absorption cross section

{{Short description|Mmeasures the probability of an absorption process}}

{{More references|date=October 2018}}

Image:Photon Cross Sections.png Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to absorption edges which were also shown.]]

In physics, absorption cross-section is a measure of the probability of an absorption process. More generally, the term cross-section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc. (Note that light in this context is described as consisting of particles, i.e., photons.) A typical absorption cross-section has units of cm²⋅molecule⁻¹. In honor of the fundamental contribution of Maria Goeppert Mayer to this area, the unit for the two-photon absorption cross section is named the "GM". One GM is 10⁻⁵⁰ cm⁴⋅s⋅photon⁻¹.{{cite web |url=https://apps.dtic.mil/sti/pdfs/ADA473083.pdf |title=Two-Photon Absorption Measurements: Establishing Reference Standards. |date=June 8, 2007 |accessdate=September 14, 2013 |publisher=Australian National University |archive-date=September 14, 2013 |archive-url=https://web.archive.org/web/20130914064457/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA473083 |url-status=live }}{{Cite journal |last=Zins |first=E-L. |last2=Guinet |first2=M. |last3=Rodriguez |first3=D. |last4=Payan |first4=S. |date=2022-06-01 |title=Absolute absorption cross section of 2-EHN in IR region |url=https://hal.sorbonne-universite.fr/hal-03630004/file/2ehn-25022022-04042022.pdf |journal=Journal of Quantitative Spectroscopy and Radiative Transfer |volume=283 |pages=108141 |doi=10.1016/j.jqsrt.2022.108141 |issn=0022-4073|doi-access=free }}

In the context of ozone shielding of ultraviolet light, absorption cross section is the ability of a molecule to absorb a photon of a particular wavelength and polarization. Analogously, in the context of nuclear engineering, it refers to the probability of a particle (usually a neutron) being absorbed by a nucleus. Although the units are given as an area, it does not refer to an actual size area, at least partially because the density or state of the target molecule will affect the probability of absorption. Quantitatively, the number $dN$ of photons absorbed, between the points $x$ and $x\; +\; dx$ along the path of a beam is the product of the number $N$ of photons penetrating to depth $x$ times the number $n$ of absorbing molecules per unit volume times the absorption cross section $\backslash sigma$:

:$\backslash frac\{dN\}\{dx\}=\; -N\; n\; \backslash sigma$.

The absorption cross-section is closely related to molar absorptivity $\backslash varepsilon$ and mass absorption coefficient.

$\backslash sigma=\; \backslash frac\{\backslash ln(10)\backslash times\; 10^3\}\{N\_\backslash text\{A\}\}\backslash times\; \backslash varepsilon$

For a given particle and its energy, the absorption cross-section of the target material can be calculated from mass absorption coefficient using:

:$\backslash sigma=\; (\backslash mu/\backslash rho)\; m\_\backslash text\{a\}/N\_\backslash text\{A\}$

where:

• $\backslash mu/\backslash rho$ is the mass absorption coefficient
• $m\_\backslash text\{a\}$ is the molar mass in g/mol
• $N\_\backslash text\{A\}$ is Avogadro constant

This is also commonly expressed as:

:$\backslash sigma=\; \backslash alpha/n$

where:

• $\backslash alpha$ is the absorption coefficient
• $n$ is the atomic number density