ABSTRACT Electron collision excitation strengths of inelastic transitions among the 52 Ðne-structure levels of the

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1 THE ASTROPHYSICAL JOURNAL, 530:1091È1104, 2000 February 20 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. ELECTRON COLLISION EXCITATION OF FINE-STRUCTURE LEVELS IN S IV S. S. TAYAL Department of Physics, Clark Atlanta University, Atlanta, GA Received 1999 June 28; accepted 1999 September 30 ABSTRACT Electron collision excitation strengths of inelastic transitions among the 52 Ðne-structure levels of the ground 3s23p and excited 3s3p2, 3s23d, 3s24s, 3p3, 3s24p, 3s3p3d, 3s24d, 3s24f, and 3s3p4s conðgurations in S IV are calculated using full Breit-Pauli R-matrix method. The target levels are represented by conðguration-interaction wave functions, and the mass, Darwin, and spin-orbit relativistic terms are included in the scattering equations. The collision strengths in the threshold energy regions are dominated by the complicated resonance structures. Our collision strengths are compared with earlier available calculations and signiðcant di erences are noted. The collision strengths are integrated over a Maxwellian distribution of electron energies to obtain e ective collision strengths over a wide temperature range. Subject headings: atomic data È atomic processes 1. INTRODUCTION The International Ultraviolet Explorer and the Goddard High-Resolution Spectrograph (GHRS) on board Hubble Space T elescope have observed strong S IV emission features at 657, 745, 816, 1070, and 1406 A in the spectra of the Io plasma torus (Durrence, Feldman, & Weaver 1983; Moos et al. 1991). The spin-forbidden emission lines of S IV from the multiplet 3s23p 2PoÈ3s3p24P are observed in the spectra of the Sun by the Skylab experiments (Feldman 1981; Dere 1982; Bhatia, Doschek, & Feldman 1980) and in the spectra of the transition region of Capella observed by the GHRS (Linsky et al. 1995). The line intensity ratios within the multiplet 3s23p 2PoÈ3s3p2 4P can provide excellent density diagnostics in the electron density range 109È1012 cm~3. The ratio of emission lines at and A from the multiplet 3s23p 2PoÈ3s3p2 2D are also density sensitive. These lines are observed in the far ultraviolet spectra of the Sun by the Naval Research Laboratory SO82-B slit spectrograph on Skylab (Feldman & Doschek 1991). The relative intensities of the S IV lines together with the strong emission lines of the abundant ions of carbon, nitrogen, and silicon can be used to determine relative element abundances. The transition probabilities and electron collision strengths for Ðne-structure levels are needed to determine theoretical line-intensity ratios that eventually may be used to infer electron temperature, density, and elemental abundances in astrophysical plasmas. Electron impact excitation collision strengths of electricdipole, intercombination, and forbidden transitions among the Ðne-structure levels of the 3s23p, 3s23d, 3s24s, 3p3, 3s3p3d, 3s24p, 3s24d, 3s24f, and 3s3p4s conðgurations of S IV are calculated using a full Breit-Pauli R-matrix approach. We considered 52 Ðne-structure levels in our calculation. These levels are represented by conðguration-interaction (CI) wave functions. The relativistic e ects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations (Scott & Burke 1980). Rydberg series of resonances converging to excited Ðne-structure levels are explicitly included in the scattering calculations. These resonance structures make substantial contributions to collision strengths for many transitions Recently Saraph & Storey (1999) reported collision data for the 2Po È2Po Ðne-structure transition in P III, SIV, 1@2 3@2 and Cl V. They included 21 LS terms of S IV in the closecoupling (CC) expansion in their elaborate R-matrix calculations. They included mass and Darwin terms of the Breit-Pauli operator explicitly in their LS R-matrix calculation and considered the spin-orbit interaction as a perturbation by the use of term-coupling coefficients (Saraph 1978). Johnson, Kingston, & Dufton (1986) reported e ective collision strengths for the ground state Ðne-structure transition 2Po È2Po in S IV and noted that the reso- 1@2 3@2 nance e ects enhance the e ective collision strengths by a factor of 4 compared to distorted wave calculation (Brocklehurst 1972). Saraph & Storey (1999) demonstrated that the positions of the resonances depend on the coupling to higher excited states. They found that the positions of resonances shift to lower energy side when channels coupled to higher excited states are included in the CC expansion. This translates to increase in e ective collision strengths at lower temperatures. The e ective collision strengths reported by Saraph & Storey (1999) are 30% higher than those of Johnson et al. (1986) at 10,000 K. Bhatia et al. (1980) reported collision strengths at 2.0, 4.0, and 6.0 ryd for Ðne-structure transitions among the levels of the 3s23p, 3s3p2, and 3s23d conðgurations that were calculated in a distorted wave approximation (Eissner & Seaton 1972). Bhadra & Henry (1980) used two-state and Ðve-state CC approximations to calculate collision strengths among the Ðne-structure levels of the 3s23p and 3s3p2 conðgurations. Bhatia et al. (1980) and Bhadra & Henry (1980) carried out their calculations in LS coupling and obtained collision strengths for Ðne-structure levels in intermediate coupling by the use of transformation code of Saraph (1978) and did not include important resonance e ects in their calculations. Electron impact excitation collision strengths of the spin-forbidden transition 3s23p 2PoÈ 3s3p2 4P were calculated by Dufton & Kingston (1980) using R-matrix method in LScoupling, while Dufton et al. (1982) reported transition probabilities and e ective collision strengths for Ðne-structure levels of the 3s23p 2Po and 3s3p2 4P terms. We recently reported oscillator strengths of electric dipole transitions in S IV (Tayal 1999).

