Question

A potential between two particles of mass m1 and m2 and angular momentum L is of the form

V(r) = k/r * e^(-r/a)

with k a constant (positive or negative depending on the type of interaction) that determines the strength of the interaction at small separations and a is a characteristic size at which the potential cuts off. This is known as the Yukawa potential. Under what circumstances are there bound circular orbits, and what is the radial oscillation frequency for small perturbations around this circular orbit? Note that you may not be able to get a simple expression for the radius of the orbit, it is ok to just leave the simplest expressions you can. You can still determine an expression for the curvature of the potential as needed and find the oscillation frequency as a function of the unknown radius of the orbit.

Answer 1