A New Quantization of Hadron System and Ultra-Low Energy Nuclear Fusion

A new quantization is proposed for an energy-dependent particle exchange potential. The quantum number corresponds not only to the branch point of the potential cut, but also to the index of a long-range hadron potential. By using the long-range potential, an ultra-low energy nuclear (ULEN) reaction is investigated. It was found that a three-body Cs + H + H plasma in a Pd \(_{12}\) ${}_{12}$ cage could be excited to \(1.36\times 10^{-4}\) $1.36\times {10}^{-4}$  eV  \(\sim 300\) $\sim 300$  eV by an electric current where the long-range potential gives one or two order larger reaction probability than the others. A ULEN reaction was compared with the thermo-nuclear fusion by using well-known critical fusion constant defined by \(C_{high/low}\) $C_{high/low}$  = (a duration time)  \(\times \) $\times$  (a plasma density)  \(\times \) $\times$  (a temperature). We found that \(C_{low}\) $C_{\mathit{low}}$ is almost the same as \(C_{high}\) $C_{\mathit{high}}$ or more. We concluded that the ULEN synthesis could occur with a high-pressure hydrogen circumstance and a high-density CsH \(_2\) ${}_2$ Pd \(_{12}\) ${}_{12}$ cluster.