Analytical Mech Homework Solutions 84

Analytical Mech Homework Solutions 84 - Before evaluating...

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Before evaluating this integral, we need to find ( ) 1 max min r = u , in other words, the distance of closest approach to the scattering center. () () 22 min min 0 2 min 11 1 22 2 k ETr Vr m v m v r =+=+= But, the angular momentum per unit mass l is … and substituting for v into the above gives … 0m i n lb v rv == 2 2 0 min min ml k mv rr += so … 2 2 0 max min 1 mv u rm l k + Solving for u max max 2 2 0 1 u k b mv = + Now we evaluate the integral for θ 0 max max 1 0 max 0 0 2 00 0 sin 2 1 u u bb u du u kk k bu mv mv mv b π θ ===  ++ −+   Solving for b () 0 0 2 0 0 2 4 k b mv = But ( 0 1 2 S ) πθ =− . Thus, we have … 2 0 2 S S SS k b mv = We can now compute the differential cross section …
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