Spectroscopy of the $\mathbf{X^2\Sigma^+(v=2) \rightarrow A^2\Pi_{1/2}(v=1)}$ Transition in MgF: Hyperfine Structures and Spectroscopic Constants
We report spectroscopic results of the \(X^2\Sigma^+(v=2) \rightarrow A^2\Pi_{1/2}(v=1)\) transition in magnesium monofluoride (MgF). Using Doppler-free Laser-Induced Fluorescence (LIF) spectroscopy on the \(X^2\Sigma^+(v=2) \rightarrow A^2\Pi_{1/2}(v=1)\) transition, we resolved 47 hyperfine components distributed over 11 transition lines in X and A states. An effective Hamiltonian -- comprising contributions from vibrational, rotational, \(\Lambda\)-doubling, and hyperfine interactions -- was presented to model the energy structure of the \(A^2\Pi_{1/2}(v=1)\) state. The spectroscopic parameters, including the rotational constant, the \(\Lambda\)-doubling parameter, and the hyperfine interaction constants, were extracted using a least-square fitting and Markov Chain Monte Carlo (MCMC) procedure. Our study reveals that the spectroscopic constants show subtle changes compared to the \(A^2\Pi_{1/2}(v=0)\) state. These results provide critical spectroscopic benchmarks for optimizing optical cycling schemes in MgF, thereby advancing optical cycling efficiency in the magneto-optical trapping of MgF.