Soft modes in the proton-neutron pairing channel as precursors of deuteron condensate in NÂ =Â Z nuclei

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 Jπ=0+ and Jπ=1+ channels of the nuclear response to the proton-neutron pair removal and addition in 56Ni and 100Sn 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.