Integral cross-section , geometric phase

Y. S. M. Wu and A. Kuppermann, Prediction of the effect of the geometric phase on product rotational state distributions and integral cross sections, Chem. Phys. Lett. 201 178 (1993). 

Figure 9 plots the degeneracy averaged partial integral cross sections for H- -H2(v = 0, j = 0) Fl2(v = 1, j = 0 — 3) + FI as a function of energy and include all J < 10. The solid curve and solid squares do not include the geometric phase. The short dashed curve and open squares include the geometric phase and are based on the vector potential approach. For the... 

These p, x coordinates have been used in all integral and differential reaction cross-section calculations which include the effect of the geometric phase reported so far [12,36,46-48]. They are closely related to several sets of coordinates described previously [49-54]. 

The cancellation of the geometric phase effects in both the integral and differential cross sections with respect to the sum over J occurs for all of the energies and all of the initial and final states that we have looked at. Some small amplitude out-of-phase behavior is seen in some of the differential cross sections but these differences are typically quite small (usually less than 5%). We estimate that our calculations are accurate to within a few... 

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