denoted by $2r_0$, the asymptotic kinetic energy of both of them transforms into the energy of the interaction particle, $$\label{Ek}
{\cal E}=2\left(\sqrt{p^2+m^2}-m\right).$$ When Newtonian gravity is added to the system and the particles are assumed to be massive, there are two effects (the mutual attraction of the two rest masses is considered as negligible): Due to gravitational attraction each particle has a potential energy $$\Delta E_1=-\frac{G{\cal E}m}{r_0}$$ in the moment when it stops at a distance $r_0$ from the scattering centre. For a rough estimate of the minimal distance in terms of the asymptotic kinetic energy we take the de Broglie wavelength $\lambda$ of the exchanged particle, whose mass is assumed to be negligible in comparison with its total energy, so that the transmitted momentum is approximately equal to $\cal E$, $$\label{l}
2r_0\approx\lambda\approx\frac{1}{\cal E},$$ and the gravitational potential energy of each of the scattered particles becomes $$\label{E1}
\Delta E_1\approx-2\,\frac{m{\cal
E}^2}{m_P^2}=-8\,\frac{m\left(\sqrt{p^2+m^2}-m\right)^2}{m_P^2},$$ where we have introduced the Planck mass $m_P=1/\sqrt{G}$, which, in our units, stands also for the Planck energy and the Planck momentum.

The second effect, which is independent of the mass of the particles, is the self-energy $\Delta\cal E$ of the exchange particle, whose order of magnitude is estimated by 