  The particle-hole dispersive optical model, developed recently, is applied to
describe properties of high-energy isoscalar monopole excitations in
medium-heavy mass spherical nuclei. We consider, in particular, the double
transition density averaged over the energy of the isoscalar monopole
excitations in $^{208}$Pb in a wide energy interval, which includes the
isoscalar giant monopole resonance and its overtone. The energy-averaged
strength functions of these resonances are also analyzed. Possibilities for
using the mentioned transition density to description of inelastic
$\alpha$-scattering are discussed.
