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

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.