Comparison of Born-Oppenheimer and hyperspherical adiabatic approximations in the trinucleon problem

Ground state energies of the three-nucleon system interacting via standard S-projected potentials are studied using Born-Oppenheimer and hyperspherical adiabatic approximations. The extreme and the uncoupled hyperspherical adiabatic approximations, which are the lower and upper bounds for the exact ground state energy, are found to define a narrow band with the Born-Oppenheimer approximation lying close to it. While the hyperspherical adiabatic approximation conserves the basic symmetry requirements, the other does not. In spite of this, the Born-Oppenheimer approximation is found to be comparable to the other for potentials with a soft core repulsion