Determination of the Difference Potential from Resonant Charge-Exchange Total Cross Sections: Analysis of RB+-Rb andCs+-Cs

Within a two-state formalism, a systematic procedure is developed for deriving the difference between the gerade and ungerade state potentials from resonant charge-exchange total cross sections. It is shown that three potential constants may be derived from (i) the relative monotonic velocity dependence of the cross sections, (ii) the absolute scaling factor, and (iii) the frequency of the interference oscillations. The method is applied to the ${\mathrm{Rb}}^{+}$-Rb and ${\mathrm{Cs}}^{+}$-Cs experimental cross-section measurements of Perel, Vernon, and Daley. The difference potential for ${\mathrm{Rb}}^{+}$-Rb is found to exhibit a maximum at 5.6 a.u. with a magnitude of 3.0 eV. The ${\mathrm{Cs}}^{+}$-Cs data are likewise analyzed and a maximum of 2.3 eV is located at 6.5 a.u. In both cases, the error estimates are about ±25%.