Equation 43 · The Valley of Stability Is a Fitness Landscape
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The rate of each step varies by a span that is difficult to convey without sounding like hyperbole, and the chart of nuclides is, among other things, a map of that variation. At the fast extreme, some of the lightest particle-unbound configurations decay in a time too short to be meaningfully called a “half-life” in the ordinary sense — lithium-5, unbound against proton emission, has a tabulated half-life of less than 10^{-21} seconds. At the slow extreme, tellurium-128’s double-beta decay to xenon-128 proceeds with a half-life of 7.7(4)10^{24} years according to NUBASE2020’s current tabulation, the longest half-life recorded for any nuclide established to be radioactive [ 2 ] . That…
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The rate of each step varies by a span that is difficult to convey without sounding like hyperbole, and the chart of nuclides is, among other things, a map of that variation. At the fast extreme, some of the lightest particle-unbound configurations decay in a time too short to be meaningfully called a “half-life” in the ordinary sense — lithium-5, unbound against proton emission, has a tabulated half-life of less than 10^{-21} seconds. At the slow extreme, tellurium-128’s double-beta decay to xenon-128 proceeds with a half-life of 7.7(4)10^{24} years according to NUBASE2020’s current tabulation, the longest half-life recorded for any nuclide established to be radioactive [ 2 ] . That is a range of more than fifty orders of magnitude in decay rate across nuclides that otherwise sit on the same chart, obeying the same landscape topography, differing only in how deep a barrier separates them from their downhill neighbor and by what mechanism that barrier can be crossed. Read as a gradient map, the half-life at each point is not a separate piece of information layered on top of the binding-energy landscape; it is a direct expression of how steep, and how tunnelable, the local slope actually is.
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