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

Riichi Kuwahara*

Kaoru Ohno†

Tsutomu Ohtsuki‡

  • Dassault Systèmes K. K., ThinkPark Tower, 2-1-1 Osaki, Shinagawa-ku, Tokyo 141-6020, Japan

  • Department of Physics, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

  • Institute for Integrated Radiation and Nuclear Science, Kyoto University, Asashiro-Nishi, Kumatori-cho, Sennan-gun, Osaka 590-0494 Japan

  • *Riichi.KUWAHARA@3ds.com
  • †ohno@ynu.ac.jp
  • ‡ohtsuki.tsutomu.d09@kyoto-u.jp
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Phys. Rev. C 109, 024609 – Published 15 February, 2024

DOI: https://doi.org/10.1103/PhysRevC.109.024609

Abstract

To discuss the half-life of the electron-capture decay of Be7 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 Be7 in metallic Be at T=5K is 1.7% longer than that of Be7@C60 at T=5K (i.e., at the center of C60). This strongly suggests that at T=5K all Be7 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 Be9 atoms only, BO can quite rapidly migrate through BS; (2) BS made of Be7 and Be9 atoms very rapidly changes into BO of Be7; and (3) Be7 stays very stably at a BO site and seldom changes its position. Therefore, Be7 stays more likely at BO than Be9 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 Be7 in Be metal between T=293K and T=5K. This means that half of Be7 atoms are at BO sites, but the other half still remain at substitutional sites at T=293K. 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 Be7, BO can very easily migrate throughout the crystal through the BO → BS → BO pathway at room temperature.

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Outline

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Phys. Rev. C 109, 024609– Published 15 February, 2024
  • Received 24 October 2023
  • Accepted 22 January 2024
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