Coupled adiabatic approximation in the three-body problem

In the framework of the hyperspherical formalism, we present a study of the coupled adiabatic approximation for the case of three nucleons interacting via central spindependent two-body potentials. We analyze the convergence of the ground state eigenvalues versus the grand orbital quantum number ($2K$) and compare the results to that of the coupled equations. We also compare with two simpler but less accurate approximations: the uncoupled adiabatic approximation and the extreme adiabatic approximation. The former provides an upper and the latter provides a lower bound to the ground state energy.NUCLEAR STRUCTURE Few body bound states, reduction of hyperspherical equations applied to triton, quantum few-body problem.