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22nd International Symposium on Plasma Chemistry July 5-10, 2015; Antwerp, Belgium Fe I electron excitation data for modelling of cool star spectra J.R. Hamilton1,2, J. Tennyson1,2, P. Barklem3 and O. Zatsarinny4 1 Quantemol Ltd., University College London, London WC1E 6BT, U.K. Department of Physics and Astronomy, University College London, London WC1E 6BT, U.K. 3 Theoterical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden 4 Department of Physics and Astronomy, Drake University, US-50311 Des Moines, Iowa, U.S.A. 2 Abstract: The B-Spline R-matrix (BSR) method (Zatsarinny, 2013) is used to calculate the electronic excitation collision cross section of electrons with atomic Fe I. The BSR method is used in conjunction with a close-coupling expansion and non-orthogonal bound and continuum orbitals (Zatsarinny, 2006). Fe I requires a semi-relativistic treatment which is provided using the Breit-Pauli approach. Results for excitation cross-sections will be reported at the conference. 1. Introduction Barklem and co-workers have performed extensive modeling of the spectra of cool stars where the atoms depart from local thermodynamic equilibrium (LTE) [1]. These models aim to study stellar properties such as chemical abundances, and processes and to understand the chemical and dynamic evolution of the galaxy. Non-LTE modelling requires large amounts of collisional data for the atomic species of interest. So far much of this work has been limited to light atoms such as Li [2], O [3], Na [4], and Mg [5, 6], as the calculation of collision data for heavier atoms presents is more complexities and often gives less accurate results. Additionally heavier atoms require a relativistic treatment which is not incorporated into many atomic collision methods. This work looks to produce a detailed set of collision data of the heavy atom Fe I, using the B-spline R-matrix (BSR) method with relativistic corrections [7]. 2. Scientific Approach After reviewing the Iron Project publications we conclude very little is currently published on electron Fe I collisions. Pelan et al. [8] studied the electronic excitation to specific low-lying states of the Fe I atom using the Belfast atomic R-matrix codes [9]. The first step in our study is to recalculate the specific transitions considered by Pelan et al. [8] for benchmarking. Then second step is to calculate an electron excitation cross section for an extended set of states: we consider the first 20 levels of Fe I. The final step is to repeat the calculation using a much larger set of states with the physical target augmented by pseudo-states which represent the hundreds of higher states in Fe I. This is necessary to get converged the results. 3. The R-Matrix Method The R-matrix method is one of many methods for solving the close-coupling equations. This method divides the physical space of the problem into two P-I-2-28 regions: an inner region containing the target atom and an outer region containing the incident electron. The met hod solves the Schrödinger equation in the inner region independent of the energy of the interacting electron and then uses this solution to solve the much simpler outer region Schrödinger equation, which is energy dependent the Belfast atomic R-matrix codes: FARM and STPF [10] are used to calculate the R-matrix from the surface amplitudes generated form the energy independent inner region calculation. The R-matrix is then used to solve the Schrödinger equation in the outer region for over a range of incident electron energies. The use of both codes will confirm numerical stability and convergent results. 4. Multi Configuration Hartree Fock Generation of States The target states of the Fe I atom are calculated using in Multi Configuration Hartree Fock (MCHF) program of Fischer [11]. The MCHF program is used to generate the expansion coefficients of electron configurations including correlative effects of all states and pseudo-states to be considered. 5. Pseudo-State Calculations For large state calculations the BSR method employs the use of pseudo-states to model the non-excited and excited continuum target states. This approach involves treating the R-matrix inner region as a potential well where within the well the continuum states become discrete (pseudo) states and outside of the R-matrix boundary the continuum wave functions equal zero. Pseudo-states are generated by treating the Fe I continuum problem as coupled Fe II + e. The Fe II + e scattering problem is solved and from this solution states and pseudo states are extracted to be used as target states for the Fe I + e calculation. 1 6. The use of B-Splines Splines are bell-shaped piece-wise polynomial functions of order, defined by a given set of points in some finite radial interval which can be taken to be the R-matrix radius. B-splines form an effectively complete basis set which avoids linear dependence problems between the bound and continuum orbitals. The use of B-splines as the R-matrix basis set was first outlined by van der Hart et al. [12], who applied the method to electron H I scattering. 7. Non-Orthodonal Orbitals In the BSR method non-orthogonal orbitals are be used to represent both the bound and continuum one-electron target states. The use of non-orthogonal orbitals means the bound and continuum states can be optimised in separate calculations. This gives a high level of accuracy can be achieved with compact configuration expansions of bound states. The use of non-orthogonal continuum orbitals can drastically reduce the pseudo-resonance problem in continuum states [13]. The use of non-orthogonal orbitals is not widely used in R-matrix calculations as the most time-consuming part of atomic structure calculations is connected with the angular integration of the orbitals. However efficient use of orthogonal orbitals with some restricted nonorthogonality makes it possible to automate to a large extent this part of the inner-region problem. 8. The Breit-Pauli Approach The Breit-Pauli approach can be considered a first order perturbative method providing a first order correction to the non-relativistic Hamiltonian operator. This perturbation corrects the Hamiltonian to include relativistic shift and relativistic splitting of the Fe I target states including also the fine structure interactions between the spin and orbital angular momenta of the target states electrons. The Breit-Pauli approach has been shown to provide accurate results for atoms with Z < 30. 3d64snl). The states Fe I (3d8 and 3d24p2) can also be considered as perturbations of these continuum states or from a close coupling expansion. Final results will be presented at the conference. 10. Acknowledgments JRH thanks STFC for a studentship and Quantemol Ltd. for support. This collaboration was supported by the CORINF ITN network. 11. References [1] P.S. Barklem, et al. Astron Astrophys., 530, A94 (2011) [2] K. Lind, M. Asplund and P.S. Barklem. Astron. Astrophys., 503, 541-544 (2009) [3] D. Fabbian, et al. Astron. Astrophys., 500, 12211238 (2009) [4] K. Lind, et al. Astron. Astrophys., 528, 103 (2011) [5] P.S. Barklem, et al. Astron. Astrophys., 541, 80 (2012) [6] L. Mashonkina. Astron. Astrophys., 550, 28 (2013) [7] O. Zatsarinny and K. Bartschat. J. Phys. B: At. Mol. Opt. Phys., 46, 112001 (2013) [8] J. Pelan and K.A. Berrington. Astron. Astrophys., Suppl. Ser., 122, 177 (1997) [9] K.A. Berrington, W.B. Eissner and P.H. Norrington. Comput. Phys. Commun., 92, 290 (1995) [10] V.M. Burke and C.J. Noble. Comput. Phys. Commun., 85, 471 (1995) [11] C.F. Fischer and O. Zatsarinny. Comput. Phys. Commun., 180, 2041 (2009) [12] H.W. van der Hart. J. Phys. B., 30, 452 (1997) [13] O. Zatsarinny. Comput. Phys. Commun., 174, 273356 (2006) 9. Fe I Fe I has ground state configuration 3d64s2 (NIST). Only excitation of the 4s electrons from this ground state will be considered. Because the Fe I bound state spectra is so rich the pseudo-state calculation will not include continuum pseudo-states. The pseudo-state method will be used to calculate bound states only: e + Fe I (3d64s2) →e + Fe I (3d64snl) Therefore an electron Fe II scattering calculation of: e + Fe II (3d7, 3d64s and 3d64p) will be carried out to calculate the target state of Fe I (3d74s) and correlated state (3d64s4p). The electron Fe II scattering calculation can also calculate the continuum states Fe I (3d64pnl, 3d64dnl and 2 P-I-2-28