What is the value of impact parameter for scattering through 180°?
Answers
no disperson occurs if light travels at 180
The impact parameter {\displaystyle b} b is defined as the perpendicular distance between the path of a projectile and the center of a potential field {\displaystyle U(r)} 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 } \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}}}}}} \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 }} v_{{\infty }} is the velocity of the projectile when it is far from the center, and {\displaystyle r_{\mathrm {min} }} r_{{\mathrm {min}}} is its closest distance from the center.