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Equation 9 · Part 1 · The Valley of Stability Is a Fitness Landscape

Symbol delta

δ(A)={+aPA−1/2even-even N,Z0odd A−aPA−1/2odd-odd N,Z\delta(A) = \begin{cases} +a_P A^{-1/2} & \text{even-even } N,Z \\ 0 & \text{odd } A \\ -a_P A^{-1/2} & \text{odd-odd } N,Z \end{cases}
δ\delta

What this part means

delta is part of the quantity the equation computes from the expression on the right.

Its job in the formula

delta is part of the quantity the equation computes from the expression on the right.

The passage around this formula

with a pairing term commonly written δ(A)={+aPA−1/2even-even N,Z0odd A−aPA−1/2odd-odd N,Z\delta(A) = \begin{cases} +a_P A^{-1/2} & \text{even-even } N,Z \\ 0 & \text{odd } A \\ -a_P A^{-1/2} & \text{odd-odd } N,Z \end{cases}. 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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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