The Collective Model of Nuclear Motion

Collective motions of a many-body system, such as translation, rotation and oscillation, may be incorporated approximately in a shell-model description by regarding the shell-model wave function as a trial function for a variational approach, and exploiting the fact that the expectation value of the energy is then independent of the location and orientation, and approximately independent of the size and shape of the potential well. If these degeneracies are removed in the usual way, one is led naturally to wave functions containing both shell-model and collective aspects and to approximate values for the translational, rotational and vibrational energies.