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 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 ≤ 7 hyper-helium isotopes. PACS numbers: 21.80.+a, 21.10.Dr, 21.60.De, 05.10.CcStrangeness impacts many fields of physics from heavy-ion collisions to nuclear and neutron star structure. Of particular interest are hypernuclei, which can be produced and studied in the laboratory. Hypernuclei are many-body systems consisting of nucleons and hyperons, baryons that carry strangeness, like the Λ 0 , Σ 0,± , or the Ξ 0,− . These hyperons are distinguishable from the nucleons and can be used as probes for the interior structure of the nucleonic core. Furthermore, hypernuclei extend the isospin SU(2), which is a good approximate symmetry in nuclei, to flavor SU(3) that is broken by the significant mass difference between the strange and the up and down quarks [1]. This breaking allows new types of baryonbaryon interactions such as antisymmetric spin-orbit forces, which are forbidden by isospin symmetry [2].A variety of experiments were performed to study properties of hypernuclei. From the early emulsion experiments (see, e.g., Ref.[3]) to modern accelerator-based experiments, a lot of effort went into the measurement of not only ground-state properties [4][5][6][7][8][9], but also the determination of hypernuclear spectra by gamma-ray spectroscopy [10][11][12][13][14]. Even transition strengths are experimentally accessible [15]. This effort was complemented by various theory developments, e.g., Skyrmeand Brueckner-Hartree-Fock models [16][17][18], the shell model [19][20][21][22][23][24], cluster models [25][26][27][28], and few-body methods [29][30][31][32][3...

Light neutron-rich hypernuclei from the importance-truncated no-core shell model

“…We compute the hypernuclear spectra using the IT-NCSM for hypernuclei [22,34] including the Λ and Σ hyperons explicitly. We start from a Hamiltonian…”

“…The importance truncation of the model space with subsequent extrapolation constitutes the IT-NCSM, which is explained in detail in Ref. [34].…”

Similarity renormalization group evolution of hypernuclear Hamiltonians

“…Also, the matrix elements are independent of the angular momentum projection M. The SRG transformation on the two-body level is given in more detail in Ref. [6].…”

“…A detailed discussion of these Hamiltonians and applications to non-strange nuclei is presented elsewhere[26].To investigate the effect of the nucleonic Hamiltonian on the properties of hypernuclei, we consider the hypernuclei Here, we compare the N 3 LO EM +N 2 LO L and the N 4 LO EMN +N 2 LO NL Hamiltonians in order to assess the effect of switching to the new generation of chiral Hamiltonians.Fig. 1shows the absolute and excitation energies of6 Li and…”

Hyperon-Nuclear Interactions From SU(3) Chiral Effective Field Theory

“…Numerous advanced few-and many-body techniques have been developed to employ such phenomenological or chiral interactions, in order to calculate the properties of nuclear systems with and without strangeness. For example, systems with three or four particles can be reliably treated by Faddeev-Yakubovsky theory [46][47][48][49], somewhat heavier (hyper)nuclei with approaches like the no-core-shell model [50][51][52][53][54][55]. In the nucleonic sector many-body approaches such as Quantum Monte Carlo calculations [56][57][58], or nuclear lattice simulations [59][60][61] have been successfully applied and can be extended to the strangeness sector.…”