COMPARISON OF BORN-OPPENHEIMER AND HYPERSPHERICAL ADIABATIC APPROXIMATIONS IN THE TRINUCLEON PROBLEM

Ground state energies of the three-nucleon system interacting via stan dard S-projected potentials are studied using Born-Oppenheimer and hyp erspherical adiabatic approximations. The extreme and the uncoupled hy perspherical adiabatic approximations, which are the lower and upper b ounds 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 symmetr y requirements, the other does not. In spite of this, the Born-Oppenhe imer approximation is found to be comparable to the other for potentia ls with a soft core repulsion.