Nuclear electromagnetic dipole response with the self-consistent Green's function formalism

Background: Microscopic calculations of the electromagnetic response of light and medium-mass nuclei are now feasible thanks to the availability of realistic nuclear interactions with accurate saturation and spectroscopic properties, and the development of large-scale computing methods for many-body physics.

Purpose: To compute isovector dipole electromagnetic (E1) response and related quantities, i.e., integrated dipole cross section and polarizability, and compare with data from photoabsorption and Coulomb excitation experiments. To investigate the evolution pattern of the E1 response towards the neutron drip line with calculations of neutron-rich nuclei within a given isotopic chain.

Methods: The single-particle propagator is obtained by solving the Dyson equation, where the self-energy includes correlations nonperturbatively through the algebraic diagrammatic construction (ADC) method. The particle-hole ($ph$) polarization propagator is treated in the dressed random phase approximation (DRPA), based on an effective correlated propagator that includes some $2p2h$ effects but keeps the same computation scaling as the standard Hartree-Fock propagator.

Results: The E1 responses for ${}^{14,16,22,24}\mathrm{O}$, ${}^{36,40,48,52,54,70}\mathrm{Ca}$, and ${}^{68}\mathrm{Ni}$ have been computed: The presence of a soft dipole mode of excitation for neutron-rich nuclei is found, and there is a fair reproduction of the low-energy part of the experimental excitation spectrum. This is reflected in a good agreement with the empirical dipole polarizability values. The impact of different approximations to the correlated propagator used as input in the E1 response calculation is assessed.

Conclusion: For a realistic interaction that accurately reproduces masses and radii, an effective propagator of the mean-field type computed by the self-consistent Green's function provides a good description of the empirical E1 response, especially in the low-energy part of the excitation spectrum and around the giant dipole resonance. The high-energy part of the spectrum improves and displays an enhancement of the strength when quasiparticle fragmentation is added to the reference propagator. However, this fragmentation (without a proper restoration of dynamical self-consistency) spoils the predictions of the energy centroid of the giant dipole resonance.

Figure 1

Expansion of the polarization propagator $\mathrm{\Pi }\left(\omega \right)$ at the RPA level. Double fermionic lines denote the fully correlated propagators (or OpRS ones) employed in the DRPA. The expansion truncated at the first row would correspond to the Tamm-Dancoff approximation (TDA).

Figure 2

Example of diagrams contributing to the $ph$ polarization propagator $\mathrm{\Pi }\left(\omega \right)$ with $2p2h$ intermediate configurations. (Left) Noninteracting $1h+2p1h$ terms that contribute to DRPA through the dressing of the reference propagator. (Right) Interaction among the $ph$ pair mediated by a phonon exchange.

Figure 3

Integrated isovector E1 photoabsorption cross section of ${}^{16}\mathrm{O}$ as a function of the excitation energy ${\mathrm{E}}_X$, computed from the ${\mathrm{NNLO}}_{\text{sat}}$ chiral Hamiltonian. The three curves correspond to $\hslash \omega$=18 (solid line), 20 (dashed line), and 22 (dotted line) MeV, for $N_{\text{max}}$=13 and Lorentzian width $\mathrm{\Gamma }$= 3.0 MeV.

Figure 4

Same as in Fig. 3 for the HO parameters $N_{\text{max}}$=11 (solid line) and 13 (dashed line) at fixed $\hslash \omega$ = 20 MeV.

Figure 5

Same as in Fig. 3 but for different many-body truncations of the Dyson propagator, $g\left(\omega \right)$, and fixed HO parameters $N_{\text{max}}=13$ and $\hslash \omega$ = 20 MeV. The RPA phonons are built from the uncorrelated HF propagator (dotted line), and from the correlated ones computed using the ADC(2) (dashed line) and ADC(3) (solid lines) truncation schemes.

Figure 6

Same as in Fig. 3 for the convoluted (upper panel) and the discrete (lower panel) response. The three convoluted curves are obtained by folding the discrete spectrum with Lorentzian widths $\mathrm{\Gamma }$ =1.0 (solid line), 3.0 (dashed line), and 5.0 (dotted line) MeV.

Figure 7

Isovector E1 photoabsorption cross sections of ${}^{14,16,22,24}\mathrm{O}$ computed with the ${\mathrm{NNLO}}_{\text{sat}}$ interaction and the SCGF many-body method. The reference $g_{\mathrm{MF}}^{\text{OpRS}}\left(\omega \right)$ propagator is computed using an ADC(3) self-energy. The curves are obtained by folding the discrete spectra with Lorentzian widths $\mathrm{\Gamma }$ = 3.0 MeV. Experimental data for ${}^{16}\mathrm{O}$ in (b) are from Ahrens et al. [47] (red squares) and from Ishkhanov et al. [49] (green circles); experimental data for ${}^{22}\mathrm{O}$ in (c) are from Leistenschneider et al. [48].

Figure 8

Same as Fig. 7 but for ${}^{36,40,48,52,54,70}\mathrm{Ca}$. Experimental data for ${}^{40}\mathrm{Ca}$ in (b) are from Ahrens et al. [47]; experimental data for ${}^{48}\mathrm{Ca}$ in (c) are from Birkhan et al. [50] (green circles) and from Ahrens et al. [47] rescaled according to Ref. [50].

Figure 9

Isovector dipole response for ${}^{68}\mathrm{Ni}$ computed using a $g_{\mathrm{MF}}^{\text{OpRS}}\left(\omega \right)$ reference from Dyson-ADC(3). The lower (upper) panel shows the discrete (convoluted) spectrum obtained from DRPA. The convolution uses a Lorentzian width $\mathrm{\Gamma }$ = 3.0 MeV. Experimental data are from Rossi et al. [52].

Figure 10

Photoabsorption cross sections of ${}^{16}\mathrm{O}$ computed with ${\tilde{g}}_{p⩽1}^{\mathrm{OpRS}}\left(\omega \right)$. The computed DRPA spectrum is convoluted with a Lorentzian width of $\mathrm{\Gamma }$ = 3.0 MeV. Experimental data are from Ahrens et al. [47] (red squares) and from Ishkhanov et al. [49] (green circles).

Figure 11

Same as Fig. 10 but with ${\tilde{g}}_{p⩽3}^{\mathrm{OpRS}}\left(\omega \right)$.

Figure 12

Integrated E1 strength of ${}^{16}\mathrm{O}$ for 5-MeV energy bins in the region of the spectrum above the GDR. The different shaded areas correspond to the mean-field $g_{\mathrm{MF}}^{\mathrm{OpRS}}\left(\omega \right)$ [shown in Fig. 7], the ${\tilde{g}}_{p⩽1}^{\mathrm{OpRS}}\left(\omega \right)$ (Fig. 10) and the ${\tilde{g}}_{p⩽3}^{\mathrm{OpRS}}\left(\omega \right)$ (Fig. 11).