Four-body calculation of the first excited state ofHe4using a realisticNNinteraction:He4(e,e′)He4(02+)and the monopole sum rule

Abstract

$^{4}\mathrm{He}$ possesses a second ${0}^{+}$ state; the transition form factor has been measured via inelastic electron scattering. The nature of the ${0}_{2}^{+}$ state's spatial structure has been controversial. An accurate four-nucleon calculation utilizing a realistic $NN$ force (Argonne $\mathrm{V}{8}^{\ensuremath{'}}$) plus phenomenological $NNN$ three-body force has been performed for both the $^{4}\mathrm{He}$ ground state and second ${0}^{+}$ state $({E}_{x}=20.21\phantom{\rule{0.3em}{0ex}}\mathrm{MeV})$ 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 $^{4}\mathrm{He}(e,{e}^{\ensuremath{'}})^{4}\mathrm{He}({0}_{2}^{+})$ agrees with the available data. The overlap of the ${0}_{2}^{+}$ 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.