Accuracy and Validity Range of a Simplified Lorentzian Approximation for Pressure-Broadened ⁸⁷Rb Hyperfine Spectra

Reliable modeling of pressure-broadened spectra is essential for maintaining physical consistency in alkali vapor-cell diagnostics. In this work, we investigate the low-power absorption spectra of isotopically enriched ⁸⁷Rb vapor cells at the D₁ and D₂ transitions, systematically comparing three fitting algorithms: single Lorentzian, hyperfine-resolved Voigt, and the doublet Lorentzian approximation. Experiments were performed across optical intensities from 40 nW to 10 mW, buffer-gas pressures from 200 Torr to 520 Torr, and temperatures between 370 K and 390 K. It is shown that when the pressure broadening dominates over Doppler broadening and the optical intensity remains below the saturation regime, the reduced doublet Lorentzian model achieves a fitting accuracy of R² > 0.996. Under the pressure conditions of 350 Torr, the fitting error for both the doublet and Voigt approximations remains below 0.3% for the D₂ line and below 0.1% for the D₁ line. At the pressures of 520 Torr and under elevated optical intensities, the spectrum evolves toward a single-peaked profile, rendering a single Lorentzian model sufficient. The quantitative applicability boundary of the doublet approximation in ⁸⁷Rb vapor cells is established, defining the operational regime where hyperfine-resolved modeling can be reduced under collision-dominated conditions in NMRG systems.