Low energy nuclear reactions through weak interactions

We consider the possibility that low energy nuclear reactions (LENRs) arise due to the conversion of a proton to a neutron through weak interactions. The resulting neutron forms a short-lived virtual state, which then gets captured by another nucleus through photon emission. This whole process happens under the framework of second-order perturbation theory. We find that the rate of this process is negligibly small in most cases. However, in the presence of a resonance the rate can be substantial and observable. As an example, we consider the transition $^{58}\mathrm{Ni}$ to $^{59}\mathrm{Ni}$ of the nickel nucleus, which shows a relatively narrow resonance at 7 keV. The rate in this case is found to be approximately ${10}^{\ensuremath{-}20}$ per second, which is experimentally observable. We argue that the mechanism is applicable to a wide range of nuclei and also for other processes which may not involve a weak interaction transition.