Is the first excited state of the $\alpha$-particle a breathing mode?
Sonia Bacca, Nir Barnea, Winfried Leidemann, Giuseppina Orlandini TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. V6J 2A3, Canada Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada Racah Institute of Physics, The Hebrew University, 91904, Jerusalem, Israel Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy Istituto Nazionale di Fisica Nucleare, TIFPA, I-38123 Trento, Italy Abstract The isoscalar monopole excitation of 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 α-particle values between 20 and 30 MeV are found.