The isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians

We present an ab-initio study of the isoscalar monopole excitations of 4He using different realistic nuclear interactions, including modern effective field theory potentials. In particular we concentrate on the transition form factor $F_{cal M}$ to the narrow $0^+$ resonance close to threshold. F_M exhibits a strong potential model dependence, and can serve as a kind of prism to distinguish among different nuclear force models. Comparing to the measurements obtained from inelastic electron scattering off 4He, one finds that the state-of-the-art theoretical transition form factors are at variance with experimental data, especially in the case of effective field theory potentials. We discuss some possible reasons for such discrepancy, which still remains a puzzle.