Quantum-mechanical vs. semi-classical spectral-line widths and shifts from the line core in the non-impact region for the Ar-perturbed/ K-radiator system

Abstract

New quantum-mechanical (QM) and semi-classical (SC) shifts (d's) and widths (HWHM's, w's) were measured from the line core of computed full spectral-line shapes for the Ar-perturbed/K-radiator system (K/Ar). The initial state of our model was based on a 4 p 2 P 3/2,1/2 pseudo-potential for the K/Ar system, and the final state on a zero potential. The Fourier transform of the line shape formed the basis for the computations. Excellent agreement was found between the QM and SC values of d and of w in a high-pressure ( P) non-impact region, which was characterized by a √ P dependence of w and a P dependence of d. These agreements were shown to be another example of a correspondence between classical (SC) quantities and QM quantities in the limit of large quantum numbers. Typically at P=1×10 6 Torr and T=400 K, w QM= 448 cm −1 and w SC =479 cm −1, where the deviation from the mean is ±3.3%. Also, d QM =−3815 cm −1 and d SC =−3716 cm −1, where the deviation from the mean is ±1.3%. A new general method was formulated which yielded a definite pressure P 0, which was defined as an upper limit to the low-pressure impact approximation and a lower limit to the non-impact region.