2008/11/30 by M. Gattobigio, A. Kievsky, M. Viviani +1 · 1 citation
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Nuclear physics research studies #nucl-th #physics.atm-clus #physics.comp-ph
paper · pdf · doi:10.1103/physreva.79.032513
published as Phys.Rev.A79:032513,2009
openalex publication_date 2009/03/20 · arxiv created 2009/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The hyperspherical harmonic basis is used to describe bound states in an A-body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry-breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example, we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.