Electric dipole response of sd-shell nuclei within the Configuration-Interaction Shell Model approach

TL;DR

The paper addresses the need for reliable predictions of the electric dipole ($E1$) strength in sd-shell nuclei for applications in nuclear astrophysics and photoabsorption data. It employs Configuration Interaction Shell Model in the full $1\hbar\omega$ valence space with the PSDPF interaction, using Lanczos strength functions to generate $B(E1)$ distributions and a Lorentzian folding to obtain photoabsorption strength functions (PSF), while renormalizing the dipole operator with an effective-charge factor. The results show that the Giant Dipole Resonance is purely isovector and that neutron-rich neon isotopes exhibit a fragmented, neutron-skin–like PDR near 8–9 MeV, with the low-energy strength being sensitive to the initial state. A universal effective charge $Q^2\approx0.64$ brings the calculated centroids and PSF into agreement with experimental data, highlighting the importance of operator renormalization in truncated spaces and enabling improved cross-section predictions for astrophysical processes. The work also demonstrates that CI-SM provides a more detailed and accurate description of $E1$ strength than QRPA, and it outlines future extensions to Ca isotopes and the inclusion of $M1$ channels for comprehensive astrophysical modeling.

Abstract

Reliable theoretical predictions of nuclear dipole excitations are crucial for various nuclear applications, particularly in nuclear astrophysics. Calculations of radiative capture cross sections often rely on theoretical gamma strength functions, with the electric dipole response being the dominant component. We aim at a systematic description of the E1 strength of nuclei with mass numbers between 17 and 40 of interest for various applications and to better understand the nature of the low-energy dipole strength in neutron-rich nuclei, known as pygmy dipole resonances. We use the Configuration Interaction shell-model framework in the p-sd-pf valence space with a previously established empirical Hamiltonian. Systematic results of photoabsorption strength show good agreement with experimental data, provided a renormalization of the dipole operator is applied. Transition densities are computed in 26Ne and confirm the pure isovector character of the Giant Dipole Resonance. The strength at 7-10MeV is shown to have a distinct structure with largely fragmented wave functions and transition densities of isovector character at the edge of the nucleus. The Configuration Interaction shell model is proved to be a valuable tool in the description of the photoresponse of light nuclei, providing more accurate results than the usually employed approaches.

Figures (12)

• Figure 1: Excitation energies of the lowest $1^-$ states in even-even $sd$-shell nuclei. Experimental results from NNDC (filled symbols) are compared to shell-model calculations with the PSDPF interaction (open symbols).
• Figure 2: Ratio of the total $E1$ strength $S_0$ computed with the PSDPF interaction in $3\hbar\omega$ and $1\hbar\omega$ model spaces as function of nuclear mass $A$. The calculations are performed for even-even $N=Z$ and $N=Z+2$$sd$-shell nuclei.
• Figure 3: Microscopic strength distribution (Eq.\ref{['Eq-SE1']}) computed in $1\hbar\omega$ and $(1+3)\hbar\omega$ model spaces in $^{20}$Ne.
• Figure 4: Reduction factors obtained as ratio of EWSR from photoabsorption data (black dots) or TRK value (red squares) to theoretical EWSR. The dashed horizontal line indicates the adopted value of $0.64$.
• Figure 5: Photoabsorption strength functions obtained in this work (black lines) versus available experimental data (points) and QRPA results from Goriely2018 (red lines). Experimental data are taken from the IAEA PSF database goriely_reference_2019.