The response function is a basic physical quantity describing the interaction of a system with external probes. Calculating this quantity is a rather challenging task. Nowadays such calculations are done using single particle basis states. In principal, the basis should respect the interaction symmetries, but for practical reasons this is not always the case.

The nuclear Hamiltonian is invariant under translations and rotations. Thus, total momentum and total angular momentum are conserved quantities. A single-particle basis used for solving the nuclear many-body problem, breaks the translational invariance, leading to results with undesirable center of mass effects.

A generic way to remove center of mass effects from calculated observables has not yet been derived, and we present a method to do this for a calculated response function.

It is well known that in configuration space one can use relative and center of mass coordinates. In that way one can separate the Hilbert space into subspaces and write the Hamiltonian as H=H_I+H_CM where H_I is the intrinsic Hamiltonian and H_CM is the center of mass Hamiltonian that satisfy [H_I,H_CM]=0.

Therefore the eigenfunctions of the system decoupled into the outer product of eigenfunctions of H_I and H_CM Ψ=Ψ_I*Ψ_CM .

Our method based on this separation and works without any information about the form of the intrinsic Hamiltonian. What one has to know are the total response function, and the shape of the center of mass wave functions.

The derivation presented here is restricted to operators that fulfill O=O_IO_CM where O_I  acts only on the intrinsic part and O_CM acts only on the center of mass.