Simple model for decay of superdeformed nuclei

One of the most interesting recent discoveries in nuclear-structure physics is the existence of superdeformation for nuclei in the mass A ∼ 150 and A ∼ 190 regions. So far, a consistent theory regarding the decay out of a superdeformed (SD) rotational band into a normaldeformed (ND) band has not been achieved. Most of the early work [1–6] on this problem attributed the decay-out process to a mixing of the SD states with ND states of equal spin. Decay out of the SD band sets in at a spin I0 for which penetration through the barrier between the SD minimum and the ND minimum is competitive with the E2 decay within the SD band. A statistical model was used [2,3] to describe the ND states, and the decay out of the SD band was determined as a function of the decay widths ΓS and ΓN in the SD and ND potential wells, respectively; the spreading (or tunneling) width Γ↓ through the barrier; and the average spacing DN of the ND states. Under the assumption that the ND states form a continuum on the scale of the other energies in the problem, the spreading width was found using Fermi’s golden rule to be [5]