Neutron Absorption & Transmission Calculator

This tool calculates how neutrons are absorbed or transmitted through a material based on its macroscopic cross-section ($\Sigma$).

Select Neutron Absorbing Material

Thickness ($t$)

Results

Transmitted Ratio ($I/I_0$): 0

Absorbed Fraction ($1-I/I_0$): 0

Macroscopic Cross-section ($\Sigma$): 0 $cm^{-1}$

Underlying Principles

Unlike photons, neutrons interact with the nucleus of an atom. Their absorption is described by the macroscopic cross-section ($\Sigma$), which is dependent on the number density ($N$) of the atoms and their microscopic cross-section ($\sigma$).

$$I = I_0 e^{-\Sigma t}$$ $$ \Sigma = N \sigma $$

Where $N$ is the number density of the absorber (atoms/$cm^3$) and $\sigma$ is the microscopic cross-section in barns ($10^{-24} cm^2$). The number density $N$ is calculated from the material's density $\rho$, atomic weight $A_w$, and Avogadro's number $N_A$.

$$N = \frac{\rho \cdot N_A}{A_w}$$

Neutron Absorption Data (Thermal Neutrons, 0.0253 eV)

This table provides simplified data for thermal neutrons.

Material	Density ($\rho$, g/$cm^3$)	Atomic Weight ($A_w$, g/mol)	Cross-section ($\sigma$, barns)	Number Density ($N$, $10^{22} cm^{-3}$)
$^{3}$He	$1.34 \times 10^{-4}$	4	5333	$2.01 \times 10^{-5}$
$^{10}$B	2.34	10.01	3835	$14.07$
$^6$Li	0.47	6.02	945	$4.70$
Cd	8.64	112.4	2520	$4.63$
Gd	7.89	157.3	49700	$3.02$

Material	Density (\(\rho\), g/\(cm^3\))	Atomic Weight (\(A_w\), g/mol)	Cross-section (\(\sigma\), barns)	Number Density (\(N\), \(10^{22} cm^{-3}\))
\(^{3}\)He	\(1.34 \times 10^{-4}\)	4	5333	\(2.01 \times 10^{-5}\)
\(^{10}\)B	2.34	10.01	3835	\(14.07\)
\(^6\)Li	0.47	6.02	945	\(4.70\)
Cd	8.64	112.4	2520	\(4.63\)
Gd	7.89	157.3	49700	\(3.02\)