Resolving all-order method convergence problems for atomic physics applications

Abstract

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 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 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 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, reduced linear equation (RLE) and direct inversion of iterative subspace (DIIS). 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.

References in corpus (10)

• Development of a configuration-interaction + all-order method for atomic calculations
• Precision determination of weak charge of ${}^{133}$Cs from atomic parity violation
• High-accuracy calculation of black-body radiation shift in ${}^{133}$Cs primary frequency standard
• Magic wavelengths for the np-ns transitions in alkali-metal atoms
• Magic frequencies for cesium primary frequency standard
• "Doubly-magic" conditions in magic-wavelength trapping of ultracold alkalis
• Blackbody radiation shift in 87Rb frequency standard
• Calculation of parity nonconservation in neutral ytterbium
• Possibility of "magic" co-trapping of two atomic species in optical lattices
• Quantum computing with magnetic atoms in optical lattices of reduced periodicity

Cited by in corpus (6)

• Ytterbium in quantum gases and atomic clocks: van der Waals interactions and blackbody shifts
• Precision lifetime measurement of the cesium $6P_{3/2}$ level using ultrafast pump-probe laser pulses
• Study of the correlation effects in Yb^+ and implications for parity violation
• Polarizability assessments of ion-based optical clocks
• Coupled-cluster calculations of properties of Boron atom as a monovalent system
• Relativistic many-body calculation of energies, lifetimes, polarizabilities, blackbody radiative shift and hyperfine constants in Lu2+