d pseudoorbital was added to allow for correlation effects. Hartree–Fock values were adopted for the 1s, 2s, 2p, 3s, and 3p orbitals (Clementi & Roetti 1974) and the remaining orbitals were optimized in the following way. 1. The 3d was optimized on the energy of the 3s2 3p3d 1 Do state and we found increasing the flexibility of this orbital by adding extra Ijnl terms in the expansion improved the energy levels obtained (see Equation (4)). 2. A 4s orbital was optimized on the energy of the 3s2 3p4s 3 Po state; the 4p orbital was optimized on the 3s2 3p4p 1 P level. 3. The 4d was optimized using the 3s2 3p4d 3 Fo level and the pseudo-orbital 5d was optimized on the energy of the 3s2 3p3d 1 Do state using the four configurations [3s2 ] 3p3d, 3p4d, 3p5d, 3p3 . The resulting orbital parameters are shown in Table 1. In addition to the target-state configurations, we expand the set of configurations Φ used in Equation (1) to include the configuration–interaction terms listed in Table 2 which

Table 2 Configurations Used Configurations Target States 3s2 3p2 , 3s3p3 , 3s2 3p3d, 3s2 3p4s, 3s2 3p4p, 3s2 3p4d Additional Configuration–Interaction Terms 3s2 3d2 , 3s2 3d4s, 3s2 3d4p, 3s2 3d4d, 3s2 4s2 , 3s2 4s4p, 3s2 4s4d, 3s2 4p2 , 3s2 4p4d, 3s2 4d2 3s3p2 3d, 3s3p2 4s, 3s3p2 4d 3s3p3d2 , 3s3p3d4s, 3s3p3d4p, 3s3p3d4d, 3s3p4s2 , 3s3p4s4p, 3s3p4s4d 3s3p4p2 , 3s3p4p4d, 3s3p4d2 3p3 3d, 3p3 4s, 3p3 4p, 3p3 4d 3p4 Also 3s2 3p5d

2


Hudson, Ramsbottom, & Scott Table 4 Fine-structure Energy Level Identifiers in Rydbergs

Table 3 LS Energy Levels in Rydbergs for the Current Work and that of Galav´ıs et al. (1995) Compared to Those from NIST J Index LS Index 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Level

NIST

3s2 3p2 3 Pe 3s2 3p2 1 De 3s2 3p2 1 Se 3s3p3 5 So 3s3p3 3 Do 3s3p3 3 Po 3s2 3p3d 1 Do 3s2 3p3d 3 Fo 3s3p3 1 Po 3s3p3 3 So 3s2 3p3d 3 Po 3s2 3p4s 3 Po 3s2 3p3d 3 Do 3s2 3p4s 1 Po 3s3p3 1 Do 3s2 3p3d 1 Fo 3s2 3p3d 1 Po 3s2 3p4p 1 Pe 3s2 3p4p 3 Do 3s2 3p4p 3 Pe 3s2 3p4p 3 Se 3s2 3p4p 1 De 3s2 3p4p 1 Se 3s2 3p4d 3 Fo 3s2 3p4d 1 Do 3s2 3p4d 3 Do 3s2 3p4d 3 Po 3s2 3p4d 1 Fo 3s2 3p4d 1 Po

0.0000 0.0981 0.2424 0.5295 0.7609 0.8948 0.9440 1.1112 1.2419 1.2530 1.2991 1.3341 1.3407 1.3472 1.3798 1.4311 1.4906 1.5217 1.5466 1.5713 1.5808 1.6077 1.6603 1.8645 1.8643 1.8790 1.8903 1.9190 1.9408

Current 0.0000 0.1229 0.2594 0.4721 0.7351 0.8779 0.9362 1.1306 1.2940 1.2778 1.3165 1.3592 1.3831 1.3587 1.4303 1.4881 1.5527 1.5251 1.5527 1.5752 1.5858 1.6264 1.7079 1.8719 1.8732 1.8906 1.8977 1.9420 1.9532

