Six-bodies calculations using the Hyperspherical Harmonics method

TL;DR

This paper demonstrates a method for calculating properties of light nuclear systems and helium clusters using hyperspherical harmonics without initial symmetry assumptions, successfully analyzing systems up to six particles.

Contribution

It introduces a novel approach to handle particle permutation symmetry in hyperspherical harmonics calculations for small clusters.

Findings

Successfully computed eigenstates for systems up to six particles.

Validated the method with nucleon and helium atom systems.

Reproduced known binding energies and scattering parameters.

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.