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The recent precise experimental determination of the monopole transition formfactor from the ground state of $^4$He to its $0^+_2$ resonance via electronscattering has reinvigorated discussions about the nature of this first excitedstate of the $\alpha$ particle. The $0^+_2$ state has been traditionallyinterpreted in the literature as the isoscalar monopole resonance (breathingmode) or, alternatively, as a particle-hole shell-model excitation. To betterunderstand the nature of this state, which lies only $\sim$ 410 keV above theproton emission threshold, we employ the coupled-channel representation of theno-core Gamow shell model. By considering the $[^3$H$ + p]$, $[^3$He$ + n]$,and $[^2$H+$^2$H] reaction channels, we explain the excitation energy andmonopole form-factor of the $0^+_2$ state. We argue that the continuum couplingstrongly impacts the nature of this state, which carries characteristics of theproton decay threshold.

Description of the proton-decaying 0$^+_2$ resonance of the $\alpha$ particle