Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics

Abstract

A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics constructed from different sets of Jacobi vectors are derived and discussed. Moreover, an algorithm to directly determine the numbers of independent symmetric hyperspherical states (in case of bosonic systems) and antisymmetric hyperspherical-spinisospin states (in case of fermionic systems) entering the expansion of the A-body wave functions is presented. Numerical implementations for systems made with up to five bodies are reported.

arXiv commentsubmitted to Computer Physics Communications

References in corpus (16)

• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Hybrid Mesons
• State Dependent Effective Interaction for the Hyperspherical Formalism
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• Few-body quark dynamics for doubly-heavy baryons and tetraquarks
• Ab initio many-body calculations of nucleon-4He scattering with three-nucleon forces
• Spectra of helium clusters with up to six atoms using soft core potentials
• Matter and charge radius of 6He in the hyperspherical-harmonics approach
• Non-symmetrized hyperspherical harmonic basis for $A$-bodies
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• The harmonic hyperspherical basis for identical particles without permutational symmetry
• Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
• Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum
• Nonsymmetrized hyperspherical harmonics with realistic NN potentials
• Constrained correlated-Gaussians for hyperspherical calculations

Cited by in corpus (3)

• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Hyperspherical cluster model for bosons: application to sub-threshold halo states in helium drops
• Theoretical calculation of nuclear reactions of interest for Big Bang Nucleosynthesis