MANY-PARTICLE SYSTEMS .6. N-FERMION SYSTEMS - DERIVATION OF A LOWER-BOUND SHELL MODEL

The programme of reducing N-particle problems to one-particle problems is extended to include the Pauli principle. To calculate the ground-state energy of a system of N fermions interacting by pair forces, a rigorous lower-bound shell model is derived. This shell model follows a building-up principle, and tends to improve with increasing number of particles as well as with increasing strength of interaction. For twenty particles antisymmetric in ordinary space interacting by square-well interaction of strength V 0a2 = 200 hslash 2/2m the shell model differs by less than 8% from the calculated upper bound, and hence a fortiori from the exact energy. In order to test the quality of the approximation for various interactions, it was necessary to calculate upper bounds.