Find the scattering amplitude in the born approximation for soft-sphere scattering at arbitrary energy. show that the formula reduces to in the low-energy limit tta equation 1: f(0,ø v 2h 3 the potential of interest is given as eq. 2 vo. (rsa) v(r)0. (r> a) note this is the finite version of hard-sphere scattering. given sufficient energy, an incoming particle could blast right through the potential. this better reflects reality in most situations for example, incident particles have a significant probability of zipping right through the vast open space between electrons and the nucleus for any given atom

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.