On the Optimized Atomic Exchange Potential method and the CASSANDRA opacity code

The CASSANDRA, average atom, opacity code uses the local density approximation (LDA) to calculate electron exchange interactions and this introduces inaccuracies due to the inconsistent treatment of the Coulomb and exchange energy terms of the average total energy equation. To correct this inconsistency, the Optimized Atomic Central Potential Method (OPM) of calculating exchange interactions has been incorporated into CASSANDRA. The LDA and OPM formalisms are discussed and the reason for the discrepancy when using the LDA is highlighted. CASSANDRA uses a Taylor series expansion about an average atom when computing transition energies and uses Janak's Theorem to determine the Taylor series coefficients. Janak's Theorem does not apply to the OPM; however, a corollary to Janak's Theorem has been employed in the OPM implementation. A derivation of this corollary is provided. Results of simulations from CASSANDRA using the OPM are shown and compared against CASSANDRA LDA, DAVROS (a detailed term accounting opacity code), the GRASP2K atomic physics code and experimental data.