A Meson Mass Formula and A Two-Nucleon Potential from a Nonlinear $\lambda\phi^5$ Theory

An exact solution of a $\lambda\phi^5$ theory\footnote{P.B. Burt, Phys. Rev. Lett. 32,1080 (1974)} which is a special case of a class of nonlinear field theories developed by Burt\footnote{P.B. Burt, Quantum Mechanics and Nonlinear Waves,(Harwood 1981)} is used to construct a propagator that has poles at $M_n=(3n+1)m_\pi$ which is the neutral scalar meson mass formula. The propagator is then used to derive a solitary wave exchange two-nucleon potential ($\lambda\phi^5$ SWEP) in the same manner as the derivation of a $\lambda\phi^4$ SWEP\footnote{M.Sebhatu, Nuovo Cimento, 16,463(1976)} and SG SWEP\footnote{M.Sebhatu, Lett. Nuovo Cimento, 16,463(1976)}. SWEPs have the virtue of describing two-nucleaon interaction with the least number ($<$ 3) parameters. The $\lambda\phi^4$ is of a special interest because it yields a neutral scalar meson mass formula that reasonably agrees with know meson and predicts others that may exist.