Soft modes in the proton–neutron pairing channel as precursors of deuteron condensate in N = Z nuclei

Abstract Relativistic nuclear response theory is formulated for the proton–neutron pairing, or deuteron transfer, channel. The approach is based on the meson–nucleon Lagrangian of Quantum Hadrodynamics (QHD) and advances the relativistic field theory to connect consistently the high-energy scale of heavy mesons, the medium-energy range of the pion and the low-energy domain of emergent collective vibrations (phonons) in a parameter-free way. Mesons and phonons build up the in-medium nucleon–nucleon interaction in spin–isospin transfer channels, in particular, the phonon-exchange part takes care of the leading-order retardation effects. In this framework, we explore J π = 0 + and J π = 1 + channels of the nuclear response to the proton–neutron pair removal and addition in 56 Ni and 100 Sn with a special focus on the lowest (soft) modes as precursors of deuteron condensate and candidates for being the mediators of the proton–neutron pairing interaction.