Giant Resonance States in Nuclei

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1.Model-independent sum rules for double giant resonance states have been derived, which correspond to the Thomas-Reich-Kuhn sum rule for single giant dipole resonance states.2.It has been shown theoretically that the width of the Mie plasmon in atomic clusters is not inversely proportional to the cluster size, but to the square root of the size. This result should be examined in detail experimentally.3.The values of the spin-dependent Landau-Migdal parameters have been determined from the recently observed Gamow-Teller strength. The obtained values are much smaller than those expected previously. As a result, the critical density of the pion condensation in nuclear matter is about two times of the normal nuclear density.4.It has been shown analitically that the anti-nucleon degrees of freedom are necessary for describing the nuclear giant monopole states in relativistic models.