Ab initio no core shell model

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

The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs---Chiral, Pionless, Halo/Cluster---highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input.

Nuclear effective field theory: status and perspectives

Heavy quarkonium in a holographic basis

We study recently proposed ultraviolet and infrared momentum regulators of the model spaces formed by construction of a variational trial wave function which uses a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. These model spaces are defined by a truncation of the expansion characterized by a counting number ($\mathcal{N}$) and by the intrinsic scale ($\ensuremath{\hbar}\ensuremath{\omega}$) of the HO basis---in short by the ordered pair ($\mathcal{N},\ensuremath{\hbar}\ensuremath{\omega}$). In this study we choose for $\mathcal{N}$ the truncation parameter ${N}_{\mathrm{max}}$ related to the maximum number of oscillator quanta, above the minimum configuration, kept in the model space. The uv momentum cutoff of the continuum is readily mapped onto a defined uv cutoff in this finite model space, but there are two proposed definitions of the ir momentum cutoff inherent in a finite-dimensional HO basis. One definition is based upon the lowest momentum difference given by $\ensuremath{\hbar}\ensuremath{\omega}$ itself and the other upon the infrared momentum which corresponds to the maximal radial extent used to encompass the many-body system in coordinate space. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. We calculate the ground-state energy of light nuclei with ``bare'' and ``soft'' nucleon-nucleon ($NN$) interactions. By doing so, we investigate the behaviors of the uv and ir regulators of model spaces used to describe ${}^{2}$H, ${}^{3}$H, ${}^{4}$He, and ${}^{6}$He with $NN$ potentials Idaho N${}^{3}$LO and JISP16. We establish practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces characterized by ($\mathcal{N},\ensuremath{\hbar}\ensuremath{\omega}$).

M. I. Avetian

Papers

Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis