Multi-configuration Dirac-Fock Calculations for Atomic Structures of Ca+

The metastable 3d 2D3/2,5/2 states of Ca+ are interesting in various experimental fields such as optical frequency standards[1], quantum information science[2], and astrophysics[3]. Ca+ is also a challenging system for the calculations of atomic structure, due to the effects of d orbitals and strong core-valence correlation effects[4]. Recently, a lot of experimental[5,6] and theoretical[5,7] research works have been done for the lifetimes of 3d 2D3/2,5/2 states of Ca+. In this letter, we calculated the 3d 2D3/2,5/2 and 4p 2P1/2,3/2 energy levels of Ca+, us-ing multi-configuration Dirac-Fock (MCDF) method with the Breit interactions and quan-tum electrodynamics corrections. Based on multi-configuration self-consistent field (MC-SCF) calculation strategies[8], we optimized a set of high-quality orbital basis. Owing to the feature of d orbital in Ca+, the obitals with approximate equal effective quantum num-ber ν = n − µ are defined as a layer, e.g. 4s, 3d and 4p constitute the ν = 2 layer. In order to consider the core-valence correlation, the configurations created by single exci-tations respectively from core 3p6 and valence 4s1 are included. In order to consider the monopole, dipole and quadrupole excitation correlations uniformly, the 4f and 5g orbital