Quantum microscopic approach to low-energy heavy ion collisions

The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of heavy ion collisions at energies around the Coulomb barrier. The competition between fusion and nucleon transfer mechanisms is investigated. For intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by reducing the Coulomb repulsion. A comparison with sub-barrier transfer experimental data shows that pairing correlations are playing an important role in enhancing proton pair transfer. For heavier and more symmetric systems, a fusion hindrance is observed due to the dominance of the quasi-fission process. Typical quasi-fission time of few zeptoseconds are obtained. Actinide collisions are also investigated both within the TDHF approach and with the Ballian-V\'en\'eroni prescription for fluctuation and correlation of one-body observables. The possible formation of new heavy neutron-rich nuclei in actinide collisions is discussed.Comment: Invited Plenary Talk given at NN201

Microscopic approaches for nuclear Many-Body dynamics: applications to nuclear reactions

These lecture notes are addressed to PhD student and/or researchers who want a general overview of microscopic approaches based on mean-field and applied to nuclear dynamics. Our goal is to provide a good description of low energy heavy-ion collisions. We present both formal aspects and practical applications of the time-dependent Hartree-Fock (TDHF) theory. The TDHF approach gives a mean field dynamics of the system under the assumption that particles evolve independently in their self-consistent average field. As an example, we study the fusion of both spherical and deformed nuclei with TDHF. We also focus on nucleon transfer which may occur between nuclei below the barrier. These studies allow us to specify the range of applications of TDHF in one hand, and, on the other hand, its intrinsic limitations: absence of tunneling below the Coulomb barrier, missing dissipative effects and/or quantum fluctuations. Time-dependent mean-field theories should be improved to properly account for these effects. Several approaches, generically named "beyond TDHF" are presented which account for instance for pairing and/or direct nucleon-nucleon collisions. Finally we discuss recent progresses in exact ab-initio methods based on the stochastic mean-field concept.Comment: 55 pages. Lecture given at the "Joliot Curie" school, Maubuisson, september 17-22, 2007. A french version is available at http://www.cenbg.in2p3.fr/heberge/EcoleJoliotCurie/coursannee/cours/CoursSimenel.pd

On compact manifolds admitting indefinite metrics with parallel Weyl tensor

Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such manifolds, namely, vanishing of the Euler characteristic and real Pontryagin classes, and infiniteness of the fundamental group. We also show that, in the Lorentzian case, each of them is at least 5-dimensional and admits a two-fold cover which is a bundle over the circle.Comment: 20 page

Do halos exist on the dripline of deformed nuclei?

A study of the effect of deformation and pairing on the development of halo nuclei is presented. Exploratory three-body $core+n+n$ calculations show that both the NN interaction and the deformation/excitation of the core hinder the formation of the halo. Preliminary self-consistent mean-field calculations are used to search for regions in the nuclear chart where halos could potentially develop. These are also briefly discussed.Comment: 5 pages and 3 figures, proceedings for CGS1

A CFD Simulation of High Altitude Testing of the Cryogenic Engine

A rocket designed to operate in outer space will show deviation in performance when tested at sea level. This is because of the large back pressure (1 bar) acting on it. Therefore it is tested by simulating high altitude conditions in controlled environment called High Altitude Testing (HAT). This is necessary not only for testing and developing the Engine but also to fully qualify it to be integrated into the launch vehicle. This report briefs about the design of a HAT facility. It presents a view on difficulties during CFD simulation and manual testing of the Engine. It provides a work-around for mesh interfacing of various parts. It shows how to select a suitable working fluid for the Ejector in order to create vacuum. It also shows the optimisation of mass flow rate of Nitrogen and Steam for the Ejector. It glimpses the Aero-Thermal behaviour of Nozzle flow with both Ejector On and Off conditions to prove self-pumping mode. It studies the Engine start up mode operation. It focusses on Engine shut down transient analysis. It also focusses on the re-entry of air into the facility during this process. It shows the role of Ejector in preventing re-entry of air and delaying flow separation in the Nozzle during this process

