The nuclear Independent Particle model: A misunderstanding

After quoting arguments against the validity of the nuclear Independent Particle model it is shown that the magic numbers governing the structure of the nuclear ground states are related to properties of homogeneous polynomials in 3-dimensional space. Then, starting from the basic property of analytical functions to be expandable in a series of harmonic polynomials, one deduces equations which yield solutions which are translationally invariant wave functions and include two-body correlations. The binding energies calculated for nuclei in their ground state are compared to those obtained by variational methods. A formula for the Coulomb energy of the nuclei is obtained analytically.