  We study the fusion of a proton with a nucleus with the emission of two
photons at low incident energy of the order of eV or smaller. We use a step
model for the repulsive potential between proton and the nuclei. We consider
the reaction both in free space and inside a medium. We make a simple model for
the medium by assuming a hard wall potential beyond a certain length scale.
This essentially leads to discretization of the energy spectrum which is
expected inside a medium and is seen both for a crystalline lattice structure
and for amorphous materials. We use second order perturbation theory to compute
the transition rate. We find that the rate in free space is very small. However
in medium, the rate may be substantial. Hence, we conclude that nuclear fusion
reactions may take place at low energies at observable rates.
