A center of mass free equation of motion method and its application to 4He

We report on an upgraded version of the equation of motion phonon method (EMPM) which exploits the singular value decomposition (SVD) of rectangular matrices to decouple completely and exactly the intrinsic from the center of mass (c.m.) translational motion under no restrictions and for an arbitrary single particle (s.p.) basis. Its numerical implementation on 4He illustrates the way such a decoupling is achieved and its important effects on spectra and nuclear response functions.