Parametrization of 5f-5f Transition Probabilities Between Stark Levels of $\mathrm{U}$ ${^{3+}}$ in LiYF${_4}$

In order to simulate intensities of the 5f-5f transitions of U$^{3+}$ in LiYF$_4$, we applied the Judd-Ofelt theory. Because of the large crystal-field splitting of the $J$-multiplets in the actinides, a set of phenomenological intensity parameters $B_{\lambda kq}$ is introduced to describe the transition probabilities between the crystal-field sublevels of U$^{3+}$. The intensities of the absorption transitions between the crystal field levels calculated and a set of six phenomenological intensity parameters give a rather good simulation of the experimental intensities, and the applicability of the Judd-Ofelt theory is discussed for the 5f$\rightarrow$ 5f transitions of the actinides. From these values, the oscillator strengths between the excited states involved in the laser transition $^4{\rm I}_{11/2}\rightarrow ^4{\rm I}_{9/2}$ are calculated and the corresponding radiative lifetime is compared to the experimental one. Moreover, a comparison between the actinide ion U$^{3+}$ (5f$^3$) and the lanthanide ions Nd$^{3+}$ (4f$^3$) and Er$^{3+}$ (4f$^{11}$) in LiYF$_4$ is made