### Lecture 4: R-Matrix Codes

```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
“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 BreitPauli 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) 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)
Astrophysical Quantities
• Absorption oscillator strengths and
photoionization cross sections  Opacities
• Line emissivities  Emission Line Diagnostics
• All atomic parameters  Non-LTE radiative
transfer models
```