Energy weighted sums for collective excitations in nuclear Fermi-liquid

Model independent, $m_1$, adiabatic, $m_{-1}$, and high-energy, $m_3$, energy weighted sums for the isoscalar and isovector nuclear excitations are investigated within the framework of the kinetic theory adopted to the description of a two-component nuclear Fermi-liquid. For both the adiabatic and scaling approaches, the connection of the EWS $m_{-1}$ and $m_3$ to the nuclear stiffness coefficients and the first- and zero-sound velocity is established. We study the enhancement factor $\kappa_{I}$ in the energy weighted sum $m'_1$ for the isovector excitations and provide the reasonable explanation of the experimental exceeding of the 100% exhaustion of sum $m'_1$ for the isovector giant dipole resonances. We show the dependence of the enhancement factor $\kappa_{I}$ on the nuclear mass number $A$ and analyse its dependence on the Landau's isovector amplitude $F'_1$.