Bulk and spectroscopic properties of ${}^4\mathrm{He}$ are studied within an equation of motion phonon method. Such a method generates a basis of $n$-phonon ($n=0,1,2,3...$) states composed of tensor products of particle-hole Tamm-Dancoff phonons and then solves the full eigenvalue problem in such a basis. The method does not rely on any approximation and is free of any contamination induced by the center of mass, in virtue of a procedure exploiting the singular value decomposition of rectangular matrices. Two potentials, both derived from the chiral effective field theory, are adopted in a self-consistent calculation performed within a space including up to three phonons. The latter basis states are treated under a simplifying assumption. A comparative analysis with the experimental data points out the different performances of the two potentials. It shows also that the calculation succeeds only partially in the description of the spectroscopic properties and suggests a recipe for further improvements.

• Received 11 October 2021
• Revised 7 January 2022
• Accepted 11 February 2022

DOI:https://doi.org/10.1103/PhysRevC.105.024326