Efficient Separation of the Isomeric State $^{26\text{m}}\text{Al}$ from the Intense Ground State Background via Sequential Optical Pumping in Collinear Laser Spectroscopy

We propose a novel, highly efficient method for isolating the isomeric state $^{26\text{m}}\text{Al}$ from an overwhelming ground-state $^{26\text{g}}\text{Al}$ background (isomeric ratio $\sim 20:1$) using optical pumping through a 2.0 m flight zone in collinear laser spectroscopy (CLS). To investigate the underlying optical pumping (OP) dynamics, we developed a comprehensive rate equation framework. While the transition pathways can be intuitively conceptualized via a primary 7-manifold scheme, our numerical simulation solves the full 47-level rate equations by explicitly accounting for all degenerate Zeeman sublevels ($m_F$) to rigorously incorporate polarization selection rules and Clebsch-Gordan coefficients. When the continuous acceleration voltage matches the resonance conditions of the $^{26\text{g}}\text{Al}$ hyperfine transitions, the ground-state atoms undergo a 100% efficient transition into uncoupled dark states within the 2.0 m flight zone. Consequently, background fluorescence from the ground state is completely suppressed in the detection chamber, whereas $^{26\text{m}}\text{Al}$ atoms utilize a closed cycling structure to survive the flight zone, yielding a high-intensity, background-free resonance peak.