The purpose of this project is to determine how the properties of atomic nuclei depend upon their temperature T and rotational spin I. Neutrons and protons move in nuclear orbitals, which vary with T and I. Each nucleus has a shape, which changes as T and I are altered. Increasing T or I generates transitions from one nuclear shape to another, for example, prolate (football), oblate (discus), spherical, etc. There are also transitions in how the shape is oriented relative to the rotation axis. The rotation axis might be parallel to or perpendicular to the symmetry axis of the shape, or at any intermediate angle. A single nucleus may also have transitions between a normal fluid phase and various kinds of superfluid phases. The superfluid phase may contain correlated pairs of two neutrons, two protons, or one neutron and one proton. The internal spins of the two particles in a pair might be parallel or anti-parallel. Because atomic nuclei are small systems, they have large fluctuations in their shape, the orientation of the shape relative to the rotation axis, and the amount of superfluidity.
