Hypernuclear No-Core Shell Model

TL;DR

This paper extends the No-Core Shell Model to include strangeness, enabling detailed ab initio calculations of hypernuclei with improved convergence and symmetry exploitation.

Contribution

It introduces two formulations of the NCSM for hypernuclei, incorporating hyperon-nucleon interactions and importance truncation, advancing ab initio hypernuclear modeling.

Findings

Validated both formulations in four-body hypernuclear systems.

Achieved converged ground-state energies for a chiral Hamiltonian.

Provided a survey of hyperhelium isotopes up to A=7.

Abstract

We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$\Lambda$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis of HO states where antisymmetrization and computation of matrix elements is simple and to which an importance-truncation scheme can be applied. For the Jacobi-coordinate formulation, we give an iterative procedure for the construction of the antisymmetric basis for arbitrary particle number and present the formulae used to embed two- and three-baryon interactions into the many-body space. For the Slater-determinant formulation, we discuss the conversion of the YN interaction matrix elements from relative to single-particle coordinates, the importance-truncation scheme that tailors the model space to the description of the low-lying spectrum, and the role of the redundant center-of-mass degrees of freedom. We conclude with a validation of both formulations in the four-body system, giving converged ground-state energies for a chiral Hamiltonian, and present a short survey of the $A\le7$ hyper-helium isotopes.