Dineutron correlations in nuclear surface

Two-neutron correlation in quasi two-dimensional (2D) neutron matter is studied by means of the BCS theory to understand formation of nn pairs in nuclear surface of neutron-rich nuclei. The spin-zero nn pair correlation in low density neutron systems confined in an infinite slab is investigated in a simplified model that neutron motion of one direction is frozen. It is found that, when the slab is thin enough, the nn pairing gap enhances and the size shrinking of nn Cooper pair occurs at finite low-density region in the quasi-2D system

Microscopic approach to large-amplitude deformation dynamics with local QRPA inertial masses

We have developed a new method for determining microscopically the fivedimensional quadrupole collective Hamiltonian, on the basis of the adiabatic self-consistent collective coordinate method. This method consists of the constrained Hartree-Fock-Bogoliubov (HFB) equation and the local QRPA (LQRPA) equations, which are an extension of the usual QRPA (quasiparticle random phase approximation) to non-HFB-equilibrium points, on top of the CHFB states. One of the advantages of our method is that the inertial functions calculated with this method contain the contributions of the time-odd components of the mean field, which are ignored in the widely-used cranking formula. We illustrate usefulness of our method by applying to oblate-prolate shape coexistence in 72Kr and shape phase transition in neutron-rich Cr isotopes around N=40.Comment: 6pages, talk given at Rutherford Centennial Conference on Nuclear Physics, 8 - 12 August 2011, The University of Mancheste

Quadrupole shape dynamics from the viewpoint of a theory of large-amplitude collective motion

Low-lying quadrupole shape dynamics is a typical manifestation of large amplitude collective motion in finite nuclei. To describe the dynamics on a microscopic foundation, we have formulated a consistent scheme in which the Bohr collective Hamiltonian for the five dimensional quadrupole shape variables is derived on the basis of the time-dependent Hartree-Fock-Bogoliubov theory. It enables us to incorporates the Thouless-Valatin effect on the shape inertial functions, which has been neglected in previous microscopic Bohr Hamiltonian approaches. Quantitative successes are illustrated for the low-lying spectra in 68Se, 30−34Mg and 58−64Cr, which display shape-coexistence, -mixing and -transitional behaviors

Numerical search of discontinuities in self-consistent potential energy surfaces

Potential energy surfaces calculated with self-consistent mean-field methods are a very powerful tool, since their solutions are, in theory, global minima of the non-constrained subspace. However, this minimization leads to an incertitude concerning the saddle points, that can sometimes be no more saddle points in bigger constrained subspaces (fake saddle points), or can be missing on a trajectory (it missing saddle points). These phenomena are the consequences of discontinuities of the self-consistent potential energy surfaces (SPES). These discontinuities may have important consequences, since they can for example hide the real height of an energy barrier, and avoid any use of a SPES for further dynamical calculations, barrier penetrability estimations, or trajectory predictions. Discontinuities are not related to the quality of the production of a SPES, since even a perfectly converged SPES with an ideally fine mesh can be discontinuous. In this paper we explain what are the discontinuities, their consequences, and their origins. We then propose a numerical method to detect and identify discontinuities on a given SPES, and finally we discuss what are the best ways to transform a discontinuous SPES into a continuous one.Comment: 14 pages, 9 figure

The nuclear energy density functional formalism

The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a {\it Hamiltonian-based} picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel $E[g',g]$ at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a {\it mathematically} meaningful fashion even if $E[g',g]$ does {\it not} derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making {\it any} reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a {\it physical} standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor