The harmonic hyperspherical basis for identical particles without permutational symmetry

Abstract

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.

References in corpus (4)

• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Are there compact heavy four-quark bound states?

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• Analytic Harmonic Approach to the N-body problem
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• Nonsymmetrized hyperspherical harmonics with realistic NN potentials
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• Computing an orthonormal basis of symmetric or antisymmetric hyperspherical harmonics
• Efimov Physics in small bosonic clusters
• Nonsymmetrized Hyperspherical Harmonics approach to A=6 system
• A Many-Body Density Energy Functional