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Lecture 4: Coupled Channel Approximation and the R-Matrix Codes Recall: To solve the (e+ion) problem we compute ion wavefunctions first, independently using Superstructure or similar atomic structure code The coupled-channel (CC) approximation couples the free electron and ion wavefunctions R-Matrix method is the most efficient for most atomic processes in plasmas

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“Stages” of the R-Matrix Codes Superstructure (SS) one-electron orbitals (sspnl), optmized over target ion wavefunctions One and two-electron Slater integrals SS (sspnl) STG1 Angular algebra: STG2 reconstructs the target ion and couplings for the (e+ion) system STG1 STG2 (non-relativistic LS coupling) STG2 RECUPD: Intermediate re-coupling LS LSJ (Breit-Pauli approximation) RECUPD STGH: (e+ion) Hamiltonian Diagonalization

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Flow Chart: Sets of R-Matrix Codes Non-relativistic R-Matrix and relativistic Breit- Pauli R-Matrix (BPRM): LS and LSJ coupling R-Matrix II codes: “Complete” (e+ion) angular treatment; large number of levels Dirac R-Matrix Codes (DARC): Use GRASP for target ion wavefunctions for high-Z systems Fig. 3.9 Flow chart

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“Asymptotic” R-Matrix Codes Following (e+ion) hamiltonian diagonalization, STGH produces an H.DAT file which is utilized by subsidiary codes to calculate: electron-ion cross sections (STGF) (e+ion) bound state energy levels (STGB) bound-bound transition probabities (STGBB) bound-free (photoionization) cross sections (STGBF)

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Astrophysical Quantities Absorption oscillator strengths and photoionization cross sections Opacities Line emissivities Emission Line Diagnostics All atomic parameters Non-LTE radiative transfer models

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