Resolving all-order method convergence problems for atomic physics applications

H. Gharibnejad*, E. Eliav, M. S. Safronova, A. Derevianko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for the study of fundamental symmetries, development of atomic clocks, ultracold atom physics, and others, as well as provided recommended values of many atomic properties critically evaluated for their accuracy for a large number of monovalent systems. This approach requires iterative solutions of the linearized coupled-cluster equations leading to convergence issues in some cases where correlation corrections are particularly large or lead to an oscillating pattern. Moreover, these issues also lead to similar problems in the configuration-interaction (CI)+all-order method for many-particle systems. In this work, we have resolved most of the known convergence problems by applying two different convergence stabilizer methods, namely, reduced linear equation and direct inversion of iterative subspace. Examples are presented for B, Al, Zn+, and Yb+. Solving these convergence problems greatly expands the number of atomic species that can be treated with the all-order methods and is anticipated to facilitate many interesting future applications.

Original languageEnglish
Article number052502
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
StatePublished - 10 May 2011


FundersFunder number
National Science Foundation0969580


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