The Molière radius is a characteristic constant of a material giving the scale of the transverse dimension of the fully contained electromagnetic showers initiated by an incident high energy

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...

. By definition, it is the radius of a cylinder containing on average 90% of the shower's energy deposition. Two Molière radii contain 95% of the shower's energy deposition. It is related to the

radiation length In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy particles electromagnetically interacting with it. Definition In materials of high atomic number (e.g. W, U, Pu) the electrons of energie ...

by the approximate relation , where is the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

. The Molière radius is useful in experimental

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...

in the design of

calorimeters A calorimeter is an object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeter ...

: a smaller Molière radius means better shower position resolution, and better shower separation due to a smaller degree of shower overlaps. The Molière radius is named after German physicist Paul Friederich Gaspard Gert Molière (1909–64).Phillip R. Sloan, Brandon Fogel, "Creating a Physical Biology: The Three-Man Paper and Early Molecular Biology" University of Chicago Press, 2011

Molière radii for typical materials used in calorimetry

* LYSO crystals: 2.07 cm * Lead tungstate crystals: 2.2 cm *

Caesium iodide Caesium iodide or cesium iodide (chemical formula CsI) is the ionic compound of caesium and iodine. It is often used as the input phosphor of an X-ray image intensifier tube found in fluoroscopy equipment. Caesium iodide photocathodes are highly ...

: 3.5 cm * Liquid

krypton Krypton (from grc, κρυπτός, translit=kryptos 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is often ...

: 4.7 cm * Liquid

argon Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as ...

: 9.04 cm * Earth's atmosphere at sea level: 79 m * Earth's atmosphere above ground: 91 m

References

Experimental particle physics {{Particle-stub