Nuclear Responses to Two-Body External Fields Studied with the Second Random-Phase-Approximation

TL;DR

This paper shows that two-body external-field excitations in $^{16}$O, interpreted as double-phonon states, are profoundly shaped by explicit $2p$-$2h$ mixing in SSRPA. While HF and SSRPA$_D$ align for two-body responses, full SSRPA$_F$ reveals substantial energy redistribution: low-lying double-phonon peaks shift downward and gain high-energy strength in $0^+$ and $2^+$ channels, whereas the double $1^-$ mode moves upward due to repulsive $np$ couplings. Collectivity arises from coherent contributions of many $2p$-$2h$ configurations, with $nn$/$pp$ and $np$ components balancing at low energies but $np$ dominance at higher energies due to state-density effects. The results emphasize that double-phonon excitations cannot be reduced to simple folding of one-body strength, and pave the way for extending the framework to heavier nuclei, other multipoles, and microscopic meson-exchange current effects in processes like muon capture.

Abstract

This study investigates nuclear responses to two-body external fields, interpreted as double-phonon excitations, within the subtracted second random-phase approximation (SSRPA) for 16O. To clarify the underlying characteristics of these modes, Hartree-Fock (HF) and SSRPA with the diagonal approximation are first examined. The resulting strength distributions are nearly identical, indicating that residual interactions in the 1p-1h sector contribute only weakly. This behavior contrasts with that of one-body excitations, where coupling between 1p-1h and 2p-2h configurations is essential for generating collectivity. In the full SSRPA calculation, which incorporates the residual interaction among 2p-2h configurations, the strength distributions are substantially modified. The double IS 0+ and 2+ modes show pronounced redistribution, with peaks shifted to lower energies and additional strength emerging at higher energies, whereas the double IV $1^{-}$ mode shifts predominantly to higher energies due to a largely repulsive interaction. Analysis of single transition amplitudes reveals that low-lying resonances are formed coherently through constructive neutron-neutron, proton-proton, and neutron-proton configurations, while high-lying resonances are dominated by neutron-proton configurations, reflecting their higher state density. These results demonstrate that double-phonon excitations cannot be described by simple folding of one-body responses; a fully microscopic treatment of 2p-2h mixing, as provided by SSRPA, is essential.

Figures (9)

• Figure 1: Strength distribution of IS $0^{+}$ excitations in $^{16}$O calculated by RPA (top) and three types of SSRPA (bottom). The distributions are folded with a Lorentzian function of width $\Gamma_{0}=1$ MeV.
• Figure 2: Same as Fig. \ref{['fig:O16_mono']}, but for IV $1^{-}$ excitations.
• Figure 3: Same as Fig. \ref{['fig:O16_mono']}, but for IS $2^{+}$ excitations.
• Figure 4: (a)–(c) Strength distributions of the one-body external fields for the IS $0^{+}$, IV $1^{-}$, and IS $2^{+}$ modes obtained with HF. (d)–(f) Strength distributions of the corresponding double multipole modes, defined in Eqs. \ref{['eq:DISM']}–\ref{['eq:DISQ']}, obtained with HF and SSRPA$_{\mathrm{D}}$.
• Figure 5: Strength distributions for the two-body external fields defined in Eqs. \ref{['eq:DISM']}--\ref{['eq:DISQ']} in $^{16}$O. Results from SSRPA$_{\mathrm{F}}$, SSRPA$_{\mathrm{D}}$, and SRPA calculations are compared.