Resonance libration and width at arbitrary inclination

ABSTRACT We apply the analytical disturbing function for arbitrary inclination derived in our previous work to characterize resonant width and libration of mean motion resonances at arbitrary inclination obtained from direct numerical simulations of the three-body problem. We examine the 2:1 and 3:1 inner Jupiter and 1:2 and 1:3 outer Neptune resonances and their possible asymmetric librations using a new analytical pendulum model of resonance that includes the simultaneous libration of multiple arguments and their second harmonics. The numerically derived resonance separatrices are obtained using the mean exponential growth factor of nearby orbits (megno chaos indicator). We find that the analytical and numerical estimates are in agreement and that resonance width is determined by the first few fundamental resonance modes that librate simultaneously on the resonant time-scale. Our results demonstrate that the new pendulum model may be used to ascertain resonance width analytically, and more generally, that the disturbing function for arbitrary inclination is a powerful analytical tool that describes resonance dynamics of low as well as high inclination asteroids in the Solar system.

Nature of Isoscalar Dipole Resonances in Heavy Nuclei

The isoscalar dipole nuclear response reveals low- and high-energy resonances. The nature of isoscalar dipole resonances in heavy spherical nuclei is studied, by using a translation-invariant kinetic model of small oscillations of finite Fermi systems. Calculations of the velocity field at the centroid energy show a pure vortex character of the low-energy isoscalar dipole resonance in spherical nuclei and confirm the anisotropic compression character of the high-energy one. The evolution of the velocity field as a function of the excitation energy of the nucleus within the resonance width is studied. It is found that the low-energy isoscalar dipole resonance retains a vortex character, while with this collective excitation also involves a compression, as the energy increases. The high-energy resonance keeps the compression character with a change in the excitation energy within the resonance width, but the compression-expansion region of the velocity field related to this resonance shifts inside the nucleus.