Electron capture (EC) decay of a ${}^7\mathrm{Be}$ atom, the rate of which is affected by the electron density at the ${}^7\mathrm{Be}$ nucleus, forms a ${}^7\mathrm{Li}$ atom and emits a neutrino. Herein, we studied the EC decay rate of ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ $(2n=24, 28, 32, 36, 50)$, in which those fullerenes have enhanced stability relative to their near neighbors, by using ab initio calculations. The stable and metastable ${}^7\mathrm{Be}$ atom sites and electron density at the ${}^7\mathrm{Be}$ nucleus in ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ were calculated. Unlike ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$, the ${}^7\mathrm{Be}$ nucleus sites in ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ $(2n=24, 28, 32, 36, 50)$ are always off center and close to the fullerene cage. Due to the bonding interaction between ${}^7\mathrm{Be}$ and the fullerene cage, the electron density at the ${}^7\mathrm{Be}$ nucleus in ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ is smaller than those of a single ${}^7\mathrm{Be}$ atom and of ${}^7\mathrm{Be}$ in ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$, leading to the result that the half-life of ${}^7\mathrm{Be}$ in ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ increases. Based on equilibrium statistical thermodynamic calculations, the temperature effect on the half-life of ${}^7\mathrm{Be}$ has been analyzed. In contrast to ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$, the temperature only slightly influences the half-life of ${}^7\mathrm{Be}$ in ${}^7\mathrm{Be}@{\mathrm{C}}_{2n}$ suggesting that the EC decay rate of ${}^7\mathrm{Be}$ could be precisely modified by using small fullerene cages.

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• Beta decay
• Electron & muon capture
• Electronic structure of atoms & molecules
• Lifetimes & widths
• Nuclear structure & decays
• 6 ≤ A ≤ 19
• Ab initio calculations