Non-symmetrized hyperspherical harmonic basis for $A$-bodies

Abstract

The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into account. This preliminary step is not strictly necessary; the direct use of the HH basis is possible, even if the basis has not a well defined behavior under particle permutations. In fact, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it. They have well defined symmetry under particle permutation and the identification of the physical states is possible, as it will be shown in specific cases. The problem related to the large degeneration of the basis is circumvented by constructing the Hamiltonian matrix as a sum of products of sparse matrices. This particular representation of the Hamiltonian is well suited for a numerical iterative diagonalization, where only the action of the matrix on a vector is needed. As an example we compute bound states for systems with $A=3-6$ particles interacting through a short-range central interaction. We also consider the case in which the potential is restricted to act in relative s-waves with and without the inclusion of the Coulomb potential. This very simple model predicts results in qualitative good agreement with the experimental data and it represents a first step in a project dedicated to the use of the HH basis to describe bound and low energy scattering states in light nuclei.

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• Resonances in the three-neutron system
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Cited by in corpus (22)

• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• Spectra of helium clusters with up to six atoms using soft core potentials
• Energy spectra of small bosonic clusters having a large two-body scattering length
• Universality and scaling in the $N$-body sector of Efimov physics
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Efimov Physics and Connections to Nuclear Physics
• Embedding nuclear physics inside the unitary window
• Nonsymmetrized hyperspherical harmonics with realistic NN potentials
• Comparative study of the direct $\alpha +d$ $\to$ ${}^6$Li + $\gamma$ astrophysical capture reaction in few-body models
• Benchmark Results for Few-Body Hypernuclei
• Microscopic three-cluster study of light exotic nuclei
• Six-bodies calculations using the Hyperspherical Harmonics method
• Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics
• Constrained correlated-Gaussians for hyperspherical calculations
• Efimov Physics in small bosonic clusters
• Nonsymmetrized Hyperspherical Harmonics approach to A=6 system
• Yakubovsky scheme to study the 4- and 5-nucleon systems in the case of alpha-state structure with spin-dependent nucleon-nucleon potentials
• Theoretical calculation of nuclear reactions of interest for Big Bang Nucleosynthesis
• Beryllium-9 in Cluster Effective Field Theory
• Ab initio calculations for non-strange and strange few-baryon systems
• The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory
• Classical Grand Angular Momentum in N-Body Problems