Low-lying 2S states of the singly charged carbon ion

In this work, we report benchmark variational calculations of the five lowest doublet S-states of the C+ ion. The wave functions of this five-electron system are expanded in terms of 16 000 all-particle explicitly correlated Gaussians (ECGs) whose nonlinear variational parameters are subject to extensive optimization. The motion of the finite-mass nucleus is explicitly included in the Hamiltonian, while relativistic corrections to the energy levels are computed in the framework of the perturbation theory. Lowest-order quantum electrodynamics (QED) corrections are also estimated. The results obtained for the energy levels enable the determination of transition frequencies with the accuracy that approaches the available experimental data and may open up avenues for future determination of nuclear charge radii of carbon isotopes.