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Equation 37 · The Valley of Stability Is a Fitness Landscape

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AA

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AA

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Each individual beta decay, then, is a single step along this fixed- A parabola: a discrete jump from one (N,Z) point to its immediate neighbor at (N-1,Z+1) or (N+1,Z-1) , taken because it lowers the mass and therefore raises binding energy per nucleon, with the released energy carried off by the emitted lepton and antineutrino or neutrino. A decay chain is a sequence of such steps, sometimes purely beta, more often threaded with alpha emissions that jump A downward by four and Z downward by two in a single move. Uranium-238’s decay chain to stable lead-206 is the standard worked example, and it takes fourteen recorded steps to complete: an alpha emission to thorium-234, a beta decay to…
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Each individual beta decay, then, is a single step along this fixed- A parabola: a discrete jump from one (N,Z) point to its immediate neighbor at (N-1,Z+1) or (N+1,Z-1) , taken because it lowers the mass and therefore raises binding energy per nucleon, with the released energy carried off by the emitted lepton and antineutrino or neutrino. A decay chain is a sequence of such steps, sometimes purely beta, more often threaded with alpha emissions that jump A downward by four and Z downward by two in a single move. Uranium-238’s decay chain to stable lead-206 is the standard worked example, and it takes fourteen recorded steps to complete: an alpha emission to thorium-234, a beta decay to protactinium-234, a second beta decay to uranium-234, then a run of five consecutive alpha emissions down through thorium-230, radium-226, radon-222, polonium-218, and lead-214, a beta decay to bismuth-214, a further beta decay to polonium-214, an alpha emission to lead-210, a beta decay to bismuth-210, a beta decay to polonium-210, and a final alpha emission to stable lead-206 [ 2 ] . At three points along that path — after polonium-218, after bismuth-214, and after bismuth-210 — a minority branch peels off toward a different intermediate nuclide entirely, only to rejoin the dominant line one or two steps later; the chain is not a single deterministic line so much as a strongly dominant path with occasional forks, each fork itself a competition between two available downhill moves at that node.

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