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An improved formula for the favored α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay half-lives

Authors
  • Xu, Yang-Yang1
  • Liu, Hong-Ming1
  • Zhu, De-Xing1
  • Pan, Xiao1
  • Zou, You-Tian1
  • Li, Xiao-Hua1, 1, 1
  • Chu, Peng-Cheng2
  • 1 University of South China, Hengyang, 421001, China , Hengyang (China)
  • 2 Qingdao University of Technology, Qingdao, 266033, China , Qingdao (China)
Type
Published Article
Journal
The European Physical Journal A
Publisher
Springer Berlin Heidelberg
Publication Date
Feb 03, 2022
Volume
58
Issue
2
Identifiers
DOI: 10.1140/epja/s10050-022-00666-1
Source
Springer Nature
Disciplines
  • Regular Article- Theoretical Physics
License
Yellow

Abstract

In the present work, based on the Hatsukawa formula (Phys Rev C 42:674, 1990), modifying the coefficient F(Z) of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay half-lives which depends on the proton number of parent nucleus Z and considering the blocking effect of unpaired nucleons, we propose an improved semi-empirical formula for evaluating the favored α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay half-lives of even–even, odd-A and odd–odd nuclei. This formula can reproduce the experimental data of favored α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay half-lives taken from NUBASE2020 well. The corresponding root-mean-square (rms) deviations are reduced from 0.316, 0.366 and 0.398 to 0.237, 0.318 and 0.273 for even–even, odd-A and odd–odd nuclei, respectively. Moreover, we extend this formula to predict the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay half-lives of 64 even–even nuclei with 104 ≤Z≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le \,Z\le $$\end{document} 128 whose α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} decay are energetically allowed or observed but not yet quantified. For comparison, the Viola–Seaborg–Sobiczewski formula (VSS) proposed by Sobiczewski et al. and the universal decay law (UDL) proposed by Qi et al. are also used. The results indicate that our predictions are basically consistent with the ones of VSS and UDL.

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