A series of experimental and theoretical investigations of time decay
features displayed by heavy nuclei having two types of excited states,
those in the first and those in the second potential well, are survey
ed. Some problems concerning the effect of nuclear viscosity on the pr
obability of populating the states of the second potential well in ind
uced-fission processes are considered. Experimental data obtained by u
sing the blocking technique to determine the lifetimes of the Pa-232,P
a- 233, U-234,U- 235, and Np-235,Np- 236,Np- 238,Np- 238 nuclei with r
espect to induced fission are analyzed on the basis of the statistical
theory of nuclear reactions by invoking the model of a two-humped fis
sion barrier. Previously unknown experimental information about the pa
rameters of two-humped fission barriers and about the energy dependenc
e of the level density in the second potential well is obtained for th
e nuclei under investigation. It is shown that data on the absolute va
lues of the level densities can be correctly described within the stan
dard phenomenological model only by assuming that the axial and mirror
symmetries of nuclear shapes are violated in the excited states of th
e second potential well.