Abstract
To discuss the half-life of the electron-capture decay of in cluster and crystal forms of beryllium, we performed density functional calculations of the electron density at the Be nucleus by assuming an inversely proportional relationship between them. We found that the electron density decreases with cluster size in Be clusters and increases at an interstitial site in crystalline Be. The electron density at the hexagonal close packed (HCP) lattice point, i.e., the substitutional site, is about 1.7% smaller than that at the center of , which perfectly coincides with the recent experimental evidence [Phys. Rev. C 108, L011301 (2023)] that the half-life of in metallic Be at is 1.7% longer than that of @ at (i.e., at the center of ). This strongly suggests that at all 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 atoms only, BO can quite rapidly migrate through BS; (2) BS made of and atoms very rapidly changes into BO of ; and (3) stays very stably at a BO site and seldom changes its position. Therefore, stays more likely at BO than at room temperature. The electron density at BO is 0.54% higher than at a substitutional site, which is about double the experimental difference of 0.26% in the half-life of in Be metal between and . This means that half of atoms are at BO sites, but the other half still remain at substitutional sites at . So, we expect that the half-life of 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 , BO can very easily migrate throughout the crystal through the BO BS BO pathway at room temperature.
5 More- Received 24 October 2023
- Accepted 22 January 2024
DOI:https://doi.org/10.1103/PhysRevC.109.024609
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