Abstract
The calculation model of the large bipolaron binding energy proposed by Verbist et al. is extended to arbitrary dimensions including fractal dimensions. It is found that the fractal dimension D = 1.25 corresponds to the lowest critical coupling constant αc = 1.9, D = 1.73 corresponds to the highest critical ratio of dielectric constants ηc = 0.163, and when D ⩽ 1.145 bipolarons can not exist for any coupling constants and ratios of dielectric constants.
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