2 1092 TAYAL TABLE 1 CALCULATED AND EXPERIMENTAL ENERGY LEVELS (IN ryd) OF S IV PRESENT CALCULATION INDEX LEVEL J Ab Initio Adjusted EXPERIMENT s23p 2Po 1/ / s3p2 4P 1/ / / s3p2 2D 3/ / s3p2 2S 1/ s3p2 2P 1/ / s23d 2D 3/ / s24s 2S 1/ p3 2Do 3/ / p3 4So 3/ s3p(3Po)3d 4Fo 3/ / / / p3 2Po 1/ / s24p 2Po 1/ / s3p(3Po)3d 4Po 5/ / / s3p(3Po)3d 4Do 1/ / / / s3p(3Po)3d 2Do 5/ / s3p(3Po)3d 2Fo 5/ / s24d 2D 3/ / s24f 2Fo 7/ / s3p(3Po)4s 4Po 1/ / / s3p(3Po)3d 2Po 3/ / s3p(3Po)4s 2Po 1/ / s3p(1Po)3d 2Po 3/ / s3p(1Po)3d 2Do 3/ / s3p(1Po)4s 2Po 1/ / COLLISION CALCULATION The one-electron orbitals 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, and 4f are used in our scattering calculation. The 1s, 2s, 2p, 3s, and 3p radial functions are chosen as the Hartree-Fock functions (Clementi & Roetti 1974) for the ground state 3s23p 2Po, and the parameters of the 3d, 4s, 4p, 4d, and 4f orbitals are optimized on various states using atomic structure code CIV3 (Hibbert 1975). The details of the wave TABLE 2 COLLISION STRENGTH FOR TRANSITIONS AMONG FINE-STRUCTURE LEVELS IN S IV PRESENT BH (1980) BDF (1980) TRANSITION È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È functions can be found in Tayal (1999), where orbital parameters, energy levels, transition probabilities and lifetimes are presented. The 24 LSstates are represented by 114 conðgurations and 257 conðgurations are used to represent 52 Ðne-structure levels. The calculated excitation energies of the Ðne-structure levels relative to the ground level 3s23p 2Po are presented in Table 1, where these are compared with 1@2 experimental results (Martin, Zalubas, & Musgrove 1990). The present ab initio results are within 4% of the experimental results except for the 3s23p 2Po level, at which theory and experimental results di er by 3@2 10%. The relativistic e ects in intermediate coupling are incorporated through the Breit-Pauli Hamiltonian. We have made small adjustments to the diagonal elements of the Hamiltonian

