Stability of the SD configurations around ³²S

It is often possible to discuss the stability of the SD configurations with the help of the total energy surfaces obtained with the Strutinsky or constrained HF methods. According to such a representation, high barriers surrounding a potential minimum are usually interpreted as a sign of a large stability of a given nucleus against, e.g., fission or shape transitions.

Strictly speaking, the physical solutions obtained with the HF method correspond to a discrete set of local minima of the HF functional. Using the language of the simple deformed shell-model: the HF minima obtained in ³²S nuclei are strongly separated in terms quadrupole moment treated as a measure of the deformation. By using the constrained HF approach we could in principle always connect those isolated points thus obtaining potential barriers analogous to the ones obtained within the Strutinsky method. However, the physical interpretation of the results should be different depending on whether very many or only very few intermediate configurations are available for a given physical system. When many solutions are densely distributed along the deformation axis, the physical system is likely to undergo a sequence of transitions between the states that differ in deformation only a little, and the Strutinsky as well as HF results can be interpreted as physically analogous. Such a situation takes place, e.g., in the SD nuclei in the A$\simeq$150 and A$\simeq$190 mass regions.

In nuclei from the vicinity of ³²S, the occupying or not occupying just two intruder orbitals makes a significant difference in terms of the quadrupole moments of the resulting HF solutions. As a consequence the potential energy surface (PES) representation (see Fig. 8 of Ref. [26] for the PES in ³²S) is most likely not the best way of getting the information about the stability of the SD configurations with respect to a decay into any other shape configuration. Indeed, the decay will be in general hindered by a difference in configurations between the initial and the final states. Such a difference remains totally invisible from, e.g., the E vs. Q₂₀ sequence of constrained HF (or HFB) solutions, which all correspond to a different mixing of merely two configurations.

The above remarks apply independently of the following, more general observation: the barrier pictures may become often strongly misleading because the barrier extensions (shapes) do not carry any direct physical relation to the behavior of the object studied. A useful physical meaning can be attributed to those objects only after having introduced a description of the collective inertia adapted to the deformation space in use. Such a description, either obtained within the generator coordinate method, or described in terms of the collective inertia tensor, implicitly takes into account the slowing down of the transition caused by the aforementioned configuration changes.