  Bulk and spectroscopic properties of 4He 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.
