# Rutherford scattering problem

1. Oct 8, 2008

### natugnaro

1. The problem statement, all variables and given/known data
Alpha particle with kinetic energy 6MeV is scatterd on gold nucleus (A=197).
Is Rutherford cross-section formula valid for this scattering? Explain !

2. Relevant equations

3. The attempt at a solution
The Coulomb barrier is Ec=(1.03MeV)*(Z1*Z2)/(A1^1/3+A2^1/3)
Z1=79 , Z2=2 , A1=197 , A2=4
Ec=1.03MeV*158/7.41=22MeV
The 6 Mev alpha particle will not go through the barrier, forces between alpha particle and gold nucleus will be coulombic so I think it is valid to use Rutherford cross-section.
But I found that Rutherford cross-section formula is valid if
$$Z1*Z2*\alpha<<1$$ is true.Since for Z1=79,Z2=2,alpha=1/137 this is not <<1 ,
so rutherford cross-section is not valid.
Where I'm going wrong?