Repulsive nature of optical potentials for high-energy heavy-ion scattering

The recent works by the present authors predicted that the real part of heavy-ion optical potentials changes its character from attraction to repulsion around the incident energy per nucleon E/A = 200 - 300 MeV on the basis of the complex G-matrix interaction and the double-folding model (DFM) and revealed that the three-body force plays an important role there. In the present paper, we have precisely analyzed the energy dependence of the calculated DFM potentials and its relation to the elastic-scattering angular distributions in detail in the case of the $^{12}$C + $^{12}$C system in the energy range of E/A = 100 - 400 MeV. The tensor force contributes substantially to the energy dependence of the real part of the DFM potentials and plays an important role to lower the attractive-to-repulsive transition energy. The nearside and farside (N/F) decomposition of the elastic-scattering amplitudes clarifies the close relation between the attractive-to-repulsive transition of the potentials and the characteristic evolution of the calculated angular distributions with the increase of the incident energy. Based on the present analysis, we propose experimental measurements of the predicted strong diffraction phenomena of the elastic-scattering angular distribution caused by the N/F interference around the attractive-to-repulsive transition energy together with the reduced diffractions below and above the transition energy.Comment: 35 pages, 13 figures, accepted for publication in Phys. Rev.

A globally convergent simplicial algorithm for stationary point problems on polytopes

Stationary Point

The classical and quantum dynamics of the inhomogeneous Dicke model and its Ehrenfest time

We show that in the few-excitation regime the classical and quantum time-evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N>>1. In the presence of a single excitation only, the leading term in an 1/N-expansion of the classical equations of motion reproduces the result of the Schroedinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schroedinger equation exactly for two excitations and a particular inhomogeneity we obtain 1/N-corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by tau_E=sqrt{N}, where sqrt{} is an effective coupling strength between the two-level systems and the boson.Comment: 14 pages, 4 figure