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Various perturbative and non-perturbative many-body techniques are discussed in this work. Especially, we will focus on the summation of so-called Parquet diagrams with emphasis on applications to finite nuclei. Here, the subset of two-body…
The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state…
Recently it was argued that it might be possible treat the conventional nuclear structure problem -- nonrelativistic point nucleons interacting through a static and rather singular potential -- as an effective theory in a shell-model basis.…
While empirical shell model calculations have successfully described low-lying nuclear data for decades, only recently has significant effort been made to quantify the uncertainty in such calculations. Here we quantify the statistical error…
Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution…
A microscopic description of nuclei is important to understand the nuclear shell-model from fundamental principles. This is difficult to achieve for more than the lightest nuclei without an effective approximation scheme. The purpose of…
The fundamental description of both structural properties and reactions of light nuclei in terms of constituent protons and neutrons interacting through nucleon-nucleon and three-nucleon forces is a long-sought goal of nuclear theory. I…
Most nuclear structure calculations, even for full configuration interaction approaches, are performed within truncated model spaces. These require consistent transformations of the Hamiltonian and operators to account for the missing…
We propose a scheme for extracting an effective three-body interaction originating from a two-nucleon interaction. This is based on the Q-box method of Kuo and collaborators, where folded diagrams are obtained by differentiating a sum of…
We present a translationally invariant formulation of the no-core shell model approach for few-nucleon systems. We discuss a general method of antisymmetrization of the harmonic-oscillator basis depending on Jacobi coordinates. The use of a…
We generalize the Jacobi no-core shell model (J-NCSM) to study double-strangeness hypernuclei. All particle conversions in the strangeness $S=-1,-2$ sectors are explicitly taken into account. In two-body space, such transitions may lead to…
We analyze the Lipkin Model using effective operator techniques. We present both analytical and numerical results for effective Hamiltonians. The accuracy of the cluster approximation is investigated.
In this contribution we present calculations performed for interacting electron systems within a non-perturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is…
The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are…
Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, realistic interactions with greatly improved links to Quantum Chromodynamics, the advent of high performance computing, and…
We apply the no-core shell model to the nuclear structure of odd-mass nuclei straddling $^{48}$Ca. Starting with the NN interaction, that fits two-body scattering and bound state data we evaluate the nuclear properties of $A = 47$ and $A =…
The Unitary Correlation Operator Method (UCOM) is applied to realistic potentials. The effects of tensor correlations are investigated. The resulting phase shift equivalent correlated interactions are used in the no-core shell model for…
We combine Halo/Cluster Effective Field Theory (H/CEFT) and the Gamow Shell Model (GSM) to describe the $0^+$ ground state of $\rm{^6He}$ as a three-body halo system. We use two-body interactions for the neutron-alpha particle and…
The nuclear shell model is one of the successful models in theoretical understanding of nuclear structure. If a convenient effective interaction can be found between nucleons, various observables such as energies of nuclear states are…
The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed…