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 spin-dependent 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