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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}

Why this formula appears here

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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A−1/2A^{-1/2}

Symbol A^-1/2

A−A^-1/2 is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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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}

Equation 9 · Evolutionary Nuclear Physics

The Valley of Stability Is a Fitness Landscape

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

  • ZZ: the mass number.
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