In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.

http://iopscience.iop.org/article/10.1088/0034-4885/77/9/096302/pdf

Coupled-cluster computations of atomic nuclei

We present an overview of recent results and developments of the no-core shell model (NCSM), an ab initio approach to the nuclear many-body problem for light nuclei. In this approach, we start from realistic two-nucleon or two- plus three-nucleon interactions. Many-body calculations are performed using a finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic inter-nucleon interactions that generate strong short-range correlations, we derive effective interactions by unitary transformations that are tailored to the HO basis truncation. For soft realistic interactions, this might not be necessary. If this is the case, the NCSM calculations are variational. In either case, the ab initio NCSM preserves translational invariance of the nuclear many-body problem. In this review, we, in particular, highlight results obtained with the chiral two- plus three-nucleon interactions. We discuss efforts to extend the applicability of the NCSM to heavier nuclei and larger model spaces using importance-truncation schemes and/or use of effective interactions with a core. We outline an extension of the ab initio NCSM to the description of nuclear reactions by the resonating group method technique. A future direction of the approach, the ab initio NCSM with continuum, which will provide a complete description of nuclei as open systems with coupling of bound and continuum states, is given in the concluding part of the review.

https://iopscience.iop.org/article/10.1088/0954-3899/36/8/083101/pdf

Recent developments in no-core shell-model calculations

The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh–Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A = 3 and 4 nuclear systems. When the wavefunction of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this review, the main aspects of the method are discussed together with its application to the A = 3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon–nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high-momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this review is twofold. The first is to present a complete description of the HH method for bound and scattering states, also including detailed formulae for the computation of the matrix elements of the NN and 3N interactions. The second is to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.

http://iopscience.iop.org/article/10.1088/0954-3899/35/6/063101/pdf

A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states

Recent experimental results in three-body systems have unambiguously shown that calculations based only on nucleon-nucleon forces fail to accurately describe many experimental observables and one needs to include effects which are beyond the realm of the two-body potentials. This conclusion owes its significance to the fact that experiments and calculations can both be performed with high accuracy. In this review, both theoretical and experimental achievements of the past decade will be underlined. Selected results will be presented. The discussion on the effects of the three-nucleon forces is, however, limited to the hadronic sector. It will be shown that despite the major successes in describing these seemingly simple systems, there are still clear discrepancies between data and the state-of-the-art calculations.

/pdf/signatures-of-three-nucleon-interactions-in-few-nucleon-2fq7ifpya8.pdf

Signatures of three-nucleon interactions in few-nucleon systems.

We consider the classical equations of the Born-Infeld-Abelian-Higgs model (with and without coupling to gravity) in an axially symmetric ansatz. A numerical analysis of the equations reveals that the (gravitating) Nielsen-Olesen vortices are smoothly deformed by the Born-Infeld interaction, characterized by a coupling constant ${\ensuremath{\beta}}^{2},$ and that these solutions cease to exist at a critical value of ${\ensuremath{\beta}}^{2}.$ When the critical value is approached, the length of the magnetic field on the symmetry axis becomes infinite.

B. Mercier

Papers

Classical solutions in the Einstein-Born-Infeld-Abelian-Higgs model