Effective interactions and the nuclear shell-model

Abstract

This review aims at a critical discussion of the interplay between effective interactions derived from various manybody approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

β-decay rates of neutron-rich Zr and Mo isotopes in the deformed quasiparticle random-phase approximation with realistic interactions

“…The details of the calculations are described in Refs. [39][40][41] as well as the parameters used in the calculations. Then, using Eq.…”

Computational aspects of nuclear coupled-cluster theory

“…Four major shells include all possible single-particle orbits of the 0s0p1s0d1p0f shells, and the total number of Slater determinants is constructed by forming all possible direct products of single-particle wavefunctions. Present shell-model codes can today reach dimensions of d ∼ 10 10 basis states [30,31,33], and Monte Carlo-based shell-model codes can attack problems with model-space dimensions d ∼ 10 15 [11,13]. It is rather obvious from table 1 that for weakly bound systems, with many more active single-particle orbits, we cannot use available large-scale diagonalization methods.…”

“…Typical examples of popular many-body methods are coupled-cluster (CC) methods [3][4][5][6][7][8][9], various types of Monte Carlo methods [10][11][12][13], perturbative expansions [14,15], Green's function methods [16], correlation operator methods [17], the unitary-model-operator approach [18,19], the density-matrix renormalization group [20][21][22][23][24][25], density-functional theory [26][27][28], and large-scale diagonalization methods [29][30][31][32][33]. The numerical algorithms cover a broad range of mathematical methods, from linear algebra problems to Monte Carlo simulations.…”

Calculating Energy Levels in <sup>49</sup>Mn/<sup>49</sup>Cr Mirror Nuclei with OXBASH Code

“…For light nuclei, there are several standard effective interactions for the p and SD shells, respectively [11,12]. Analysis of neutron-rich SD nuclei has been of high interest in recent years as they present new aspects of nuclear structure.…”