Transition frequencies between 2S and 2P states of lithium-like ions

The Schrödinger equation for the 2S and 2P states of the lithium-like ions Z=5–7,9–10 is solved by using the Rayleigh-Ritz variational method in Hylleraas coordinates.The leading-order relativistic and QED corrections are calculated perturbatively and higher-order corrections are estimated.The transition frequencies between the 2S_(1/2)and 2P_(J)(J=1/2,3/2)states are determined and compared with experimental and other theoretical results.Specifically,isotope shifts are also calculated for B^(2+).

Fine and hyperfine structures of pionic helium atoms

The fine and hyperfine structures of pionic helium metastable states is calculated within the formalism of the Breit-Pauli Hamiltonian by using the variationally generated wave functions in Hylleraas coordinates.Our results not only verify the existing values of Hori et al.[Phys.Rev.A 89,042515(2014)]for the fine structure of π^(4)He^(+),but also determine the hyperfine structure of π^(3)He^(+).

Complex coordinate rotation method based on gradient optimization

In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.