Radioactive Decay Speedup at $T=5\mathrm{K}$: Electron-Capture Decay Rate of ${}^7\mathrm{Be}$ Encapsulated in ${\mathrm{C}}_{60}$

The electron-capture (EC) decay rate of ${}^7\mathrm{Be}$ in ${\mathrm{C}}_{60}$ at the temperature of liquid helium ($T=5\mathrm{K}$) was measured and compared with the rate in Be metal at $T=293\mathrm{K}$. We found that the half-life of ${}^7\mathrm{Be}$ in endohedral ${\mathrm{C}}_{60}$ (${}^7\mathrm{Be}@{\mathrm{C}}_{60}$) at a temperature close to $T=5\mathrm{K}$ is $52.47\pm 0.04\mathrm{d}$, a value that is 0.34% faster than that at $T=293\mathrm{K}$. In this environment, the half-life of ${}^7\mathrm{Be}$ is nearly 1.5% faster than that inside Be metal at room temperature ($T=293\mathrm{K}$). We then interpreted our observations in terms of calculations of the electron density at the ${}^7\mathrm{Be}$ nucleus position inside the ${\mathrm{C}}_{60}$; further, we estimate theoretically the temperature dependence (at $T=0\mathrm{K}$ and 293 K) of the electron density at the Be nucleus position in the stable center inside ${\mathrm{C}}_{60}$. The theoretical estimates were almost in agreement with the experimental observations.

Figure 1

(a) Experimental setup for the measurement of the half-lives of ${}^7\mathrm{Be}$ in the ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ and of the ${}^7\mathrm{Be}$ reference metal. (b) Typical $\gamma$-ray spectrum of ${}^7\mathrm{Be}$ in the sample of ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ cooled down to $T=5\mathrm{K}$.

Figure 2

Exponential decay curves of ${}^7\mathrm{Be}$ in samples of the ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ at $T=5\mathrm{K}$ (red circles) and the Be metal (${}^7\mathrm{Be}$) at $T=293\mathrm{K}$ (blue circles). Insets corresponding to the decay intervals of 0–20 d and 140–170 d are displayed with an expanded scale.

Figure 3

Half-lives ($T_{1/2}$) measured in this time period are plotted as red circles for the ${}^7\mathrm{Be}@{\mathrm{C}}_{60}$ at $T=5\mathrm{K}$. The green circles are half-lives measured previously at $T=293\mathrm{K}$ ($T=293\mathrm{K}$) (previous work [18]). The blue circles represent the half-lives used as reference samples of Be metal (${}^7\mathrm{Be}$) (e.g., shown by arrows). Points shown by the asterisk are the half-lives of Be metal (${}^7\mathrm{Be}$) samples compared to other samples [22]. Half-lives previously measured span the thick yellow bar.

Figure 4

Schematic view of the wave functions for the HOMO (and $\mathrm{HOMO}\mathrm{\text{−}}1$) of the ${\mathrm{C}}_{60}$ molecules with a Be atom incorporated at the center (upper left, front view, and side view), below a single bond (lower left, front view, and side view), below a five-membered ring (middle, front view, and side view), and below a six-membered ring (right, front view, and side view).