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

TL;DR

This paper generalizes a high-spin state description method to include complex multiphonon structures, using a self-consistent RPA approach with Skyrme energy-density functional, applied to $^{208}$Pb, $^{40}$Ca, and $^{90}$Zr.

Contribution

It extends the previous model for high-spin states to account for multiphonon structures using a non-linear RPA approach with Skyrme functionals.

Findings

Successfully applied the method to experimental data for $^{208}$Pb, $^{40}$Ca, and $^{90}$Zr.

Demonstrated the importance of beyond-RPA correlations in describing high-spin states.

Provided a unified framework for analyzing complex multiphonon excitations in doubly and semi-magic nuclei.

Abstract

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