  We consider the model of the self-gravity driven spontaneous wavefunction
reduction proposed by L. Diosi, R. Penrose et al. and based on a
self-consistent system of the Schrodinger and Poisson equations. An analogous
system of coupled Dirac and Maxwell-like equations is proposed as a
relativization. Regular solutions to the latter form a discrete spectrum in
which all the "active" gravitational masses are always positive, and
approximately equal to inertial masses and to the mass $m$ of the quanta of
Dirac field up to the corrections of order $\alpha^2$. Here
$\alpha=(m/M_{pl})^2$ is the gravitational analogue of the fine structure
constant negligibly small for nucleons. In the limit $\alpha \to 0$ the model
reduces back to the nonrelativistic Schrodinger-Newton one. The equivalence
principle is fulfilled with an extremely high precision. The above solutions
correspond to various states of the same (free) particle rather than to
different particles. These states possess a negligibly small difference in
characteristics but essentially differ in the widths of the wavefunctions. For
the ground state the latter is $\alpha$ times larger the Compton length, so
that a nucleon cannot be sufficiently localized to model the reduction process
