An Algorithmic Approach to Ion Structure and Dynamics in Astrophysical and Laboratory Plasmas

Abstract

For astrophysical photoionized plasmas, the atomic process of dielectronic recombination (DR) is critically important in ionization balance modeling and the determination of elemental abundances in the Universe. DR rate coefficients are known to have large uncertainties at low temperatures. In this work, this issue is addressed by the development of a decision tree algorithm, called CRISTAL (Complex Resolved Ion Spectroscopy Tree ALgorithm) that selects large configuration sequences for configuration-interaction atomic structure calculations.

CRISTAL is designed to exploit the rules for configuration mixing for dimensional reduction of the configuration space: it compares computed energies against measured values and iteratively reduces the selected configuration sequence. We compute energies, resonance heights, and Maxwellian rate coefficients for Lithium-like and Beryllium-like Carbon and Nitrogen and compare the results to storage ring measurements and archived data to make the improvements clear. We report an average difference for selected resonance positions on the order of 0.1eV at a maximum $n$-shell of 6. Additionally, the scaling of the number of configurations with number of orbitals is reduced from quintic to cubic in the Beryllium-like case and from quartic to quadratic in the Lithium-like case.

The code results demonstrated that the optimum CRISTAL configuration sequence was invariant along both isoelectronic sequences, motivating a general proof of this invariance for any isoelectronic sequence. Thus, higher members of an isoelectronic sequence can be calculated once an optimum configuration set is generated.

It is standard practice to use the first-order approximation known as Fermi's Golden rule to calculate the Auger rates in DR calculations. We derive a method to assign an upper bound on the uncertainty in Auger rates using the Dyson series, the exact perturbative expansion of the evolution operator.

Currently, CRISTAL neglects the configuration-interaction rule for angular momentum. In the interest of improving the algorithm, we test a novel approach for calculating angular momentum coupling coefficients for the 2-particle case and outline a generalization for the N-particle case.

With the method outlined above, significant progress has been made in improving the method to calculate low temperature DR rate coefficients. The work opens up a number of interesting future directions.