Theory and computational methods for high precision spectra of few-electron atomic systems

Abstract

Due to modern precision laser technology, the spectra of some few-electron atomic systems (such as hydrogen, helium, lithium, beryllium) could be measured to very high accuracy. A comparison between high precision experimental and theoretical results supplies us with a practicable method to test fundamental physical theories, to determine fundamental physical constants, and to extract nuclear properties, such as the nuclear charge radius. However, it is not an easy task to calculate the spectrum of an atom to a precision that matches the corresponding experimental precision. In order to achieve this goal, we need to take electron correlation effects, relativistic effects, and quantum electrodynamic (QED) effects into consideration and evaluate them to a sufficiently high accuracy. In the past several decades, significant progress has been made on high precision calculations of few-electron atomic systems, due to advances of computer technologies and persistent efforts in this area. The main purpose of this article is to give a survey on high precision calculations of few-electron atomic systems, including the effective Hamiltonian, the solutions to the Schrodinger equation, calculations of relativistic and QED effects, the finite nuclear mass effect, and the effect due to the nuclear charge radius. Finally, we give some perspectives for the future.