Molière radius

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 or photon. 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 $X 0$ by the approximate relation $R M = 0.0265 X 0 (Z + 1.2)$ , where $Z$ is the atomic number.[1] The Molière radius is useful in experimental particle physics in the design of calorimeters: a smaller Molière radius means better shower position resolution, and better shower separation due to a smaller degree shower overlaps.

The Molière radius is named after German physicist Paul Friederich Gaspard Gert Molière (1909–64).[2]

Molière radii for typical materials used in calorimetry

Caesium iodide: 3.5 cm[3]
Liquid argon: 9.04 cm [4]
Liquid krypton: 4.7 cm[5]
Lead tungstate crystals: 2.2 cm[6]
Earth's atmosphere above ground: 91 m[7]
Earth's atmosphere at sea level: 79 m[8]

References

Molière Radius Archived 2007-10-02 at the Wayback Machine
Phillip R. Sloan, Brandon Fogel, "Creating a Physical Biology: The Three-Man Paper and Early Molecular Biology" University of Chicago Press, 2011
http://pdg.lbl.gov/2014/AtomicNuclearProperties/HTML/cesium_iodide_CsI.html
http://pdg.lbl.gov/2012/AtomicNuclearProperties/HTML_PAGES/289.html
http://cds.cern.ch/record/256569/files/P00019924.pdf
The CMS Collaboration (2006). "Chapter 1. Introduction". CMS Physics : Technical Design Report Volume 1: Detector Performance and Software. CERN. p. 14. ISBN 9789290832683. CMS has chosen lead tungstate scintillating crystals for its ECAL. These crystals have short radiation (X0 = 0.89 cm) and Moliere (2.2 cm) lengths, are fast (80% of the light is emitted within 25 ns) and radiation hard (up to 10 Mrad).
Pierre Auger Collaboration (2009). "Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory". Astroparticle Physics. 32 (2): 89–99. arXiv:0906.5497. doi:10.1016/j.astropartphys.2009.06.004.
Greisen, Kenneth (1960). "Cosmic Ray Showers". Annual Review of Nuclear Science. Laboratory of Nuclear Studies, Cornell University, Ithaca, N. Y. 10: 71. doi:10.1146/annurev.ns.10.120160.000431.

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[1] Molière Radius Archived 2007-10-02 at the Wayback Machine

[:0-2] Phillip R. Sloan, Brandon Fogel, "Creating a Physical Biology: The Three-Man Paper and Early Molecular Biology" University of Chicago Press, 2011

[3] ttp://pdg.lbl.gov/2014/AtomicNuclearProperties/HTML/cesium_iodide_CsI.html

[4] ttp://pdg.lbl.gov/2012/AtomicNuclearProperties/HTML_PAGES/289.html

[5] ttp://cds.cern.ch/record/256569/files/P00019924.pdf

[6] The CMS Collaboration (2006). "Chapter 1. Introduction". CMS Physics : Technical Design Report Volume 1: Detector Performance and Software. CERN. p. 14. ISBN 9789290832683. CMS has chosen lead tungstate scintillating crystals for its ECAL. These crystals have short radiation (X0 = 0.89 cm) and Moliere (2.2 cm) lengths, are fast (80% of the light is emitted within 25 ns) and radiation hard (up to 10 Mrad).

[7] Pierre Auger Collaboration (2009). "Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory". Astroparticle Physics. 32 (2): 89–99. arXiv:0906.5497. doi:10.1016/j.astropartphys.2009.06.004.

[8] Greisen, Kenneth (1960). "Cosmic Ray Showers". Annual Review of Nuclear Science. Laboratory of Nuclear Studies, Cornell University, Ithaca, N. Y. 10: 71. doi:10.1146/annurev.ns.10.120160.000431.