NUC-20

Neutron 1/v capture

σ_a = σ₀ (v₀ / v). Thermal capture falls as 1/velocity.

Reading speed

Nuclear1/v law

Governing equation

\sigma_a=\sigma_0 v_0/v

where

\sigma_0: σ at v₀ (b)
v_0: Reference speed (m/s)
v: Neutron speed (m/s)
\sigma_a: Absorption (b)

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-20 — Neutron 1/v capture) is the form associated with 1/v law. Working symbols: $\sigma_0$ , $v_0$ , $v$ $\rightarrow$ $\sigma_a$ . s-wave capture. Resonances break the law; 2200 m/s is the thermal reference.

Purpose

Purpose: compute

\sigma_a

from

\sigma_0

v_0

v

in Nuclear physics via

\sigma_a=\sigma_0 v_0/v

σ_a = σ₀ (v₀ / v). Thermal capture falls as 1/velocity. 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

\sigma_0 = 98.700\,\mathrm{b}

v_0 = 2200.000\,\mathrm{m/s}

v = 2200.000\,\mathrm{m/s}

, the governing relation

\sigma_a=\sigma_0 v_0/v

yields

\sigma_a = 98.700\,\mathrm{b}

. A σ(v) that falls, a thermal mark. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

σ at v₀ \sigma_098.7 bReference speed v_02200 m/sNeutron speed v2200 m/s

Outputs

Absorption \sigma_a98.700 b

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Narration of this film

A σ(v) that falls, a thermal mark.

s-wave capture. Resonances break the law; 2200 m/s is the thermal reference.

Reading speed

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