NUC-27

SEMF pairing term

δ = ±12 / √A MeV (even–even +, odd–odd −, odd A → 0). Weizsäcker pairing.

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NuclearSEMF pairing

Governing equation

\delta=\pm 12/\sqrt{A}\,\mathrm{MeV}

$A \in \left[12, 240\right]$

where

A: Mass number (—)
s: Sign +1/−1/0 (—)
\delta: Pairing (MeV)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\delta=\pm 12/\sqrt{A}\,\mathrm{MeV}

$A \in \left[12, 240\right]$

$A = 12$ $\delta = 3.464$

Along the curve

②

Domain of the variable — blue

A_{\min} = 12,\quad A_{\max} = 240

$A \in \left[12, 240\right]$

$A = 12$ $A = 12$

Along the curve

③

Response curve — green

\delta=\pm 12/\sqrt{A}\,\mathrm{MeV}

$A \in \left[12, 240\right]$

$A = 12$ $\delta = 3.464$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\delta}{\mathrm{d}A}

$A \in \left[12, 240\right]$

$A = 13.43$ $\delta^{\prime} = -0.123$

Along the curve

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-27 — SEMF pairing term) is the form associated with SEMF pairing. Working symbols: $A$ , $s$ $\rightarrow$ $\delta$ . The last SEMF ingredient after volume, surface, Coulomb and asymmetry.

Purpose

Purpose: compute

\delta

from

A

s

in Nuclear physics via

\delta=\pm 12/\sqrt{A}\,\mathrm{MeV}

δ = ±12 / √A MeV (even–even +, odd–odd −, odd A → 0). Weizsäcker pairing. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 56.000\,\mathrm{—}

s = 1.000\,\mathrm{—}

, the governing relation

\delta=\pm 12/\sqrt{A}\,\mathrm{MeV}

yields

\delta = 1.604\,\mathrm{MeV}

. A pairing zigzag on the mass surface. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass number A56 —Sign +1/−1/0 s1 —

Outputs

Pairing \delta1.604 MeV

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Narration of this film

A pairing zigzag on the mass surface.

The last SEMF ingredient after volume, surface, Coulomb and asymmetry.

Reading speed

Watch on YouTube