← All parts of this equation

Equation 9 · Part 3 · The Valley of Stability Is a Fitness Landscape

Symbol a_P

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}
aPa_P

What this part means

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

Its job in the formula

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

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…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.