Abstract
This contribution deals with the problem of implementing the Pauli principle in a variational calculation of the binding energy of a fermionic system on the hyperspherical harmonics (HH) basis. We summarize the main points of a method that avoids the antysimmetrization of the basis functions. In fact this gets increasingly cumbersome as the number of particles increases. The method is tested on the binding energies of two nuclei ( 4 He and 6 Li), using various nuclear potential models, including a realistic one.
Highlights
In order to antisymmetrize the hyperspherical harmonics (HH) basis functions an efficient symmetrization method had been developed in [1] and successfully applied in many applications up to a number of particle N=6
A different strategy has been proposed [2, 3], where the HH symmetrization is avoided by using non-symmetrized HH (NSHH)
Where En,Γ are the eigenvalues of H with symmetry Γ ( i.e. Γ stands for symmetric (S), antisymmetric (A) or any mixed (M) symmetry) and λΓ indicate the eigenvalues of the Casimir operator
Summary
In order to antisymmetrize the hyperspherical harmonics (HH) basis functions an efficient symmetrization method had been developed in [1] and successfully applied in many applications up to a number of particle N=6. This method requires considerable computational resources as the number of particles increases. The approach has been limited to treat central ( spin dependent) potentials. What we present here is a somewhat modified approach, which has allowed to use isospin dependent non central interactions and nuclear realistic potentials
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