  The relationship between deexcitation energies of superdeformed secondary
minima relative to ground states and the density dependence of the symmetry
energy is investigated for heavy nuclei using the relativistic mean field (RMF)
model. It is shown that the deexcitation energies of superdeformed secondary
minima are sensitive to differences in the symmetry energy that are mimicked by
the isoscalar-isovector coupling included in the model. With deliberate
investigations on a few Hg isotopes that have data of deexcitation energies, we
find that the description for the deexcitation energies can be improved due to
the softening of the symmetry energy. Further, we have investigated
deexcitation energies of odd-odd heavy nuclei that are nearly independent of
pairing correlations, and have discussed the possible extraction of the
constraint on the density dependence of the symmetry energy with the
measurement of deexcitation energies of these nuclei.
