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The cold fusion phenomenon (CFP) has shown various events ranging from huge excess energy to various nuclear transmutations in solids containing high density of hydrogen isotopes (both protium and/or deuterium) without any satisfactory explanation until now. CFP has several characteristics which require consistent explanation with modern physics: sporadic occurrence of the events, their qualitative reproducibility, localization of nuclear products in small (\teido \mikuro m) regions at surfaces of samples, occasionally simultaneous occurrence of several events, and so forth. We have tried to explain CFP as a whole consistently using a model (called the TNCF model) with a single adjustable parameter and several premises based on experimental facts. To give physical bases for the premises in the TNCF model, which has shown its ability to give consistent explanation of CFP, we have worked with neutron bands in solids. In this paper, we show a possibility of neutron bands originating in excited states of neutrons in atomic nuclei on lattice points (in lattice nuclei) mediated by band states of protons (deuterons) occluded in the transition-metal hydrides (deuterides). An indirect nuclear interaction between neutrons in lattice nuclei (the super-nuclear interaction) becomes effective in those crystals when the density of hydrogen isotopes is high and the neutrons are in excited states with wide-spread wave functions in lattice nuclei. The super-nuclear interaction, then, results in the formation of neutron bands which give rise to nuclear reactions observed as anomalous nuclear reactions in solids, the so-called cold fusion phenomenon (CFP). A relation between the physics of transition-metal hydrides (deuterides) and CFP is investigated using the trapped neutron catalized fusion (TNCF) model, which has been successful in the systematic explanation of many phases of CFP.