Effective interactions and operators in no-core shell model

TL;DR

This paper reviews two approaches—unitary transformations and effective field theory—for constructing effective interactions and operators in the no-core shell model, addressing effects of model space truncation and physical terms in nuclear and atomic systems.

Contribution

It compares and discusses the application of unitary transformation and EFT methods for effective interactions in the NCSM, including recent results and extensions to the Gamow shell model.

Findings

Unitary transformation approach effectively accounts for truncation effects in light nuclei.

EFT-based interactions incorporate symmetries and power counting, applicable to nuclear and atomic systems.

Application of EFT to Gamow shell model extends its usefulness to unbound nuclear states.

Abstract

Solutions to the nuclear many-body problem rely on effective interactions, and in general effective operators, to take into account effects not included in calculations. These include effects due to the truncation to finite model spaces where a numerical calculation is tractable, as well as physical terms not included in the description in the first place. In the no-core shell model (NCSM) framework, we discuss two approaches to the effective interactions based on (i) unitary transformations and (ii) effective field theory (EFT) principles. Starting from a given Hamiltonian, the unitary transformation approach is designed to take into account effects induced by the truncation to finite model spaces in which a numerical calculation is performed. This approach was widely applied to the description of nuclear properties of light nuclei; we review the theory and present representative results. In the EFT approach, a Hamiltonian is always constructed in a truncated model space according to the symmetries of the underlying theory, making use of power counting to limit the number of interactions included in the calculations. Hence, physical terms not explicitly included in the calculation are treated on the same footing with the truncation to a finite model space. In this approach, we review results for both nuclear and trapped atomic systems, for which the effective theories are formally similar, albeit describing different underlying physics. Finally, the application of the EFT method of constructing effective interactions to Gamow shell model is briefly discussed.