Asymptotic equations for two-body correlations

► The series in the projection function is calculated asymptotically for bosons in the 1s state. ► The kinetic energy centrifugal barrier becomes asymptotically a harmonic oscillator potential. ► Applications show that the weight function approximation becomes the asymptotic equation. ► The eigenpotential becomes a r−2 attractive potential contrary to nuclei. ► It explains the collapse of bosons systems in the ground state.