3 TABLE 3 EFFECTIVE COLLISION STRENGTHS FOR TRANSITIONS IN S IV 1È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

4 TABLE 3ÈContinued 2È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

5 TABLE 3ÈContinued 3È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

6 TABLE 3ÈContinued 4È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

7 TABLE 3ÈContinued 6È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

8 TABLE 3ÈContinued 7È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

9 TABLE 3ÈContinued 9È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È È

10 1100 TAYAL Vol. 530 TABLE 3ÈContinued 10È È È È È È È È È È È È matrices calculated in the ab initio calculation to bring the calculated energies as close as possible to the experimental results. These adjusted energies are also listed in Table 1. These adjustments also caused small changes in the weights of some eigenvectors. We have used adjusted energies and eigenvectors in the scattering calculation. The total wave function representing the scattering of electrons by S IV ion for each total angular momentum J and parity n is expanded in the inner region (r ¹ a) inthe R-matrix basis as (Scott & Taylor 1982; Berrington et al. 1987) ( (Jn) \ A ; c ' J(x, x,..., x ; x, p ) k ijk i 1 2 N N`1 N`1 ij ] u (x ) ] ; d / J(x, x,..., x ), (1) ij N`1 jk j 1 2 N`1 j where A is the antisymmetrization operator; ' J are channel i functions representing the 52 Ðne-structure target levels coupled with angular and spin functions of the scattered electron to form channel functions of J and n; / J are j (N ] 1) electron conðgurations formed from the atomic orbitals and are included to ensure completeness of the total wave function expansions and to allow for short-range correlations; and u are the orthogonal set of continuum ij basis. The coefficients c and d are obtained by diagonal- ijk jk izing the (N ] 1) electron Breit-Pauli Hamiltonian in the inner region. We have chosen the boundary radius a \ 15.9 AU and included 22 continuum orbitals for each angular momentum to obtain convergence in the energy range up to 8.5 ryd. The maximum number of channels retained in our calculation is 241. The coupled equations are solved in the asymptotic region using a perturbation method to yield K-matrices and then the collision strengths. The Breit-Pauli R-matrix method is used to calculate partial collision strengths from J \ 0toJ \ 20. The higher partial waves contributions for the dipole-allowed transitions are calculated using the Bethe approximation (Burgess & Sheorey 1974), and top-up ÏÏ is used for other transitions. The electron excitation rates are obtained by averaging total collision strengths over a Maxwellian distribution of electron energies. The excitation rate coefficients for a transition from state i to a state f at electron temperature T is e given by 8.63 ] 10~6 B C(i ] f ) \ c(i ] f )exp A[*E if cm3 s~1, g T 1@2 KT i e e (2) where g \ (2j ] 1) is the statistical weight of the lower level i i i, *E \ E [ E is the excitation energy, and c(i ] f ) is the if f i e ective collision strength given by c(i ] f ) \ P 0= )(i ] f ) exp A[v f kt e B. (3) Here )(i ] f ) is the total collision strength for transition between levels i and f, v is the energy of incident electron f TABLE 4 COMPARISON OF EFFECTIVE COLLISION STRENGTHS ELECTRON TEMPERATURE 10,000 K 40,000 K 100,000 K 400,000 K TRANSITION Present Dufton Present Dufton Present Dufton Present Dufton 1È È È È È È È È È È

11 No. 2, 2000 ELECTRON COLLISION EXCITATION IN S IV 1101 with respect to the upper level f, T is the electron temperature, and k is the Boltzmann constant. e 3. RESULTS AND DISCUSSION We chose a Ðne energy mesh (0.001 ryd) for collision strengths calculation in the thresholds energy region. This allowed us to delineate the resonance structures in the collision strengths. In Table 2 we present total collision strengths at incident electron energies 4 and 6 ryd and compare these with the calculations of Bhadra & Henry (1980) and Bhatia et al. (1980), which are denoted BH ÏÏ and BDF,ÏÏ respectively. These energies are above the highest excitation threshold in our calculation. It may be noted that the incident electron energy 2 ryd lies in the resonance region in our calculation, which is why we did not compare our results with the available earlier calculations at this energy in Table 2. The keys to the lower and upper levels involved in a transition are given in Table 1. The agreement between the present results and those of Bhadra & Henry (1980) is 40% or better except for a few transitions with smaller collision strengths. There are larger di erences (up to a factor of 2) with the distorted wave calculation of Bhatia et al. (1980). The main reason for the discrepancies at these energies with the calculation of Bhatia et al. (1980) may be the use of limited correlation e ects in their calculation. We have plotted total collision strengths as a function of electron energy in the region of thresholds from the threshold to 0.7 ryd in Figure 1 for the ground state Ðne-structure transition 2Po È2Po and in Figures 2, 3, and 4 for the 1@2 3@2 transitions 2Po È3s3p2 4P, 2Po È3s3p2 4P, and 1@2 1@2 1@2 3@2 2Po È3s3p2 4P, respectively, from the threshold to 1.2 ryd. 1@2 The results 5@2 of our full Breit-Pauli R-matrix calculation are shown by solid curves. It is clear from these Ðgures that there are complicated resonance structures in collision strengths. Since all the previous calculations were performed in the LS coupling scheme and the transformation code JAJOM (Saraph 1978) is then used to obtain collision strengths of Ðne-structure levels, we also carried out LS R-matrix plus JAJOM calculation, and these results are shown by dashed curves in these Ðgures. The mass and Darwin terms of the Breit-Pauli operator are included in our LScalculation. We used the same wave functions in the two calculations, but the energies in our LS calculation were adjusted in order to experiment. Some signiðcant differences in the resonance structures from the two calculations may be noted from these Ðgures. It is well known that the transformation of LS K-matrices to intermediate coupling using the JAJOM code (Saraph 1978) has two limitations. In this method the Ðne-structure splittings of the target terms are neglected, and in the resonance region, where there are both open and closed channels, only those components of term-coupling coefficients are used for which channels are open. Both of these approximations may lead to some inaccuracies in collision strengths depending upon the spin-orbit interaction. Recently Griffin, Badnell, & Pindzola (1998) studied electron impact excitation of Fe XV and presented detailed comparison of the collision strengths obtained in full Breit-Pauli R-matrix and pure LScoupling plus transformation to intermediate coupling using JAJOM and found signiðcant discrepancies between the two sets of results COLLISION STRENGTH ELECTRON ENERGY IN RYDBERGS FIG. 1.ÈCollision strength for the 3s23p 2Po È3s23p 2Po transition in S IV as a function of electron energy in rydbergs: present full Breit-Pauli R-matrix calculation (solid curve) and LSR-matrix plus JAJOM 1@2 (dashed 3@2 curve).

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