  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 $\omega\gamma$ =
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.
