On the Validity of the Geiger-Nuttall Alpha-Decay Law and its Microscopic Basis

Abstract

The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with the energy of the escaping $\alpha$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $\alpha$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $\alpha$ decay of neutron-deficient nucleus ${}^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude.

arXiv comment4 pages, 5 figures, to appear in Phys. Lett. B

References in corpus (6)

• Quantum Tunneling in Nuclear Fusion
• Radioactive decays at limits of nuclear stability
• Universal decay law in charged-particle emission and exotic cluster radioactivity
• Microscopic mechanism of charged-particle radioactivity and generalization of the Geiger-Nuttall law
• Effects of formation properties in one-proton radioactivity
• Alpha Decay Hindrance Factors: A Probe of Mean Field Wave Functions

Cited by in corpus (18)

• r-Process Nucleosynthesis: Connecting Rare-Isotope Beam Facilities with the Cosmos
• Recent developments in radioactive charged-particle emissions and related phenomena
• Systematic study of $\alpha$ decay half-lives for even-even nuclei within a two-potential approach
• Systematic study of $\alpha$ decay for odd-$A$ nuclei within a two-potential approach
• Alpha decay as a probe for the structure of neutron-deficient nuclei
• $N=Z$ nuclei: A laboratory for neutron-proton collective mode
• Large-scale shell-model calculations on the spectroscopy of $N<126$ Pb isotopes
• $\alpha$ Decay Half-life Estimation and Uncertainty Analysis
• Systematic study of $\alpha$ decay half-lives based on Gamow--like model with a screened electrostatic barrier
• Design and performance of an ionisation chamber for the measurement of low alpha-activities
• Cluster-Daughter Overlap as a New Probe of Alpha-Cluster Formation in Medium-Mass and Heavy Even-Even Nuclei
• Alpha decay law of excited nuclei and its role in stellar decay rates
• The Fine Structure Constant and Habitable Planets
• Ternary fission with the emission of long-range $\alpha$ particles in fission of the heaviest nuclei
• Limitations of the Geiger-Nuttall Law in heavy cluster decay
• Localisation and alpha radioactivity
• Large-scale configuration interaction description of the structure of nuclei around ${}^{100}$Sn and ${}^{208}$Pb
• Unified description of the proton, alpha, cluster decays and spontaneously fissions half- life