  Background: Deep third minima have been predicted in some non-self-consistent
models to impact fission pathways of thorium and uranium isotopes. These
predictions have guided the interpretation of resonances seen experimentally.
On the other hand, self-consistent calculations consistently predict very
shallow potential-energy surfaces in the third minimum region. Purpose: We
investigate the interpretation of third-minimum configurations in terms of
dimolecular states. We study the isentropic potential-energy surfaces of
selected even-even thorium and uranium isotopes at several excitation energies.
In order to understand the driving effects behind the presence of third minima,
we study the interplay between pairing and shell effects. Methods: We use the
finite-temperature superfluid nuclear density functional theory. We consider a
traditional functional, SkM*, and a recent functional, UNEDF1, optimized for
fission studies. Results: We predict very shallow or no third minima in the
potential-energy surfaces of 232Th and 232U. In Th and U isotopes with N=136
and 138, the third minima are deeper. We show that the reflection-asymmetric
configurations around the third minimum can be associated with dimolecular
states involving the spherical doubly magic 132Sn and a lighter deformed Zr or
Mo fragment. The potential-energy surfaces for 228,232Th and 232U at several
excitation energies are presented. Conclusions: We show that the neutron shell
effect that governs the existence of the dimolecular states around the third
minimum is consistent with the spherical-to-deformed shape transition in the Zr
and Mo isotopes around N=58. We demonstrate that the thermal reduction of
pairing and enhancement of shell effects at small excitation energies help to
develop deeper third minima. At large excitation energies, shell effects are
washed out and third minima disappear altogether.
