This study investigates nuclear responses to two-body external fields, interpreted as double-phonon excitations, within the subtracted second random-phase approximation (SSRPA) for ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$. To clarify the underlying characteristics of these modes, Hartree–Fock and SSRPA with the diagonal approximation are first examined. The resulting strength distributions are nearly identical, indicating that residual interactions in the one-particle–one-hole (1p-1h) sector contribute only weakly. This behavior contrasts with that of one-body excitations, where coupling between 1p-1h and two-particle–two-hole (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 isoscalar $0^{+}$ and $2^{+}$ modes show pronounced redistribution, with peaks shifted to lower energies and additional strength emerging at higher energies, whereas the double isovector $1^{-}$ mode shifts predominantly to higher energies due to a largely repulsive interaction, resulting in a resonance around twice the peak energy of the single giant dipole resonance. 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.

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• Giant resonances
• Nuclear structure & decays
• 6 ≤ A ≤ 19