Comments on a Full Quantization of the Torus

Gotay showed that a representation of the whole Poisson algebra of the torus given by geometric quantization is irreducible with respect to the most natural overcomplete set of observables. We study this representation and argue that it cannot be considered as physically acceptable. In particular, classically bounded observables are quantized by operators with unbounded spectrum. Effectively, the latter amounts to lifting the constraints that compactify both directions in the torus.Comment: 10 pages. New "Discussion" section. References added. To appear in IJMP

An Abramov formula for stationary spaces of discrete groups

Let (G,mu) be a discrete group equipped with a generating probability measure, and let Gamma be a finite index subgroup of G. A mu-random walk on G, starting from the identity, returns to Gamma with probability one. Let theta be the hitting measure, or the distribution of the position in which the random walk first hits Gamma. We prove that the Furstenberg entropy of a (G,mu)-stationary space, with respect to the induced action of (Gamma,theta), is equal to the Furstenberg entropy with respect to the action of (G,mu), times the index of Gamma in G. The index is shown to be equal to the expected return time to Gamma. As a corollary, when applied to the Furstenberg-Poisson boundary of (G,mu), we prove that the random walk entropy of (Gamma,theta) is equal to the random walk entropy of (G,mu), times the index of Gamma in G.Comment: 16 page

TIME-DEPENDENT HARTREE-FOCK DESCRIPTION OF HEAVY IONS FUSION

A microscopic mean-field description of heavy ions fusion is performed in the framework of the Time-Dependent Hartree-Fock (TDHF) theory using a Skyrme interaction with the SLy4d parametrization. A good agreement with experiments is obtained on the position of the fusion barriers for various total masses, mass asymmetries and deformations. The excitation function of the 16O+208Pb is overestimated by about 16% above the barrier. The restriction to an independent particles state in the mean-field dynamics prevents the description of sub-barrier fusion. Effect of transfer on fusion is discussed

Time-Depentent Hartree-Fock description of heavy ions fusion

7 pages, 5 figures, Contribution to XIV Nuclear Physics Workshop at Kazimierz Dolny, Poland, Sept. 26-29, 2007International audienceA microscopic mean-field description of heavy ions fusion is performed in the framework of the Time-Dependent Hartree-Fock (TDHF) theory using a Skyrme interaction with the SLy4d parametrization. A good agreement with experiments is obtained on the position of the fusion barriers for various total masses, mass asymmetries and deformations. The excitation function of the 16O+208Pb is overestimated by about 16% above the barrier. The restriction to an independent particles state in the mean-field dynamics prevents the description of sub-barrier fusion. Effect of transfer on fusion is discussed

Structure and direct decay of Giant Monopole Resonances

We study structure and direct decay of the Giant Monopole Resonance (GMR) at the RPA level using the Time-Dependent Energy Density Functional method in the linear response regime in a few doubly-magic nuclei. A proper treatment of the continuum, through the use of large coordinate space, allows for a separation between the nucleus and its emitted nucleons. The microscopic structure of the GMR is investigated with the decomposition of the strength function into individual single-particles quantum numbers. A similar microscopic decomposition of the spectra of emitted nucleons by direct decay of the GMR is performed. In this harmonic picture of giant resonance, shifting every contribution by the initial single-particle energy allows to reconstruct the GMR strength function. The RPA residual interaction couples bound 1-particle 1-hole states to unbound ones, allowing for the total decay of the GMR. In this article, we then intend to get an understanding of the direct decay mechanism from coherent one-particle-one-hole superpositions, while neglecting more complex configurations. Time-dependent beyond mean-field approaches should be use, in the future, to extend this method.Comment: 11 pages, 10 figures. Major revisions including new formal development, new calculations and figures, comparison to experimental data and added references and discussion