Fine-Tuning of Atomic Energies in Relativistic Multiconfiguration Calculations

Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in agreement with experiment. The process gives more accurate measures of the mixing than can be obtained in ab initio calculations. Fine-tuning requires the Hamiltonian matrix to be diagonally dominant, which is generally not the case for calculations based on jj-coupled configuration state functions. We show that this problem can be circumvented by a method that transforms the Hamiltonian in jj-coupling to a Hamiltonian in LSJ-coupling for which fine-tuning applies. The fine-tuned matrix is then transformed back to a Hamiltonian in jj-coupling. The implementation of the method into the General Relativistic Atomic Structure Package is described and test runs to validate the program operations are reported. The new method is applied to the computation of the 2s(21)S(0)-2s2p(1,3)P(1) transitions in C III and to the computation of Rydberg transitions in B I, for which the 2s(2)p(22)S(1/2) perturber enters the 2s(2)ns(2)S(1/2) series. Improved convergence patterns and results are found compared with ab initio calculations.

Automated summary

Fine-tuning of the Hamiltonian matrix improves the accuracy of calculated energy separations by adjusting the diagonal elements to match experimental results. In calculations based on jj-coupled configuration state functions, the diagonally dominant requirement is often not met. An alternative method that transforms the matrix to LSJ-coupling and then back to jj-coupling is presented to overcome this problem. Implementation of this method in the General Relativistic Atomic Structure Package leads to improved convergence and results in the computation of transitions in C III and Rydberg transitions in B I.