A nonlinear classical model for the decay widths of Isoscalar Giant Monopole Resonances

The decay of the Isoscalar Giant Monopole Resonance (ISGMR) in nuclei is studied by means of a nonlinear classical model consisting of several noninteracting nucleons (particles) moving in a potential well with an oscillating nuclear surface (wall). The motion of the nuclear surface is described by means of a collective variable which appears explicitly in the Hamiltonian as an additional degree of freedom. The total energy of the system is therefore conserved. Although the particles do not directly interact with each other, their motions are indirectly coupled by means of their interaction with the moving nuclear surface. We consider as free parameters in this model the degree of collectivity and the fraction of nucleons that participate to the decay of the collective excitation. Specifically, we have calculated the decay width of the ISGMR in the spherical nuclei $^{208}\rm{Pb}$, $^{144}\rm{Sm}$, $^{116}\rm{Sn}$ and $^{90}\rm{Zr}$. Despite its simplicity and its purely classical nature, the model reproduces the trend of the experimental data which show that with increasing mass number the decay width decreases. Moreover the experimental results (with the exception of $^{90}\rm{Zr}$) can be well fitted using appropriate values for the free parameters mentioned above. It is also found that these values allow for a good description of the experimentally measured $^{112}\rm{Sn}$ and $^{124}\rm{Sn}$ decay widths. In addition, we give a prediction for the decay width of the exotic isotope $^{132}Sn$ for which there is experimental interest. The agreement of our results with the corresponding experimental data for medium-heavy nuclei is dictated by the underlying classical mechanics i.e. the behaviour of the maximum Lyapunov exponent as a function of the system size.