Question

when is Impact Parameter minimum

Answer 1

The impact parameter {\displaystyle b} is defined as the perpendicular distance between the path of a projectile and the center of a potential field {\displaystyle U(r)} created by an object that the projectile is approaching (see diagram). It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics.

The impact parameter is related to the scattering angle {\displaystyle \theta } by[1]

{\displaystyle \theta =\pi -2b\int _{r_{\mathrm {min} }}^{\infty }{\frac {dr}{r^{2}{\sqrt {1-(b/r)^{2}-2U/mv_{\infty }^{2}}}}}}

where {\displaystyle v_{\infty }} is the velocity of the projectile when it is far from the center, and {\displaystyle r_{\mathrm {min} }} is its closest distance from the center.
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