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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
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Lecture 4: Coupled Channel Approximation and the R-Matrix Codes • Recall: • To solve the (e+ion) problem we compute ion wavefunctionsfirst, 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
“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
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
“Asymptotic” R-Matrix Codes • Following (e+ion) hamiltoniandiagonalization, 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)
Astrophysical Quantities • Absorption oscillator strengths and photoionization cross sections Opacities • Line emissivities Emission Line Diagnostics • All atomic parameters Non-LTE radiative transfer models