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Equation 15 · Part 1 · The Valley of Stability Is a Fitness Landscape

Symbol a_A

−aA(A−2Z)2/A-a_A (A-2Z)^2/A
aAa_A

What this part means

aAa_A is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

aAa_A is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Read as a fitness landscape, each term is a distinct cost or bonus of viability rather than an abstract fitting parameter. The volume term, aVa_V A , is the baseline: every nucleon in the interior feels attraction from its immediate neighbors, so binding energy grows roughly in proportion to the number of nucleons, the way a population’s raw fitness might scale with sheer numbers before any structural penalty is applied. The surface term, -aSa_S A2/3A^{2/3} , subtracts a cost proportional to surface area, because nucleons at the boundary have fewer neighbors to bind to — a tax on being exposed at the edge of the configuration, heaviest for small A where the surface-to-volume ratio is largest. The…

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