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Equation 24 · Part 4 · The Valley of Stability Is a Fitness Landscape

Symbol c^2

M(A,Z) c2≈α(A)−β(A) Z+γ(A) Z2∓δ(A)M(A,Z)\,c^2 \approx \alpha(A) - \beta(A)\,Z + \gamma(A)\,Z^2 \mp \delta(A)
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

The passage around this formula

Fix the mass number A and let Z vary. Because the Coulomb and asymmetry terms in the semi-empirical mass formula are both approximately quadratic in Z at fixed A , the atomic mass along an isobaric chain is, to good approximation, a parabola in Z : M(A,Z) c2≈α(A)−β(A) Z+γ(A) Z2∓δ(A)M(A,Z)\,c^2 \approx \alpha(A) - \beta(A)\,Z + \gamma(A)\,Z^2 \mp \delta(A). 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…

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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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