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Latest Results for Few-Body Systems

04 December 2023

• 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.

• Calculation of Relativistic Single-Particle States

  Abstract

  A computational method is proposed to calculate bound and resonant states by solving the Klein–Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb–Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green’s operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein–Gordon and Dirac equations into an effective Schrödinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.

• An Alternative Scheme for Pionless EFT: Neutron-Deuteron Scattering in the Doublet S-Wave

  Abstract

  Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly.