Resonant nuclear fusion at second order
Phys. Rev. C 112, 014624 – Published 25 July, 2025
DOI: https://doi.org/10.1103/gf4g-j5jc
Abstract
We study the possibility of a low-energy nuclear fusion reaction assisted by a low-energy resonance. We use a simple potential model and replace repulsive Coulomb barrier with the step potential barrier. This is convenient since it allows us to perform analytic calculations and have better control on approximations. The fusion process involves a proton and another nucleus. We first consider a process in which this transition takes place by emission of a photon at first order in perturbation theory. The cross section for this process is highly suppressed due to the presence of repulsive barrier. We next consider another process, which involves emission of two photons. This process gets dominant contribution at second order in perturbation theory. We find a fairly large cross section provided the initial energy is taken to be significantly larger than the resonant energy. The exponential suppression factors cancel out in this calculation leading to a cross section much larger than the first-order process. As an example, for a particular set of potential parameters and initial state energy chosen in this paper, we find an enhancement of 29 orders of magnitude. Assuming a fixed initial energy, the experimental signature for this process is two-photon emission within a narrow range of energies. One of the photon would be emitted at low energy of order of the initial state energy and the second would correspond to nuclear energy.
