Impact parameter

Impact parameter b and scattering angle θ.

The impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of the field U(r) created by an object that the projectile is approaching (see diagram). It is often referred to in Nuclear Physics (see Rutherford Scattering), as well as in Classical Mechanics.

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

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

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

See also

Tests of general relativity

References

  1. ↑ Landau LD and Lifshitz EM (1976) Mechanics, 3rd. ed., Pergamon Press. ISBN 0-08-021022-8 (hardcover) and ISBN 0-08-029141-4 (softcover).