Jacobi-Lie systems: Fundamentals and low-dimensional classification

A Lie system is a system of differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. We define and analyze Lie systems possessing a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields relative to a Jacobi manifold, the hereafter called Jacobi-Lie systems. We classify Jacobi-Lie systems on $\mathbb{R}$ and $\mathbb{R}^2$. Our results shall be illustrated through examples of physical and mathematical interest.Comment: 15 pages. Examples, references and comments added. Based on the contribution presented at "The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications", July 07-11, 2014, Madrid, Spain. To appear in the Proceedings of the 10th AIMS Conferenc

Differential Cross Sections for Neutron Elastic and Inelastic Scattering on 23

Measurements of neutron elastic and inelastic scattering from 23Na have been performed for sixteen incident neutron energies above 1.5 MeV with the 7-MV University of Kentucky Accelerator using the 3H(p,n) reaction as the neutron source. These measurements were complemented by γ-ray excitation functions using the (n,n'γ) reaction. The time-of-flight technique is employed for background reduction in both neutron and γ- ray measurements and for determining the energy of the scattered neutrons. Cross section determinations support fuel cycle and structural materials research and development. Previous reaction model evaluations [1] relied primarily on total cross sections and four (n,n0) and (n,n1) angular distributions in the En = 5 to 9 MeV range. The inclusion of more inelastic channels at lower neutron energies provides additional information on direct couplings between elastic and inelastic scattering as a function of angular momentum transfer. Reaction model calculations examining direct collective and statistical properties were performed

Nuclear Structure Studies of 106

Excited states in 106Pd and 106Cd have been studied using the (n,n′γ) reaction. The data include level lifetimes, spins, branching ratios, and multipole mixing ratios, and give a comprehensive view of excitations with spin ≤6ħ. The determined E2 strengths show serious discrepancies with the quadrupole phonon structure expected in these nuclei