An iodine saturated absorption spectrometer has been constructed to calibrate a laser for precision laser spectroscopy studies at the Facility for Rare Isotope Beams at Michigan State University. Accurately modeling and fitting experimental iodine hyperfine spectra is imperative for a precise determination of laser frequency. For a given rovibrational level in iodine, the hyperfine spectrum consists of 15 or 21 hyperfine levels that are described by the effective hyperfine Hamiltonian. Coupling between many hyperfine levels must be considered. Thus, the energy of each hyperfine level is obtained by diagonalizing a Hamiltonian matrix, comprised of either 45 or 63 states for both the lower and upper levels of the iodine transition. In this work, a Python-based program was written to construct and diagonalize the hyperfine Hamiltonian. After matrix diagonalization, the spectrum can be modeled as a function of four hyperfine coupling constants for both the ground and excited levels. Additionally, a nonlinear curve fitting routine was implemented to fit a full iodine hyperfine spectrum and deduce the hyperfine coupling constants and hyperfine spectrum centroid. The coupling contributions from the 45 or 63 states are considered during the fitting routine, which allows precise fitting of all 15 or 21 hyperfine transitions simultaneously to deduce a single centroid value for the transition. The creation of this application will be presented, and future prospects using this tool for laser frequency calibration will be discussed.

Deducing coupling constants from molecular iodine hyperfine spectra

ACS Spring Meeting 2021

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