Impact parameter

In physics, the impact parameter is defined as the perpendicular distance between the path of a projectile and the center of a potential field 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 by : \theta = \pi - 2b\int_{r_\text{min}}^\infty \frac{dr}{r^2\sqrt{1 - (b/r)^2 - 2U/(mv_\infty^2)}}, where is the velocity of the projectile when it is far from the center, and is its closest distance from the center.

In physics, the impact parameter is defined as the perpendicular distance between the path of a projectile and the center of a potential field 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 by \theta = \pi - 2b\int_{r_\text{min}}^\infty \frac{dr}{r^2\sqrt{1 - (b/r)^2 - 2U/(mv_\infty^2)}}, where is the velocity of the projectile when it is far from the center, and is its closest distance from the center. ==Scattering from a hard sphere== The simplest example illustrating the use of the impact parameter is in the case of scattering from a sphere. Here, the object that the projectile is approaching is a hard sphere with radius R . In the case of a hard sphere, U(r) = 0 when r > R , and U(r) = \infty for r \leq R . When b > R , the projectile misses the hard sphere. We immediately see that \theta = 0 . When b \leq R , we find that b = R \cos\tfrac{\theta}{2}. ==See also== Distance of closest approach Tests of general relativity ==References== http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html

Text derived from https://en.wikipedia.org/w/index.php?oldid=1313135484 under CC BY-SA 4.0; modifications have been made.