Differential cross-section , geometric

The differential cross-section of this process for the range of impact parameters between b and b - db is given geometrically from Eq. (2.1) as follows ... 

The differential cross sections reported in this paper are absolute measurements for an apparatus having our geometry and resolution. The geometrical and resolution corrections are dependent, to some extent, on knowledge of an intermolecular potential and are included in the theoretical calculations. The largest corrections are for the finite resolution of the detector. 

Figures 5 and 6 plot the degeneracy averaged rotational distribution and differential cross sections for D + H2 (v = 1, y = 1) HD v = 1, j ) + H at Etot = l-8eV smmned over aU values of J < 34, respectively. There are two sets of curves in Figs. 5 and 6. The solid curves and data points do not include the geometric phase. The short dashed curves and open squares include the geometric phase. In Fig. 5 the results which include the geometric phase are identical to those which do not include the geometric phase (i.e. the open squares cover the solid squares). Figure 5 also contains two additional curves which include the geometric phase but are summed over J < 33 and 32. These curves correspond to the short dashed curves with the smaller open squares. The results which are summed over J = 32, 33, and 34 are nearly the same which indicates that this rotational distribution is converged with respect to the sum over J. In Fig. 6 the results which...

Figure 7 plots the degeneracy averaged differential cross section for D - -H2 v = 1, j = 1) —> HD v = 1, j = 8) -h H at F tot = l-SeV. There are four sets of curves in Fig. 7. The solid curves and data points do not include the geometric phase. The short dashed curves and open squares include...

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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