Abstract
In some regions of the periodic table nuclei show an energy spectrum characteristic of a rotator and appear to have a non-spherical equilibrium shape. Such nuclei have been described successfully by a unified model which exhibits both collective and individual particle aspects of nuclear structure. The model ascribes wave functions to the low nuclear states which are products of collective wave functions, representing the rotation of the nuclear deformation, with wave functions representing the intrinsic motion of nucleons inside the nucleus.
Sequences of levels showing the rotational spectrum correspond to states with the same intrinsic wave function, but with different collective motions. The rotational wave functions are represented by rotation matrices, and the collective motion is closely analogous to the quantum mechanical rotations of a symmetric top with moment of inertia about half that of an equivalent rigid body.
The intrinsic state is approximated by a Hartree-Fock type wave function, with the individual particle orbitals defined by a deformed potential determined by the nuclear shape. Magnetic dipole and electric quadrupole moments are given by the corresponding intrinsic moments modified by a projection factor depending upon the mode of collective rotation. Hence the intrinsic deformation of the nuclear charge gives rise to large electric quadrupole moments. Within a rotational sequence, electromagnetic transition probabilities depend on the intrinsic electric or magnetic moments and on the rotational modes of the initial and final states. Between rotational sequences, where the intrinsic particle state changes, the transition probabilities depend on an `intrinsic transition probability' modified by parameters determined uniquely by the collective motion.
Other nuclei show an energy spectrum of a type which can be associated with a vibration of the nuclear surface.
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