(0.0000) (0.0248) (0.0170) (−0.0574) (−0.0258) (−0.0169) (−0.0078) (0.0194) (0.0521) (0.0248) (0.0174) (0.0251) (0.0424) (0.0115) (0.0505) (0.0570) (0.0621) (0.0034) (0.0061) (0.0039) (0.0050) (0.0187) (0.0476) (0.0074) (0.0089) (0.0116) (0.0074) (0.0230) (0.0124)

Galav´ıs et al.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

0.0000 (0.0000) 0.1165 (0.0184) 0.2601 (0.0177) 0.4912 (−0.0383) 0.7562 (−0.0047) 0.8930 (−0.0018) 0.9584 (0.0144) 1.1364 (0.0252) 1.3023 (0.0604) 1.2945 (0.0415) 1.3364 (0.0373) 1.3620 (0.0279) 1.3809 (0.0402) 1.3999 (0.0527) 1.4484 (0.0686) 1.5189 (0.0878) 1.5899 (0.0993) ... ... ... ... ... ... ... ... ... ... ... ...

Note. Values in parentheses give the difference from NIST.

wave were monitored, with particular attention being paid to the transitions of interest here, i.e., those within the ground-state configuration of 3s2 3p2 . We find that the major contributions are from the 2J = 5, 7, 9 symmetries and that by 2J = 11 the contributions have fallen off significantly—for 2J = 11 only a few percent more is added at most for the transitions of interest and only for some of the temperatures. Thus, for this work, which focuses on the forbidden transitions within the groundstate configuration, we have considered contributions beyond 2J = 15 to be negligible. For allowed lines, contributions from higher partial waves may have an effect and these will be examined in a subsequent paper. An R-matrix radius of 16 au was adopted, and 20 continuum orbitals per orbital angular momentum were included in the calculation. In the resonance region (up to the energy of the last target-state threshold at 1.95 Ryd), an energy resolution of 0.0002 Ryd was used to properly delineate the resonances. Beyond the resonance region, we use a coarser mesh of 0.04 Ryd to achieve a background level up to an energy of 12 Ryd. In total, this generates collision strengths which are calculated at around 10,000 energy points. In comparison, the work of Tayal & Gupta (1999) determines the collision strengths at 821 energy points in the resonance region, so the current work has a resolution which is finer by more than a factor of 10. The collision strength (Ωij ) between an initial state “i” and final state “j” is defined in terms of the collision cross section (σij ) as (2Ji + 1)ki2 σij , Ωij = (5) π

Level

Energy

3s2 3p2 3 Pe0 3s2 3p2 3 Pe1 3s2 3p2 3 Pe2 3s2 3p2 1 De2 3s2 3p2 1 Se0 3s3p3 5 So2 3s3p3 3 Do1 3s3p3 3 Do2 3s3p3 3 Do3 3s3p3 3 Po2 3s3p3 3 Po1 3s3p3 3 Po0 3s2 3p3d 1 Do2 3s2 3p3d 3 Fo2 3s2 3p3d 3 Fo3 3s2 3p3d 3 Fo4 3s3p3 1 Po1 3s3p3 3 So1 3s2 3p3d 3 Po0 3s2 3p3d 3 Po1 3s2 3p3d 3 Po2 3s2 3p4s 3 Po0 3s2 3p3d 3 Po1 3s2 3p3d 3 Po2 3s2 3p3d 3 Do1 3s2 3p3d 3 Do2 3s2 3p3d 3 Do3 3s2 3p4s 1 Po1 3s3p3 1 Do2 3s2 3p3d 1 Fo3 3s2 3p3d 1 Po1 3s2 3p4p 1 Pe1 3s2 3p4p 3 Do1 3s2 3p4p 3 Do2 3s2 3p4p 3 Do3 3s2 3p4p 3 Pe0 3s2 3p4p 3 Pe1 3s2 3p4p 3 Pe2 3s2 3p4p 3 Se1 3s2 3p4p 1 De2 3s2 3p4p 1 Se0 3s2 3p4d 3 Fo2 3s2 3p4d 3 Fo3 3s2 3p4d 1 Do2 3s2 3p4d 3 Fo4 3s2 3p4d 3 Do1 3s2 3p4p 3 Do2 3s2 3p4p 3 Do3 3s2 3p4d 3 Po2 3s2 3p4d 3 Po1 3s2 3p4d 3 Po0 3s2 3p4d 1 Fo3 3s2 3p4d 1 Po1

