Simplified α+4nmodel for theHe8nucleus

A simple five-body cluster orbital shell model approximation is proposed to describe the ground state wave function of the ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ neutron-halo nucleus. The spatial angular correlations, the geometry of the system, the α-particle, and the valence neutron momentum distribution are calculated analytically. With a single free parameter the model is able to reproduce the experimental geometry of ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ as well as the experimental transverse momentum distribution of the ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ nucleus from ${}_{}{}^8{}_{}{}^{}\mathrm{He}$ fragmentation on a carbon target, at high energy.