Six-bodies calculations using the Hyperspherical Harmonics method

Abstract

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He-He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy.

Presented at the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, Erice, Sicily, October 2011

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• Efimov physics in bosonic atom-trimer scattering
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• The helium trimer with soft-core potentials
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• Embedding nuclear physics inside the unitary window
• The Faddeev-Yakubovsky symphony
• Improvement of the Envelope Theory for Systems with Different Particles
• Compact equations for the envelope theory