Low Energy Nuclear Reactions Explained by Nuclear Oscillation--The End of Tunnelling

Low energy nuclear reactions can be explained through a nuclear oscillation factor using classical mechanics eliminating the need for a tunnelling explanation. Consider an incoming positive charge approaching vibrating nucleus. If the amplitudes of oscillating are equal in all directions and x the position of the incoming charge to the nucleus, then the position of the particle is r = [(x + AcosX)$^2$ + (AcosY)$^2$ + (AcosZ)$^2$]$^{1/2}$. Then KE needed = Barrier Height = kQ(n)q(i)/[(x + AcosX)$^2$ + (AcosY)$^2$ + (AcosZ)$^2$]$^{1/2}$. If the nuclear reaction takes place on the x-axis and contact with the nuclear surface is considered to be contact with the nuclear well, x = AcosX, the magnitude for r after collecting terms is r = [4(AcosX)$^2$ + (AcosY)$^2$ + (Acos Z)$^2$]$^{1/2}$. The KE needed to mount the barrier height is KE = kQ(n)q(i)/[4(AcosX)$^2$ + (AcosY)$^2$ + (Acos Z)$^2$]$^{1/2}$. If the maximum for all cos values is +1 and for all minimum values is -1, r = (6)$^{1/2}$A. and average cos value is RMScos = (1/2)$^{1/2}$, r = (3)$^{1/2}$A. For a static nucleus r = 0. The barrier height minimum is KE = kQ(n)q(i)/(6)$^{1/2}$A, maximun KE = kQ(n)q(i)/0 and average KE = k(q(n)q(i)/(3)$^{1/2}$A. Therefore the Coulomb barrier is different at different times accounting classically for all nuclear reactions.