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

TL;DR

This paper demonstrates the application of the finite amplitude method (FAM) within QRPA to efficiently analyze giant dipole resonances in heavy rare-earth nuclei, revealing the impact of the TRK sum rule enhancement factor on GDR properties.

Contribution

It introduces an efficient FAM-QRPA computational scheme for heavy nuclei and investigates the role of the TRK enhancement factor in GDR characteristics.

Findings

FAM-QRPA reproduces GDR frequency and width with reasonable accuracy.

Increment of TRK enhancement factor shifts GDR strength to higher energies.

Systematic deficiencies suggest need for beyond-QRPA approaches or EDF parameter optimization.

Abstract

Background: The quasiparticle random phase approximation (QRPA), within the framework of the nuclear density functional theory (DFT), has been a standard tool to access the collective excitations of the atomic nuclei. Recently, finite amplitude method (FAM) has been 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 a remarkable efficiency, which enables to perform systematic analysis of GDR for heavy rare-earth nuclei. Theoretical deficiency of photoabsorption cross section could not be improved by only adjusting the TRK enhancement factor, suggesting the necessity of beyond the self-consistent QRPA approach, and/or a more systematic optimization of the EDF parameters.