Four-body calculation of the first excited state of⁴He using a realistic NN interaction: ⁴He(e,e′)⁴He(0 ₂⁺) and the monopole sum rule

⁴He possesses a second 0⁺ state; the transition form factor has been measured via inelastic electron scattering. The nature of the 0₂⁺ state's spatial structure has been controversial. An accurate four-nucleon calculation utilizing a realistic NN force (Argonne V8′) plus phenomenological NNN three-body force has been performed for both the ⁴He ground state and second 0⁺ state (E _x = 20.21 MeV) using the Gaussian expansion method. The calculated one-body densities and transition density show a significant difference between the states. The resulting impulse approximation transition form factor ⁴He(e,e′) He(0₂⁺) agrees with the available data. The overlap of the 0₂⁺ wave function with the trinucleon ground state suggests that the structure is primarily a loosely bound 3N+N system and not a breathing mode. It is found that a major part of the energy-weighted E0 sum rule value is exhausted by nonresonant, low-energy continuum states other than the second 0⁺ state, in contrast to heavier nuclei where a dominant fraction of the sum-rule limit is exhausted by the second 0⁺ state because it corresponds to a collective, breathing mode.