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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)

Why this formula appears here

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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MM

Symbol M

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ZZ

Symbol Z

Z is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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α\alpha

Symbol α

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γ\gamma

Symbol gamma

gamma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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δ\delta

Symbol delta

delta is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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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)

Equation 24 · Evolutionary Nuclear Physics

The Valley of Stability Is a Fitness Landscape

This equation gives an approximation: it relates the quantities while allowing an approximation.

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…

Meanings in this article

  • AA: the fix the mass number.
  • β\beta: the sometimes purely.
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