0.00000 0.00272 0.00759 0.10318 0.24751 0.53466 0.76564 0.76589 0.76637 0.89983 0.90002 0.90008 0.94917 1.11283 1.11543 1.11902 1.24701 1.25816 1.30400 1.30418 1.30425 1.33680 1.33717 1.34090 1.34459 1.34587 1.34636 1.35231 1.38493 1.43625 1.49576 1.52686 1.54707 1.54978 1.55508 1.57315 1.57455 1.57825 1.58595 1.61280 1.66542 1.86428 1.86876 1.86944 1.87322 1.88213 1.88334 1.88553 1.89446 1.89639 1.89737 1.92413 1.94594

where ki2 is the channel energy of the continuum electron and Ji is the J-value of the initial level. The resulting collision strength (Ωij ) between initial state “i” and final state “j” is then averaged over a Maxwellian distribution of electron velocities to give the effective collision strength (ϒij ): ϒij (Te ) = 0

3

∞

Ωij (Ej ) exp(−Ej /kTe )d(Ej /kTe ),

(6)



Table 5 Effective Collision Strengths within the 3s2 3p2 3 P0,1,2 ; 1 D and 1 S Levels, Labeled 1, 2, 3, 4, and 5, Respectively log10 Te (K)

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0

Transition i–j 1–2

1–3

1–4

1–5

2–3

2–4

2–5

3–4

3–5

4–5

2.08 2.10 2.13 2.20 2.27 2.26 2.17 2.07 1.97 1.84 1.63 1.36 1.07 0.81 0.59 0.41

9.74−1 9.49−1 9.36−1 9.50−1 9.73−1 1.02 1.11 1.23 1.31 1.31 1.22 1.06 8.74−1 6.96−1 5.45−1 4.23−1

6.98−1 7.33−1 7.38−1 7.20−1 7.10−1 7.29−1 7.65−1 7.91−1 7.86−1 7.44−1 6.60−1 5.48−1 4.30−1 3.23−1 2.34−1 1.64−1

8.27−2 8.89−2 9.58−2 1.04−1 1.14−1 1.25−1 1.38−1 1.54−1 1.71−1 1.78−1 1.72−1 1.55−1 1.32−1 1.09−1 8.72−2 6.84−2

4.82 4.80 4.79 4.90 5.03 5.10 5.19 5.31 5.36 5.19 4.73 4.03 3.25 2.52 1.92 1.44

2.09 2.19 2.19 2.14 2.11 2.17 2.28 2.36 2.35 2.23 1.98 1.64 1.29 9.65−1 6.98−1 4.90−1

2.17−1 2.36−1 2.57−1 2.79−1 3.05−1 3.30−1 3.54−1 3.84−1 4.08−1 4.05−1 3.65−1 3.01−1 2.31−1 1.69−1 1.18−1 8.04−2

3.90 4.07 4.08 3.99 3.94 4.02 4.19 4.30 4.26 4.01 3.55 2.95 2.32 1.75 1.27 8.99−1

3.54−1 3.87−1 4.21−1 4.60−1 5.04−1 5.45−1 5.85−1 6.34−1 6.73−1 6.66−1 5.99−1 4.94−1 3.80−1 2.77−1 1.95−1 1.33−1

8.63−1 8.66−1 8.72−1 9.50−1 1.14 1.38 1.60 1.79 1.94 1.98 1.90 1.73 1.54 1.35 1.18 1.02

Note. a −n = a × 10−n .

