Gravitationally induced transition to classical behavior above 10^10 proton masses

The localization length for the center of mass motion of a matter lump, induced by gravitation, is obtained, without using any phenomenological constants. Its dependence from mass and volume is consistent both with unitary evolution of microscopic particles and with the classical behavior of macroscopic bodies required to account for wave function collapse in quantum measurements, the transition between the two regimes being rather sharp. The gravitational interaction of nonrelativistic matter is modelled by a Yukawa Hamiltonian with vanishing pion mass, no gravitational background is needed and the only hypothesis consists in assuming unentanglement between matter and the Yukawa field.