Impact parameter differential collision cross-section

In Figs. 24 and 25 we show the measured double differential cross sections for electron emission at zero degrees in collisions of 100-keV protons with He and H2 [39] compared to CDW-EIS predictions [39]. Uncertainties associated with the experimental results vary from 1% near the electron capture to the continuum peak to about 15% near the extreme wings of the distribution. These results have been scaled to provide a best fit with CDW-EIS calculations. In both cases there is satisfactory agreement between the CDW-EIS calculations and experiment, particularly with excellent agreement for electrons with velocities greater than v, where v is the velocity of the projectile. For lower-energy electrons the eikonal description of the initial state may have its limitations, especially for lower-impact parameters. 

The collision parameters can be specified further if the double differential cross section is measured. This is usually written as d2a /dEdQ, where E and Q refer to the energy and solid angle of either the scattered positron or the ejected electron. Measurements of this quantity have been made for positron impact and will be described below and compared with data for electrons. 

From the relation between the deflection function and the phase shift, equation (22), one obtains the phase. shift for the collision as a function of the impact parameter (or angular momentum) necessary for determination of the differential cross section. 

Since the scattering angle is related to the impact parameter b, the experiment answers the questions which impact parameters contribute preferentially to collision-induced vibrational or rotational transitions and how the transferred angular momentum AJ depends on impact parameters, initial state (vj",Jj") and the collision partner B [13.112]. In Fig. 13.29 some differential cross sections a(6) for Naj+Ne collisions are plotted versus the... 

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