# Halfthickness

Halfthickness is abbreviation of the more usual term half-value thickness.

For the linear absorption with exponential decay of intensity of some intensity \( I \), id eat,

\( I(z)= I(0) \exp(-\mu z) \)

where \(\mu\) is absorption decrement.

Halfthickness appears as length, at which the intensity drops to a half of its initial value.

Halfthickness is sometimes denoted as \( d_{1/2}\), in analogy with the halftime \( t_{1/2}\).

Halfthickness is related to the absorption e \(\mu\) with the simple relation

\( \displaystyle d_{1/2} = \frac{\ln(2)}{\mu} \)

## Gamma rays

Usually, gamma-rays or gamma-radiation refers to electromagnetic waves of energy of order of MeV, say, from 0.1 MeV to 10 MeV.

Here is table of halfthickness of various materials for the gamma-rays of different energy.

Examples of half-value thicknesses are measured in cm

\( \begin{array}{c}\rm \phantom{Energy} \\ \rm 0.1 MeV \phantom{1^1}\\ \rm 0.5 MeV \phantom{1^1}\\ \rm 1~ MeV \phantom{1^1}\\ \rm 2~ MeV \phantom{1^1}\\ \rm 5~ MeV \phantom{1^1} \end{array}\) \( \begin{array}{l}\rm Lead ~~ \\ 0.014 \phantom{1^1}\\ 0.41 \phantom{1^1}\\ 0.88 \phantom{1^1}\\ 1.36 \phantom{1^1}\\ 1.46 \phantom{1^1}\end{array} \) \( \begin{array}{c}\rm aluminium \\ 1.7 \phantom{1^1}\\ 3.0 \phantom{1^1}\\ 4.3 \phantom{1^1}\\ 5.7 \phantom{1^1}\\ 9.5 \phantom{1^1} \end{array} \) \( \begin{array}{r}\rm Air ~ ~ \\ 3.6\times 10^3 \\ 5.9 × 10^3 \\ 8.3 × 10^3 \\ 13.4 × 10^3 \\ 21.5 × 10^3\end{array} \) \( \begin{array}{r} \rm Water ~ ~\\ 4.1\phantom{1^1}\\ 7.3\phantom{1^1}\\ 9.9\phantom{1^1}\\ 17.3 \phantom{1^1}\\ 21.7 \phantom{1^1} \end{array}\)

For example, in the air, the gamma-rays of emery 5MeV are absorbed to half of its initial value at distance 215 meter. At a distance of one km, it losses Nire than an order of magnitude; and at 10 km, it losses more than 10 orders of magnitude.

The table is by Matthias Hengsberger
^{[1]}.

## References

- ↑ https://www.physik.uzh.ch/~matthias/espace-assistant/manuals/en/anleitung-ab_e.pdf Matthias Hengsberger. Absorption of γ-rays – Determination of the Half-value Thickness of Absorber Materials. (2019) Laboratory Manuals for Physics Majors - Course PHY112/122 Tabelle 1.1.