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Equation 36 · Part 4 · The Valley of Stability Is a Fitness Landscape

superscript

2 aPA−1/22\,a_P A^{-1/2}
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

where α\alpha , β\beta , and γ\gamma collect the volume, surface, Coulomb, and asymmetry contributions and the pairing term δ(A)\delta(A) shifts the curve up or down depending on whether N and Z are both even or both odd. For odd A , exactly one of N , Z is even and the pairing term vanishes, giving a single parabola with one minimum: one value of Z at that mass number is the most tightly bound, and every other isobar decays toward it by beta-minus emission (if it sits to the neutron-rich side) or by positron emission or electron capture (if it sits to the proton-rich side). For even A , the pairing term splits the curve into two parabolas — one for even-even nuclei sitting lower in mass (more…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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