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 in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

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 particles that can ...

. 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 particle physics, the radiation length is a characteristic of a material, related to the energy loss of high energy elementary particle, particles electromagnetically interacting with it. It is defined as the mean length (in cm) into the mate ...

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 its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...

. The Molière radius is useful in experimental

particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...

in the design of

calorimeters A calorimeter is a device 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 calorimeters ...

: 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 Stolzite is a mineral, a lead tungstate; with the formula Pb W O4. It is similar to, and often associated with, wulfenite which is the same chemical formula except that the tungsten is replaced by molybdenum. Stolzite crystallizes in the tetragona ...

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 highl ...

: 3.5 cm * Liquid

krypton Krypton (from 'the hidden one') is a chemical element; it has symbol (chemistry), symbol Kr and atomic number 36. It is a colorless, odorless noble gas that occurs in trace element, trace amounts in the Earth's atmosphere, atmosphere and is of ...

: 4.7 cm * Liquid

argon Argon is a chemical element; it has 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 abu ...

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

References

Experimental particle physics Radii {{Particle-stub