In the work, the Schr�dinger-Newton equations are numerically investigated, which describe the interaction of neutral massive particles (neutrons) in neglecting their spin with the gravitational field surrounding them. An anti-screening effect of the gravitational charge of bare neutrons was found, what leads to an increase in the gravitational charge of the neutron at small distances (in galactic scale) while maintaining the Newtonian character of the gravitational potential. At large distances, the character of the gravitational potential differs from that of Newtonian, and the direction of the action of the gravitational force changes to the opposite. This allows one to qualitatively explain the phenomena known as dark matter and dark energy.