A proposal for an experiment to investigate a new physical object (called the “E-cell”) is presented. The E-cell can be used as an appropriate “catalyst” for nuclear fusion reactions in solids. The E-cell is a radiation defect of a crystalline lattice of some light metal (6Li, 7Be, 10B) hydride that is formed after a fission (as a result of a thermal neutron capture) of a metal atom nucleus. If the pressure in the crystal is in the megabar range, the following two features of the E-cell are of interest: 1. The average density of free electrons in the central region of the E-cell exceeds 1024 cm−3; this results in a large suppression of the Coulomb barrier between hydrogen nuclei; the value of the screening parameter exceeds ≃109 cm−1. 2. The potential energy of the preliminary compressed crystalline lattice can be transformed into the kinetic energy of the collision of a pair of hydrogen nuclei. This energy can reach some hundreds of electron-volts, and it provides the possibility of an approach between hydrogen nuclei to a distance of ≤10−9 cm. The summary result is the effective catalysis of hydrogen nuclear fusion to a detectable rate. The experimental investigation of the E-cell can lead to the creation of conditions for the effective enhancement of the fusion rate to values that are of practical interest.