22.101 · Nuclear binding

Binding Energy Landscape

B/A over the (A, Z) plane for every ground state in NUBASE2020. Rotate the surface, then pick a cut on the right to see which one-dimensional slice a textbook "B/A vs A" curve is.

Surface over the nuclide plane

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Energy sign

One-dimensional cut

Table of this cut

Semi-empirical mass formula

Edit a coefficient or refit; every SEMF curve, surface and residual updates.
B(Z,A) = aVA − aSA2/3 − aCZ(Z−1)/A1/3 − aA(N−Z)²/A ± aPA−3/4

Pairing sign: + for even-even, 0 for odd A, − for odd-odd. The B/A-vs-A SEMF curve is evaluated along the valley Z₀(A) = [4a_A + (m_n − m_H) + a_C A−1/3] / [8a_A/A + 2a_C A−1/3] with the pairing term set to zero.

Potential well: the −B/A button draws binding as depth. The nuclides then sit in a trough, the valley of stability, deepest near ⁶²Ni and ⁵⁶Fe. Fusion of light nuclei and fission of heavy ones both run downhill toward that floor.

Side view: looking along Z collapses every isobar onto one A, so the cloud becomes a band. Its upper edge is what the stable-nuclide curve traces.

Shell residual: press Fit first (the rounded textbook coefficients leave a large smooth trend), then set the height to B − B_SEMF and use the top view in N and Z. Ridges appear at N, Z = 28, 50, 82, 126. In the 2D panel, plot the residual against N or Z to see the same thing.

Mass parabolas: choose "Isobars: fixed A". For even A you get two SEMF parabolas (even-even and odd-odd), with the measured isobars zig-zagging between them.