Investigation of the energy-averaged double transition density of isoscalar monopole excitations in medium-heavy mass spherical nuclei

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.