Direct Determination of Scattering Phase Shifts from Differential Cross Sections

As the first step in the analysis of molecular beam scattering data, a computational method has been developed for the determination of the asymptotic phase shifts from the differential cross sections. The phase shifts were represented by a linear combination of two Gaussian functions and an exponential function, and the parameters of this empirical function were determined from a least-squares fit of the observed cross sections. The computational time required was less than 10 sec per iterative cycle on the IBM 7090 computer. In order to obtain a unique fit of the positive phase shifts, it was necessary to use data from a range of scattering angles wide enough to include at least the first minimum and second maximum of the differential cross sections.