Some Properties of Nuclear Normal Modes

Energy levels and antisymmetric eigenfunctions are calculated, with the aid of normal coordinates, for a nuclear Hamiltonian containing inter-nucleon potentials of the Hooke's law type. Such a nuclear model exhibits the same shell structure as do the same nucleons moving without interaction in a common harmonic-oscillator central field. Modifications in the Hamiltonian—use of force parameters which depend on $A$, cutting off of forces at finite range, inclusion of spin-orbit forces—are discussed in connection with shell structure and the nuclear photoeffect.