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Equation 9 · Part 6 · The Valley of Stability Is a Fitness Landscape

Symbol Z

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}
ZZ

What this part means

the mass number.

Its job in the formula

Z is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

Binding energy per nucleon is the landscape’s fitness function The quantity that plays fitness’s role has a name in nuclear physics already: binding energy per nucleon, B(A,Z)/A , where A = N + Z is the mass number.

The passage around this formula

…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 Coulomb term, -aCa_C Z(Z-1)/A1/3A^{1/3} , is a pure liability: mutually repelling protons cost binding energy in proportion to roughly Z2Z^2 , which is why the landscape eventually tilts against very proton-heavy states no matter how favorable the other terms are. The asymmetry term, -aAa_A (A-2Z)^2/A , penalizes any departure…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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