Simplest collective operators and giant resonances of highest multipolarity

Random-phase-approximation equations are solved in the limit of large A in the translationally invariant oscillator-potential model for density-dependent delta forces. The energy spectrum and intensities of electric isoscalar and isovector excitations of multipolarities l = 3, 4, and 5 are obtained, as well as intensities of orbital magnetic excitations with 3< or =l< or =6. The approach suggested is compared with other zero-picture descriptions of giant multipole resonances