Calculation of bound and scattering states for four nucleons

The properties of the bound and scattering states of four nucleons are calculated with a realistic nuclear hamiltonian containing two-and three-nucleon potential terms. The method consists in expanding the wave function in terms of correlated Hyperspherical Harmonic functions and using suitable variational principles. The presence of correlations allows for an easy handling of the large repulsion contained in the nuclear potential at short distances. This method has been proved very accurate for the case of three nucleons. The calculated binding energy of the α-particle is in good agreement with the values obtained either by solving the Faddeev-Yakubovsky equations or using the Green-Function Monte-Carlo method, although small differences still remain to be understood. Results will be presented for the neutron + triton and proton +3He scattering lengths, phase shifts, etc. The possibility of accurate calculations of four-nucleon scattering states makes feasible the study of the excited states of the α-particle and of the fusion reactions as, for example the d+d radiative capture reaction