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The method of description of the high-spin states, which was previouslydeveloped and applied for the states of this type in $^{208}$Pb, is generalizedfor the case of the states having more complex multiphonon structure. In thismethod, the harmonic approximation with the renormalized phonons is used inwhich the phonons themselves are determined within the non-linear version ofthe model based on the random-phase approximation (RPA) and including both theRPA correlations and the beyond-RPA ones. The mean field and the residualinteraction are derived within the framework of the self-consistent RPA fromthe energy-density functional of the Skyrme type. The method is applied for theanalysis of the available experimental data in doubly magic $^{208}$Pb and$^{40}$Ca and in semi-magic $^{90}$Zr.

Multiphonon structure of high-spin states in $^{40}$Ca, $^{90}$Zr, and $^{208}$Pb