Lectures at BMinNT Workshop
L. BONNEAU (CENBG):
This non exhaustive course is a brief overview of the main ideas behind the chiral effective potentials, which are increasingly used in so-called "ab-initio" theoretical approaches to Nuclear Structure. In particular we will address the questions of the Wilsonian renormalization, illustrated in a simple example, and the chiral symmetry in the effective Lagrangian. From a technical point of view, we shall use basic knowledge of group-representation theory to build the most general 2N potential in momentum-spin-isospin space and classify the various terms according to their isospin content. Then we will illustrate at leading order the methods to derive the chiral potential. Finally we will discuss some recent applications to nuclear-structure calculations.
R. LAZAUSKAS (IPHC):
This lecture aims to give a short introduction to few-body methods based on Faddeev-Yakubovsky equations. More specifically, the following items will be discussed:
- Numerical methods for simple bound and scattering state problems
(with excercises for a 2-body case) - Highlights of the formalism of Faddeev-Yakubovsky equations
- 3-body Faddeev equation in configuration space
H. MOLIQUE (IPHC):
Group theory is considered a major tool in many branches of physics. We will illustrate how rich and powerful group theoretical approaches are for theoretical nuclear physics applications. The basic concepts will be recalled, and applied to some selected examples.
A short Introduction to Group Theory
Ph. QUENTIN (CENBG):
I) Independent-particle states:
Pauli principle, Second quantization, Hartree-Fock approximation
II) Correlations
Quasi-particles, particle-hole excitations, pairing correlations, BCS approximation and a particle number conserving approach
III) Symmetry breaking
Translation, Rotation, Isospin (spurious or physical) symmetry breaking cases
Nuclear Structure self-consistant Mean Fields
N. SMIRNOVA (CENBG):
The present lecture proposes an introduction to the nuclear shell model ---
a powerful microscopic approach to nuclear structure. Within the shell model, a general non-relativistic nuclear Hamiltonian, containing nucleonic kinetic energies and nucleon-nucleon interactions, is separated into a schematic spherically-symmetric independent particle Hamiltonian (e.g., harmonic oscillator) and a residual two-body interaction. The eigenvalue problem is solved by the diagonalization of the full Hamiltonian matrix in a many-body basis of the independent particle Hamiltonian eigenstates.
We introduce the techniques for the basis construction and diagonalization of the Hamiltonian matrix, as well as perform resolution of sample problems in small model spaces and calculation of the matrix elements of various operators. We will also discuss the ways to construct residual interactions (microscopic, empirical or schematic).
To illustrate, we will demonstrate applications of the shell model to the structure of nuclei far from the beta stability region, calculation of the weak processes on nuclei and implications for nuclear astrophysics.
Finally, computer sessions will be proposed to get familiar with the shell-model code Antoine developed by E. Caurier, F. Nowacki at IPHC, Strasbourg.
A. ZUKER (IPHC):
EXCEPTIONNAL SEMINAR: "Beyond the shell model"
