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.

Figure 1

Photoabsorption cross sections of ${}^{144,154}\mathrm{Sm}$ from the FAM-QRPA calculation with 20 harmonic oscillator shells. The components from the $K=0$ and $K=\pm 1$ modes are separately plotted, where $K=\pm 1$ refers to a sum of $+1$ and $-1$ modes. The total photoabsorption cross section, calculated with 22 oscillator shells, is also included in the plot. The experimental data are taken from Ref. [53].

Figure 2

Photoabsorption cross sections of Gd, Dy, and Er isotopes as a function of photon energy. For the FAM-QRPA calculation, the smearing width $\mathrm{\Gamma }=1.0$ MeV is used. The experimental data sets A, B (photoabsorption), and C (neutron yield) are taken from Refs. [54, 55, 56], respectively.

Figure 3

The same as Fig. 2 but for Yb, Hf, and W isotopes. The experimental data sets A, B (photoabsorption), D (neutron yield), and E (neutron product) are taken from Refs. [54, 55, 57, 58], respectively. For Yb and Hf, the results obtained with the smearing width of $\mathrm{\Gamma }=0.5$ MeV are also plotted with dotted lines.

Figure 4

Photoabsorption cross sections of ${}^{174}\mathrm{Yb}$ obtained with different values of the smearing width $\mathrm{\Gamma }$. The shown experimental data are the same as those in Fig. 3.

Figure 5

The total HFB energy and the IVD enhancement factor of ${}^{174}\mathrm{Yb}$ as functions of the axial deformation. The HFB ground state is indicated by the vertical dotted line.

Figure 6

Isovector dipole transition strength in ${}^{174}\mathrm{Yb}$, calculated with SV-kap20, SV-bas, and SV-kap60 parametrizations of Ref. [44].

Figure 7

Photoabsorption cross sections of ${}^{174}\mathrm{Yb}$ calculated with SV-kap20, SV-bas, and SV-kap60 parametrizations. The shown experimental data are the same as in Fig. 3.