Ultra Low Energy Nuclear Synthesis via Three-Body Resonances in Cuboctahedron CsH\(_2\)Pd\(_{12}\) Cluster

Abstract

The three-body nuclear and molecular resonances for \(^{135}_{~55}\)Cs+\(^2_1\)H+\(^2_1\)H, and \(^{133}_{~55}\)Cs+\(^3_1\)H+\(^3_1\)H systems are calculated in “cuboctahedron \(^{135}_{~55}\)Cs\(^2_1\)H\(_2\) \(^\textrm{A}_{46}\)Pd\(_{12}\) and \(^{133}_{~55}\)Cs\(^3_1\)H\(_2\) \(^\textrm{A}_{46}\)Pd\(_{12}\) clusters” in a very wide range from 0.01[fm] to several hundreds of nm in “one stretch” with more than “100 significant figures”, where the mass number A of Pd could be 102, 104, 105, 106, 108, 110 but neglected hereafter, because Pd isn’t concerned directly with the nuclear reaction. We obtained several new “three-ion resonance states” between the expected molecular CsH\(_2\) ground state and the first excited state in cuboctahedron CsH\(_2\)Pd\(_{12}\) cluster, where H represents either a \(^1_1\)H, a \(^2_1\)H, or a \(^3_1\)H, respectively. The molecular “ground and the first excited states” in the cluster are derived by the Kohn-Sham equation or the ADF package which could mainly describe many electrons rather than cores of ions. We found that the E2 transition times from some CsH\(_2\) \((7/2^+)\) resonance states (or the IOS states) to the nuclear \(^{139}_{~57}\)La \((7/2^+)\) ground state are about \(\tau =10^{-1}\sim 10^{-6}\)sec for five traditional potentials, and \(\tau =10^{-2}\sim 10^{-8}\)sec for six potentials with our long range three-body force (3BLF) where the “molecular resonances” can strongly interfere with the “nuclear resonances”. The thermal nuclear “critical reaction value” (or fusion constant) and/or ultra low energy corresponding value: \(C_\mathrm{high/low}\)=(duration time)\(\times \)(density)\(\times \)(energy or temperature) are compared. It was found that \(C_\textrm{low}\) is almost the same order as \(C_\textrm{high}\) or more. Finally, an ignition method for the synthesis will be discussed.