Neutron tunneling between neutron-rich nuclei in inhomogeneous dense matter encountered in neutron star crusts can release enormous energy on a short-timescale to power explosive phenomena in neutron stars. In this work we clarify aspects of this process that can occur in the outer regions of neutron stars when oscillations or cataclysmic events increase the ambient density. We use a time-dependent Hartree-Fock-Bogoliubov formalism to determine the rate of neutron diffusion and find that large amounts of energy can be released rapidly. The role of nuclear binding, the two-body interaction and pairing, on the neutron diffusion times is investigated. We consider a one-dimensional quantum diffusion model and extend our analysis to study the impact of diffusion in three-dimensions. We find that these novel neutron transfer reactions can generate energy at the amount of $simeq 10^{40}-10^{44}$ ergs under suitable conditions.
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