Variable Differential Cross Section Due to Nuclear Motion

The standard differential cross section formula assumes a motionless massive point nucleus. However, nuclear oscillation is a reality, changing the position of the impact parameter in relation to the incoming beam of particles or ions thereby affecting the cross section. If the static differential cross section is $d\sigma/d\Omega = (Ze^2\csc^2 \theta/8\pi\epsilon_0T)^2$, an oscillator can be added to the formula describing the movement of the cross section so that the resulting formula for differential cross section is $(Ze^2\csc^2\theta/2/8\pi\epsilon_0T)^2 (A_x\cos\alpha i + A_y\cos\beta j +Az\cos\gamma k$. By taking in ot account nuclear motion there will be some reconciliation between experimental and theoretical values.