Parameterized analysis of the ab initio calculation of Pr3+ energy levels

The energy levels of Pr3+ ions from various relativistic coupled-cluster calculations and from measurements are studied based on the parametrized semi-empirical Hamiltonian. The results show that a set of energy levels obtained from ab initio calculation may be converted into a set of semi-empirical parameters. Parameter values have advantages because the interpretation of the interaction mechanisms is simpler and they may be easily combined with semi-empirical methods. We propose calculation of parameters by combining relativistic coupled-cluster theory with many body perturbation theory instead of calculation of energy levels directly in future ab initio calculations.