Energies, Fine Structures, and Hyperfine Structures of the States for the Beryllium Atom

Energies and wave functions of the states for the beryllium atom are calculated with the full-core plus correlation wave functions. Fine structures and hyperfine structures are calculated with the first-order perturbation theory. For the state, the calculated energies, fine structure, and hyperfine structure parameters are in good agreement with the latest theoretical and experimental data in the literature; it is shown that atomic parameters of the low-lying excited states for the beryllium atom can be calculated accurately using this theoretical method. For the ( ) states, the present calculations may provide valuable reference data for future theoretical calculations and experimental measurements. 1. Introduction In recent years, studies of energies, fine structures, and hyperfine structures of the low-lying excited states for the beryllium atom [1–10] have been of great interest to spectroscopists because there are many strong optical transitions suitable for spectral and hyperfine structure measurements. On the other hand, studies of the low-lying excited states for the beryllium atom play an important role in developing the excited state theory of multielectron atoms and better understanding the complicated correlation effects between electrons. The fine structure comes from the spin-orbit, spin-other-orbit, and spin-spin interactions. The hyperfine structure of atomic energy levels is caused by the interaction between the electrons and the electromagnetic multipole moments of the nucleus. The leading terms of this interaction are the magnetic dipole and electric-quadrupole moments. The fine and hyperfine structure is sensitive to the correlation effects among electrons. Experimentally, some properties of the atomic nucleus can be obtained by investigating the hyperfine structure of the atomic energy levels. The nuclear electric-quadrupole moment, which is difficult to measure directly with nuclear physics techniques, can be determined using the measured hyperfine structure and the accurate theoretical results. The state of the beryllium atom is of interest since it is the lowest excited state in which hyperfine effects can occur, and the ground state has no hyperfine splitting because it is . It is generally a very demanding task to calculate hyperfine structure accurately. Polarization of the closed shells in the ？？core, due to the Coulomb interaction with open shells, can have a large effect on the hyperfine structure. Up till now, the most sophisticated theoretical calculations of the hyperfine structure parameters for the state of the Be atom