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Equation 8 · Part 10 · The Valley of Stability Is a Fitness Landscape

Symbol delta

B(A,Z)=aVA−aSA2/3−aCZ(Z−1)A1/3−aA(A−2Z)2A+δ(A)B(A,Z) = a_V A - a_S A^{2/3} - a_C \frac{Z(Z-1)}{A^{1/3}} - a_A \frac{(A-2Z)^2}{A} + \delta(A)
δ\delta

What this part means

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

Its job in the formula

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

The passage around this formula

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. It is the energy that would have to be supplied to disassemble a nucleus into Z free protons and N free neutrons, divided by the number of nucleons, and a higher value means a more tightly bound, lower-energy configuration — precisely the sense in which a fitness function assigns a scalar payoff to a state. The theoretical account of how that payoff varies across the chart is the semi-empirical mass formula, first written down by Carl Friedrich von Weizsäcker in 1935 as a liquid-drop model of the nucleus [ 11 ] . In one common form, the…

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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 surrounding passage

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