Selection rules for 4f2→4f2 electric dipole transitions by considering mixing with 4f5d components of Pr3+ in SrAl12O19

A set of selection rules is deduced for the 4f2 transitional levels that mix with explicit 4f5d components. Based on these selection rules the dipole-allowed transitions between the 4f2 crystal field levels are determined in Pr3+ doped SrAl12O19. Meanwhile, the main 4f5d components mixed into 4f2 transitional levels are identified by determining the nonzero matrix elements of both the odd-rank crystal-field and the electric dipole operator. The selection rules have been applied to analyze the transitions from 1S0 and 3P0 to lower crystal field levels.