Notes on certain Newton gravity mechanisms of wavefunction localization and decoherence

Both an additional nonlinear term in the Schrodinger equation and an additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localization and decoherence of macro-objects, resp., contain the same Newtonian interaction potential formally. We discuss certain aspects that are common for both equations. In particular, we calculate the enhancement of the proposed localization and/or decoherence effects, which would take place if one could lower the conventional length-cutoff and resolve the mass density on the interatomic scale.