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Semi-empirical mass formula (Bethe-Weizsacker)

What you are seeing: the binding energy per nucleon B/AB/A along the valley of stability (A,Z(A))(A, Z^*(A)), computed from the Bethe-Weizsacker formula B=aVAaSA2/3aCZ(Z1)/A1/3aA(NZ)2/A+δ.B = a_V A - a_S A^{2/3} - a_C Z(Z-1)/A^{1/3} - a_A (N-Z)^2/A + \delta. The peak near A60A \approx 60 at B/A8.8B/A \approx 8.8 MeV is iron-peak territory; fusion releases energy below it, fission releases above.

Hover (slide) the mass number AA slider to see the four terms individually. The Coulomb term grows like Z2/A1/3Z^2/A^{1/3} and dominates the fall-off above iron; the asymmetry term grows quadratically with NZN-Z (neutron excess); the pairing term oscillates by parity.

Figure 1. Bethe-Weizsacker B/A vs A.
A56

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.