Electron-capture decay rate of Be7 in cluster and crystal forms of beryllium: A first-principles study

To discuss the half-life of the electron-capture decay of ⁷Be in cluster and crystal forms of beryllium, we performed density functional calculations of the electron density ρ(0) at the Be nucleus by assuming an inversely proportional relationship between them. We found that the electron density ρ(0) decreases with cluster size in Be clusters and increases at an interstitial site in crystalline Be. The electron density ρ(0) at the hexagonal close packed (HCP) lattice point, i.e., the substitutional site, is about 1.7% smaller than that at the center of C₆₀, which perfectly coincides with the recent experimental evidence [Phys. Rev. C 108, L011301 (2023)] that the half-life of ⁷Be in metallic Be at T=50.16em0exK is 1.7% longer than that of ⁷Be@C₆₀ at T=50.16em0exK (i.e., at the center of C₆₀). This strongly suggests that at T=50.16em0exK all ⁷Be stay at substitutional sites of the Be metal. For an interstitial Be atom, we found that the basal octahedral (BO) site is energetically most stable, and the basal split (BS) dumbbell structure is second most stable. Performing first-principles MD simulations of a system having an interstitial Be atom at room temperature, we found that (1) in a system having ⁹Be atoms only, BO can quite rapidly migrate through BS; (2) BS made of ⁷Be and ⁹Be atoms very rapidly changes into BO of ⁷Be; and (3) ⁷Be stays very stably at a BO site and seldom changes its position. Therefore, ⁷Be stays more likely at BO than ⁹Be at room temperature. The electron density ρ(0) at BO is 0.54% higher than ρ(0) at a substitutional site, which is about double the experimental difference of 0.26% in the half-life of ⁷Be in Be metal between T=2930.16em0exK and T=50.16em0exK. This means that half of ⁷Be atoms are at BO sites, but the other half still remain at substitutional sites at T=2930.16em0exK. So, we expect that the half-life of ⁷Be can be further shortened at higher temperatures. Performing unit cell relaxation of a Be crystal, we found that the difference in the total energy between BO and BS is only 0.03 eV. Thus, if there is no ⁷Be, BO can very easily migrate throughout the crystal through the BO → BS → BO pathway at room temperature.