Kinetic Energy of Nuclei in the Hartree Model

In the present note the question of the separation of the kinetic energy of the center of gravity from the total kinetic energy of the nucleus is considered. This separation is necessitated in the calculation of nuclear energy levels by the use of the Hartree method. It is found that under certain conditions the wave function for the whole nucleus in absolute coordinates can be replaced by a product of the same function of the coordinates of the particles relative to the center of gravity and a $1s$ wave function for the center of gravity. These conditions are that oscillator wave functions be used for the individual particles and that the nucleus contain only one partly filled shell in both protons and neutrons with all shells of lower energy quantum number filled. It then follows that the kinetic energy of the nucleus is equal to the value calculated in absolute coordinates minus the energy of a single $1s$ particle.