431(6): The m Theory of the Nuclear Strong Force and Conditions for LENR
This note derives the differential equation Eq. (5) which can be solved by computer for the m(r) of the nuclear strong force. The correct Woods Saxon force is given in Eq. (1), checked by computer algebra and it is equated with the m force to give Eq. (5), a differential equation for the m(r) of the nuclear strong force. The resonance condition (7) of m theory is shown to correspond to an infinitely thin surface layer of the nucleus, which is made up of a hard outer surface layer of neutrons and an interior of neutrons and protons. At the surface of the nucleus, r = R, the differential equation (12) may be used to find m (r ) at the nuclear surface. The 1954 Woods Saxon potential is a mean field theory based on the shell model of the nucleus. The shell model can be used to give magic numbers which indicate which nuclei are stable. Wigner et al were awarded a Nobel prize for the nuclear shell model, which can be extended to describe spin and spin orbit interaction. The shell model could be developed with m theory. Google "Surface thickness of a nucleus" to find that the surface thickness a sub N in lead is of the order of ten power minus sixteen metres according to the latest experiments. So it makes perfect sense to deduce that the force of attraction between Ni64 and p is maximized when the shell thickness is minimized, reduced to zero by the resonance condition of the m theory. The shell thickness is the "protective armour" of the nucleus, an outer layer of neutrons. Inside is a mixture of neutrons and protons. Ni64 is the isotope of nickel which has the most number of neutrons. So it is overloaded with neutrons but it is stable. Once a proton enters by m space resonance, it becomes unstable, and transmutes to Cu63, megabytes of energy and other particles. The challenge is therefore to solve Eq. (5) by computer. The result would be dm(r) / dr and m(r) for the nuclear strong force.