The isoscalar monopole excitation of ${}^4\mathrm{He}$ is studied within a few-body ab initio approach. We consider the transition density to the low-lying and narrow $0^{+}$ resonance, as well as various sum rules and the strength energy distribution itself at different momentum transfers $q$. Realistic nuclear forces of chiral and phenomenological nature are employed. Various indications for a collective breathing mode are found: (i) the specific shape of the transition density, (ii) the high degree of exhaustion of the non-energy-weighted sum rule at low $q,$ and (iii) the complete dominance of the resonance peak in the excitation spectrum. For the incompressibility $K$ of the $\alpha$ particle, two different definitions give two rather small values (22 and 36 MeV).

• Received 17 March 2014
• Revised 5 January 2015

DOI:https://doi.org/10.1103/PhysRevC.91.024303