Nuclear Barrier Height a Variable Potential Wave Due to Nuclear Vibrations

Because the nucleus is vibrating, It is repeatedly changing position thereby causing the coulomb barrier height to vary over time. If the nucleus is considered as a point charge and vibrating, the distance between the nucleus and an incoming positive charge is repeatedly changing. The distance to the nucleus from an incoming charge is ${r+ A\cos2\pi ft}$. Therefore the nuclear barrier height is given by ${KE=kQ_1Q_2/(r + Acos2\pi ft)}$, where A is the average amplitude of nuclear vibration. If ${RMScos = 0.707}$, and ${r=0}$ at the point of contact of an incoming charge, the average nuclear barrier height is given by ${KE= kQ_1Q_2/ 0.707A}$.