Resolving all-order method convergence problems for atomic physics applications

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.052502· OSTI ID:21546751

Gharibnejad, H; Derevianko, A ^[1]; Eliav, E ^[2]; Safronova, M S ^[3]

---

1. Department of Physics, University of Nevada, Reno, Nevada 89557 (United States)
2. Department of Chemistry, Tel Aviv University, Tel Aviv (Israel)
3. Department of Physics, University of Delaware, Newark, Delaware 19716 (United States)

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{sup +}, and Yb{sup +}. 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.

• OSTI ID: 21546751
• Journal Information: Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.052502; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ACCURACY
ALUMINIUM IONS
ATOMIC CLOCKS
ATOMIC PHYSICS
BORON IONS
CONFIGURATION INTERACTION
CONVERGENCE
CORRECTIONS
CORRELATIONS
EXCITATION
HARTREE-FOCK METHOD
ITERATIVE METHODS
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
RELATIVISTIC RANGE
WAVE FUNCTIONS
YTTERBIUM IONS
ZINC IONS
APPROXIMATIONS
CALCULATION METHODS
CHARGED PARTICLES
ENERGY RANGE
ENERGY-LEVEL TRANSITIONS
FUNCTIONS
IONS
PHYSICS