we consider here. For transition 1–2 (3s2 3p2 3 P0 − 3s2 3p2 3 P1 ) in Tayal & Gupta (1999; displayed in Figure 6) it appears from the plot displayed that no resonances are resolved in the near threshold region until an energy of approximately 0.1 Ryd. When the resonance structure does appear, the first feature encountered is rather large in magnitude. Such large features at threshold, when integrated over using the formula given in Equation (6), have the effect of greatly enhancing the effective collision strength in the low-temperature region. This results from the energy Ej being incorporated via a negative exponential, meaning that the structures at the onset of the collision strength have a more dominant effect than those at higher energies. In comparison, in the current calculation, values for the collision strength are generated once the energy of the upper level has been reached, i.e., for transition 1–2 the collision strength begins when the 3s2 3p2 3 P1 threshold is opened at 0.0027 Ryd (see Table 4). The structures appearing in the present calculation’s collision strength are smaller in the near threshold region and so a much smaller effective collision strength is generated in the lower temperature region. However, once we go beyond the first 0.1 Ryd or so, the collision strength of Tayal & Gupta (1999) and that from the current work are quite similar in shape and magnitude of the background level, although much more resonance structure is observed in the current work since the resolution is a factor of 10 or more better. Thus, it appears that the calculation of Tayal & Gupta (1999) may have missed some of the near threshold resonance structures. To investigate this possibility, we have truncated our collision strength by excluding the first 0.1 Ryd (approximately 500 points) from our values and have processed these to yield effective collision strengths. The comparison here was performed over the temperatures for which the Tayal & Gupta data are given and we have added the results to Figure 1. While the exact shape of the Tayal & Gupta data is not reproduced, we certainly do find that the level of the effective collision strength is raised at low temperatures to almost match that of Tayal & Gupta. Transition 1–3: 3s2 3p2 3 P0 − 3s2 3p2 3 P2 . In Figure 2, the collision strength and effective collision strengths are displayed for the 3s2 3p2 3 P0 − 3s2 3p2 3 P2 transition. Again there is a

where Ej is the final kinetic energy of the ejected electron, Te is the electron temperature in Kelvin, and k is Boltzmann’s constant. 4. RESULTS AND DISCUSSION The effective collision strengths have been calculated at electron temperatures ranging from log10 Te = 3.0 to 6.0, where Te is the electron temperature in Kelvin. The values obtained for the transitions between the fine-structure levels of the groundstate configuration 3s2 3p2 are given in Table 5 at intervals of 0.2 dex. The data are also presented visually in Figures 1–6, where the effective collision strengths from the works of Tayal & Gupta (1999) and Galav´ıs et al. (1995) are compared. The corresponding collision strengths from the current calculation are also shown in Figures 1–6 over the incident electron energy range 0–2 Ryd. The collision strengths and effective collision strengths behind Figures 1–6, plus other transitions not shown, are available in the online version. A discussion about each of the plots follows: Transition 1–2: 3s2 3p2 3 P0 − 3s2 3p2 3 P1 . The collision strength and effective collision strength data for the 3s2 3p2 3 P0 − 3s2 3p2 3 P1 transition are presented in Figure 1. From the effective collision strength plot, the type of discrepancy noted by Rubin (2008) between the two earlier works is very clear, with the effective collision strengths of Tayal & Gupta (1999) being a factor of two larger in the low-temperature region before converging to a value close to Galav´ıs et al. (1995) at higher temperatures. We find that the current work shows strong agreement with the earlier IRON Project calculation of Galav´ıs et al. (1995). The large deviation in effective collision strength exhibited by Tayal & Gupta (1999) here is perhaps a little surprising, since the current calculation is similar in size to that of Tayal & Gupta (1999) and both use the CIV3 code to optimize the orbital parameters before proceeding to use R-matrix codes to perform the scattering calculation. Insight into a possible explanation can be gained when the collision strength data are examined. Collision strength plots are given by Tayal & Gupta (1999) for some of the transitions 4



8

5

7 4

Effective Collision Strength

Collision Strength

6 5 4 3

3

2

2 1

1 0

0

0.2

0.4

0.6

0.8 1 1.2 1.4 Incident Electron Energy (Ryd)

1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 1. Collision strength and effective collision strength for transition 1–2 (3s2 3p2 3 P0 − 3 P1 ) show results derived from our truncated collision strength. Also plotted are effective collision strengths from Galav´ıs et al. (1995; •) and Tayal & Gupta (1999; ). (A color version of this figure is available in the online journal.) 7

10

6 8


Collision Strength

5

4

3

2

6

4

2

1

0

0

0.2

0.4

0.6


1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 2. Collision strength and effective collision strength for transition 1–3 (3s2 3p2 3 P0 − 3 P2 ) show results derived from our truncated collision strength. Also plotted are effective collision strengths from Galav´ıs et al. (1995; •) and Tayal & Gupta (1999; ). (A color version of this figure is available in the online journal.) 2

