Limitations of the Geiger-Nuttall Law in heavy cluster decay
arXiv:2005.06578 · doi:10.1103/PhysRevC.103.024610
Abstract
Geiger-Nuttall Law is the simplest relation in radioactive decay relating the half-life and the decay energy. Initially restricted to decay of individual isotopes, generalizations unifying different isotopes and decay modes under a single set of constant coefficients were subsequently achieved. This motivates investigating to what extent such generalizations are possible. We also examine whether there exists a universal Geiger-Nuttall Law that can simultaneously describe all decay modes and nuclei including heavy clusters. We show that the validity of Geiger-Nuttall Law and its generalizations hinges on the assumption that half-life can be approximated linearly as a function of the square root of the ratio of the decay energy to the Coulomb barrier height. Systematic calculation of the ratio across the nuclear chart for 12 decay modes reveals that it varies over its whole range between 0 and 1. Consequently, no linear approximation can unify all the nuclei and decay modes under a single set of coefficients, and thus no universal Geiger-Nuttall Law is possible in contrast to previous claims. In cluster decay, the ratio varies within 0.6-1 where non-linearity becomes significant such that no generalized Geiger-Nuttall description of heavy clusters is possible. In the ongoing attempts of unification, it might be necessary to go beyond the Geiger-Nuttall Law and incorporate additional terms proportional to the decay energy and/or its square root.
arXiv comment12 pages, 8 figures. Same as the published version. Title changed in v3 and v4 (this version)
References in corpus (20)
- Surface diffuseness correction in global mass formula
- Universal decay law in charged-particle emission and exotic cluster radioactivity
- Heavy particle radioactivities of superheavy nuclei
- Microscopic mechanism of charged-particle radioactivity and generalization of the Geiger-Nuttall law
- Alpha-decay half-lives, alpha-capture and alpha-nucleus potential
- particle preformation in heavy nuclei and penetration probability
- Recent developments in radioactive charged-particle emissions and related phenomena
- Proton radioactivity within a generalized liquid drop model
- Effects of formation properties in one-proton radioactivity
- Shell and isospin effects in nuclear charge radii
- A new semiempirical formula for exotic cluster decays of nuclei
- First direct mass measurements of nuclides around with a Multireflection Time-of-Flight Mass Spectrograph
- Cluster Radioactivity in Super Heavy Nuclei
- On the Validity of the Geiger-Nuttall Alpha-Decay Law and its Microscopic Basis
- New Geiger-Nuttall law for proton radioactivity
- Alpha decay as a probe for the structure of neutron-deficient nuclei
- Experimental searches for rare alpha and beta decays
- Detailed illustration of accuracy of presently used nuclear-mass models
- Single universal curve for Alpha decay derived from semi-microscopic calculations
- Statistical errors in Weizsaecker-Skyrme mass model