Stability of nuclear rotational states

The stability of rotational states described by using a procedure of the Hartree-Fock-Bogoliubov method is discussed. The stability condition is obtained in a general form and some of its properties are examined with the aid of simplifying approximations. It is pointed out in conclusion that the Coriolis force might lead to the instability of rotational states for sufficiently large angular momenta. The instability of rotational states is caused by the instability of the pairing density, and also by that of the nuclear density distribution. In the former case it is shown that below the critical angular momentum, a first-order phase transition takes place and in some cases the rotational band breaks off. In the latter case, it might be considered that the assumption of an axially symmetric deformation is broken or large change of the equilibrium deformation is brought suddenly. Then discontinuous change of the rotational level might be seen at the unstable point.