20 18

1.6


16

Collision Strength

14 12 10 8 6

1.2

0.8

0.4

4 2 0

0

0.2

0.4

0.6


1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 3. Collision strength and effective collision strength for transition 2–3 (3s2 3p2 3 P1 − 3 P2 ) how results derived from our truncated collision strength. Also plotted are effective collision strengths from Galav´ıs et al. (1995; •) and Tayal & Gupta (1999; ). (A color version of this figure is available in the online journal.)

significant difference between the effective collision strengths of Tayal & Gupta (1999) and those of Galav´ıs et al. (1995), and here also we find that the current work agrees with the IRON Project data of Galav´ıs et al. (1995). When the collision strengths

are compared, the same situation exists here as described above for transition 1–2. The current work produces data from an energy of ∼0.0076 Ryd (the energy of the upper level in the transition) while the work of Tayal & Gupta (1999; the plot 5


10

2.5

8

2


Collision Strength


6

4

1

0.5

2

0

1.5

0

0.2

0.4

0.6


1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 4. Collision strength and effective collision strength for transition 4–5 (3s2 3p2 1 D2 – 1 S0 ). Also plotted are effective collision strengths from Galav´ıs et al. (1995) (•) and Tayal & Gupta (1999) (). (A color version of this figure is available in the online journal.) 10

20 18

8


16

Collision Strength

14 12 10 8 6

6

4

2

4 2 0

0

0.2

0.4

0.6


1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 5. Collision strength and effective collision strength for transitions 1, 2, 3–4 (3s2 3p2 3 P0,1,2 – 1 D2 ). Also plotted are effective collision strengths from Galav´ıs et al. (1995) (•) and Tayal & Gupta (1999) (). (A color version of this figure is available in the online journal.) 2

8 7

1.5


Collision Strength

6 5 4 3

1

0.5

2 1 0 0.2

0.4

0.6


1.6

1.8

0

2

3

3.5

4

4.5 log10T(K)

5

5.5

6

Figure 6. Collision strength and effective collision strength for transitions 1, 2, 3–5 (3s2 3p2 3 P0,1,2 − 1 S0 ). Also plotted are effective collision strengths from Galav´ıs et al. (1995) (•) and Tayal & Gupta (1999) (). (A color version of this figure is available in the online journal.)

displayed in Figure 7) shows values only from ∼0.1 Ryd upward, again suggesting that a portion of the low energy region has been missed. Thus the near threshold detail will be substantially different for Tayal & Gupta (1999), leading

to a significantly different effective collision strength. As with the previous transition, the collision strength we show here in Figure 2 compares well with that of Tayal & Gupta (1999) when we consider the region above 0.1 Ryd. When our data 6



