Galilean invariance in the exponential model of atomic collisions

Using the $X^{n+}$(1$s^2$)+${\mathrm{He}}^{2+}$ colliding systems as specific examples, we study the origin dependence of results in the application of the two-state exponential model, and we show the relevance of polarization effects in that study. Our analysis shows that polarization effects of the ${\mathrm{He}}^{+}$(1s) orbital due to interaction with $X^{(n+1)+}$ ion in the exit channel yield a very small contribution to the energy difference and render the dynamical coupling so strongly origin dependent that it invalidates the basic premises of the model. Further study, incorporating translation factors in the formalism, is needed.