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.

[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.

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