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In this research, we investigated the gap-to-[Formula: see text] ratio of LaH[Formula: see text] and LaD[Formula: see text] superconductors by using modification of the BCS theory. The assumption of carriers under high pressure was in a new state, revealing a novel dispersion relation and providing a peak located in density of state. The precise formula of the gap-to-[Formula: see text] ratio was derived and achieved. The numerical results were examined, and subsequently a greater value than the one in the BCS was obtained. Our gap-to-[Formula: see text] results showed the best fit with the first-principle calculation of LaH[Formula: see text] ([Formula: see text]–5.25) and LaD[Formula: see text] ([Formula: see text]–5.20) superconductors. Finally, those results were carried out to the gap-to-[Formula: see text] ratio of metal-hydrides such as H3S, CaH6, YH4, YH6, YH7, YH9, CeH9, CeH[Formula: see text], ThH9 and ThH[Formula: see text] yielding the positive outcome and interpretation.

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