The cross sections of nuclear reactions between the radioisotope $^7$Be and deuterium, a possible mechanism of reducing the production of mass-7 nuclides in Big-Bang nucleosynthesis, were measured at center-of-mass energies between 0.2 MeV and 1.5 MeV. The measured cross sections are dominated by the $(d,alpha)$ reaction channel, towards which prior experiments were mostly insensitive. A new resonance at 0.36(5)~MeV with a strength of $omegagamma$ = 1.7(5)~keV was observed inside the relevant Gamow window. Calculations of nucleosynthesis outcomes based on the experimental cross section show that the resonance reduces the predicted abundance of primordial $^7$Li, but not sufficiently to solve the primordial lithium problem.
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