Hypernuclear no-core shell model

Abstract

We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-Λ 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 introduce 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 report on 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 end with a confirmation 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 ≤ 7 hyper-helium isotopes.