Direct calculation of 4f³-4f³ transition intensities in Nd³⁺-doped YPO₄ system involving explicit effects of 4f²5d configuration

The effects of the 4f²5d configuration on the intraconfigurational electric dipole transitions of Nd³⁺ doped YPO₄ are taken into account by a 'direct' calculation. A simple model is applied to analyze the opposite-parity 4f²5d configuration admixing into 4f³ transitional states. The matrix elements of the odd-rank crystal-field interaction and the interconfigurational electric dipole transition are directly expressed using a standard tensor operator method. A set of selection rules for f-d mixing and f-f electric dipole transitions is built up. The admixture effect is considered including both explicit 4f²5d configuration and other opposite-parity states such as the 4f²n ^′g configuration which is treated by a closure procedure. Using this calculation method in combination with the experimental data from the absorption spectrum, a set of intensity parameters is obtained. The transition intensities originating from the high-lying ²G_9/2(2) level to the lower energy levels are then calculated, demonstrating a good agreement with the experimental results. The new calculation method is suitable for the electric dipole transitions within the 4f^N configurations of trivalent lanthanide ions with more than two f-electrons.