From atoms to nuclei, quarks and bejond...

Latest Results for Few-Body Systems

09 December 2023

• Detailed Studies of 12C Structure and Reactions

  Abstract

  We are reporting here on a series of theoretical investigations with both algebraic models and geometric cluster models of alpha clusters in \(^{12}\) C, focusing on the structure of the ground state, the first excited \(0^+\) state and the second excited \(2^+\) state with the purpose, in particular, of establishing if the rotational bands are compatible with rigid structures or rather if they are quantum mixture of different configurations. In a first series of paper (Vitturi et al., Transition densities and form factors in the triangular \(\alpha \) -cluster model of 12C with application to 12C+ \(\alpha \) scattering. Phys Rev C 101:014315, 2020; Casal et al., Alpha-induced inelastic scattering and alpha-transfer reactions in 12C and 16O within the Algebraic Cluster Model. Eur Phys J A 57:33, 2021), we assume a rigid equilateral triangle shape and study in detail several properties that descend from the algebraic framework, such as the energy spectrum, electromagnetic observables and calculate the transition densities in order to extract elastic and inelastic cross-sections for various processes. In a second series of papers (Moriya et al., Three- \(\alpha \) Configurations in the 0 \(^+\) States of 12C. Few-Body Syst 62:46, 2021; Moriya et al., Three- \(\alpha \) configurations of the second \(J^\pi \) = 0 \(^+\) state in 12C. Eur. Phys J A 59:37, 2023), we solve the three-body Schrödinger equation with orthogonality conditions using the stochastic variational method with correlated Gaussian basis functions. The two-body density distributions indicate that the main configurations of both the \(0_2^+\) and \(2_2^+\) states are acute iscosceles triangle shapes coming from \(^8\) Be( \(0^+\) )+ \(\alpha \) configurations and find some hints that the second \(2^+\) state is not an ideal rigid rotational band member of the Hoyle state band.

• 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.