The Rutherford differential cross section [tex]\frac{d\sigma}{d\Omega}[/tex] goes like(adsbygoogle = window.adsbygoogle || []).push({});

cosec([tex]\vartheta[/tex])^4

which means at [tex]\vartheta[/tex]=0 the differential cross section is infinite, which is ok.

My question is, given that the differential cross section is proportional to theprobability per unit solid angle[tex]\frac{dP}{d\Omega}[/tex], which is proportional to the expected rate of scattered particles, why/how does the expected rate go to infinity at [tex]\vartheta[/tex]=0?

I take i've got something a little/very wrong...

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# Singularity in Rutherford cross section

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