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We report a method for the precision measurement of the oscillator strengths and the branching ratios of the decay channels of the $6d7p$ $^3F_2$ state in $^{226}$Ra. This method exploits a set of metastable states present in Ra, allowing a measurement of the oscillator strengths that does not require knowledge of the number of atoms in the atomic beam. We measure the oscillator strengths and the branching ratios for decays to the $7s6d$ $^3D_1$, $7s6d$ $^3D_2$, and $7s6d$ $^1D_2$ states and constrain the branching ratio to the $7s6d$ $^3D_3$ state to be less than 0.4$\%$ (68$\%$ confidence limit). The lifetime of the $^3F_2$ state is determined to be $15 \pm 4$ ns., Comment: 6 pages, 4 figures. Submitted to Physical Review A

Optical trapping techniques are an efficient way to probe limited quantities of rare isotopes. In order to achieve the highest possible measurement precision, it is critical to optimize the optical trapping efficiency. This work presents the development of a three-dimensional semi-classical Monte Carlo simulation of the optical trapping process and its application to optimizing the optical trapping efficiency of Radium for use in the search of the permanent electric dipole moment of $^{225}$Ra. The simulation includes an effusive-oven atomic beam source, transverse cooling and Zeeman slowing of an atomic beam, a three-dimensional magneto-optical trap, and additional processes such as collisions with residual gas molecules. We benchmark the simulation against a well-characterized $^{88}$Sr optical trap before applying it to the $^{225}$Ra optical trap. The simulation reproduces the relative gains in optical trapping efficiency measured in both the $^{88}$Sr and $^{225}$Ra optical traps. The measured and simulated values of the overall optical trapping efficiencies for $^{88}$Sr are in agreement; however, they differ by a factor of $30$ for $^{225}$Ra. Studies of several potential imperfections in the apparatus or systematic effects, such as atomic beam source misalignment and laser frequency noise, show only limited effects on the simulated trapping efficiency for $^{225}$Ra. We rule out any one systematic effect as the sole cause of the discrepancy between the simulated and measured $^{225}$Ra optical trapping efficiencies; but, we do expect that a combination of systematic effects contribute to this discrepancy. The accurate relative gains predicted by the simulation prove that it is useful for testing planned upgrades to the apparatus., Comment: 13 pages, 9 figures, submitted to Physical Review A