Finite amplitude method applied to the giant dipole resonance in heavy rare-earth nuclei

Background: The quasiparticle random phase approximation (QRPA), within the framework of nuclear density functional theory (DFT), has been a standard tool to access the collective excitations of atomic nuclei. Recently, the finite amplitude method (FAM) was developed in order to perform the QRPA calculations efficiently without any truncation on the two-quasiparticle model space. Purpose: We discuss the nuclear giant dipole resonance (GDR) in heavy rare-earth isotopes, for which the conventional matrix diagonalization of the QRPA is numerically demanding. A role of the Thomas-Reiche-Kuhn (TRK) sum rule enhancement factor, connected to the isovector effective mass, is also investigated. Methods: The electric dipole photoabsorption cross section was calculated within a parallelized FAM-QRPA scheme. We employed the Skyrme energy density functional self-consistently in the DFT calculation for the ground states and FAM-QRPA calculation for the excitations. Results: The mean GDR frequency and width are mostly reproduced with the FAM-QRPA, when compared to experimental data, although some deficiency is observed with isotopes heavier than erbium. A role of the TRK enhancement factor in actual GDR strength is clearly shown: its increment leads to a shift of the GDR strength to higher-energy region, without a significant change in the transition amplitudes. Conclusions: The newly developed FAM-QRPA scheme shows remarkable efficiency, which enables one to perform systematic analysis of GDR for heavy rare-earth nuclei. The theoretical deficiency of the photoabsorption cross section could not be improved by only adjusting the TRK enhancement factor, suggesting the necessity of an approach beyond self-consistent QRPA and/or a more systematic optimization of the energy density functional (EDF) parameters.