are truncated by removing the first 0.1 Ryd from the collision strength, we again observe an increase in the effective collision strength at low temperatures. Transition 2–3: 3s2 3p2 3 P1 − 3s2 3p2 3 P2 . Data for the third transition within the ground-state level are given in Figure 3. The effective collision strength plot again shows the severity of the discrepancy between the values of Tayal & Gupta (1999) and Galav´ıs et al. (1995) in the low-temperature region before the two reconcile at higher temperatures. The collision strength plot of Tayal & Gupta (1999; their Figure 8) once again displays similar features to our current results once we move above 0.1 Ryd. Here also we note that our truncated collision strength yields an effective collision strength which raises toward that of Tayal and Gupta. Transition 4–5: 3s2 3p2 1 D2 − 3s2 3p2 1 S0 . For this transition, we see that the effective collision strengths from all three calculations agree quite well. The shape of the Tayal & Gupta (1999) data does not show any significant divergence, suggesting that the suspected problems with the earlier transitions have now been resolved. As noted from our collision strength plot in Figure 4, data are generated from around 0.24 Ryd (corresponding to the energy of the 3s2 3p2 1 S0 level) and so any missing data in the 0–0.1 Ryd region are no longer an issue. Transition 1,2,3–4: 3s2 3p2 3 P − 3s2 3p2 1 D. Here in order to compare with the collision strength data given by Tayal & Gupta (1999) and the effective collision strengths of Galav´ıs et al. (1995), we have considered the transition to the 1 D level from the 3 P LS level by summing over the transitions from all three of the fine-structure levels 3s2 3p2 3 P0,1,2 . The effective collision strengths of Tayal & Gupta (1999) were also summed over to be added to Figure 5. We see again that since the onset of the collision strength is beyond 0.1 Ryd, the three works produce data which are in very good agreement. Comparing with the Tayal & Gupta (1999) collision strength (Figure 1), we see good agreement in the shape and magnitude with the current work. Transition 1,2,3–5: 3s2 3p2 3 P − 3s2 3p2 1 S0 . The data have been grouped again here in Figure 6 by summing over the 3s2 3p2 3 P0,1,2 states to allow comparison with the collision strength plot of Tayal & Gupta (1999; Figure 2) and the effective collision strength values of Galav´ıs et al. (1995). We see the calculations of Tayal & Gupta (1999) and Galav´ıs et al. (1995) are now in much better agreement than for the earlier transitions, and from the mid-temperature region onward, the current work also agrees well. Toward low temperatures, however, the current results fall considerably lower than those of Galav´ıs et al. (1995) who provide data down to log10 T(K) = 3. The values of

Tayal & Gupta (1999) appear as if they will lower slightly, although perhaps not as much as the present work. This difference is due to sensitivity of the effective collision strength to the detail of the collision strength in the initial energy region. Comparing the collision strength in Figure 6 with the Tayal & Gupta (1999) plot, while the overall shape compares favorably, we see that the first feature encountered by Tayal & Gupta (1999) attains a height of ∼2, whereas the current work achieves a height of ∼1. This would account for a lower effective collision strength to be realized through the current work than that of Tayal & Gupta (1999). 5. CONCLUSIONS We have performed a 29-state R-matrix calculation to determine effective collision strengths for the electron impact excitation of S iii. Data for the fine-structure transitions within the 3s2 3p2 terms have been examined and compared to previous works where a significant discrepancy existed. We find the current work to agree with the IRON Project data from the calculation of Galav´ıs et al. (1995) and offer possible explanation as to why the Tayal & Gupta (1999) data were significantly different for some of the transitions. The collision strength and effective collision strength data presented are available by contacting the author or online at the Web site www.am.qub.ac.uk/apa/data. This work has been supported by PPARC/STFC under the auspices of a Rolling Grant. REFERENCES Ballance, C. P., & Griffin, D. C. 2004, J. Phys. B: At. Mol. Opt. Phys., 37, 2943 Burke, P. G., Burke, V. M., & Dunseath, K. M. 1994, J. Phys. B: At. Mol. Opt. Phys., 27, 5341 Cassidy, C. M., Ramsbottom, C. A., Scott, M. P., & Burke, P. G. 2010, A&A, 513, A55 Clementi, E., & Roetti, C. 1974, At. Data Nucl. Data Tables, 14, 177 Galav´ıs, M. E., Mendoza, C., & Zeippen, C. J. 1995, A&AS, 111, 347 Hibbert, A. 1975, Comput. Phys. Commun., 9, 141 Hummer, D. G., Berrington, K. A., Eissner, W., et al. 1993, A&A, 279, 298 Lebouteiller, V., Bernard-Salas, J., Brandl, B., et al. 2008, ApJ, 680, 398 Ralchenko, Yu., Kramida, A. E., Reader, J., & NIST ASD Team 2008, NIST Atomic Spectra Database, version 3.1.5 (Gaithersburg, MD: National Institute of Standards and Technology), Online available at http://physics.nist.gov/asd3 (2010 March 29) Rubin, R. H., Simpson, J. P., Colgan, S. W. J., et al. 2008, MNRAS, 387, 45 Tayal, S. S., & Gupta, G. P. 1999, ApJ, 526, 544 Wasson, I. R., Ramsbottom, C. A., & Norrington, P. H. 2010, A&A, 524, A35 Wu, Y., Bernard-Salas, J., Charmandaris, V., et al. 2008, ApJ, 673, 193

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