Non-Symmetrized Hyperspherical Harmonics Method for Non-Equal Mass Three-Body Systems

The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the ${}^3$H, ${}^3$He nuclei and ${}_{\mathrm{\Lambda }}^3$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NN\mathrm{\Lambda }$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between ${}^3$H and ${}^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the ${}_{\mathrm{\Lambda }}^3$H hypernucleus binding energy is calculated using different $NN$ and $\mathrm{\Lambda }N$ potential models. The results have been compared with those present in the literature, finding a very nice agreement.