Molière radius
{{other uses|Molière (disambiguation)}}
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 {{math|X{{sub|0}}}} by the approximate relation {{math|R{{sub|M}} {{=}} 0.0265 X{{sub|0}} (Z + 1.2)}}, where {{math|Z}} is the atomic number.[http://rkb.home.cern.ch/rkb/PH14pp/node115.html Molière Radius] {{webarchive|url=https://web.archive.org/web/20071002225755/http://rkb.home.cern.ch/rkb/PH14pp/node115.html#SECTION0001150000000000000000 |date=2007-10-02 }} 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 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{{Cite arXiv| eprint=2203.05505 | last1=Collaboration | first1=PIONEER | last2=Altmannshofer | first2=W. | last3=Binney | first3=H. | last4=Blucher | first4=E. | last5=Bryman | first5=D. | last6=Caminada | first6=L. | last7=Chen | first7=S. | last8=Cirigliano | first8=V. | last9=Corrodi | first9=S. | last10=Crivellin | first10=A. | last11=Cuen-Rochin | first11=S. | last12=Di Canto | first12=A. | last13=Doria | first13=L. | last14=Gaponenko | first14=A. | last15=Garcia | first15=A. | last16=Gibbons | first16=L. | last17=Glaser | first17=C. | last18=Escobar Godoy | first18=M. | last19=Göldi | first19=D. | last20=Gori | first20=S. | last21=Gorringe | first21=T. | last22=Hertzog | first22=D. | last23=Hodge | first23=Z. | last24=Hoferichter | first24=M. | last25=Ito | first25=S. | last26=Iwamoto | first26=T. | last27=Kammel | first27=P. | last28=Kiburg | first28=B. | last29=Labe | first29=K. | last30=LaBounty | first30=J. | title=Testing Lepton Flavor Universality and CKM Unitarity with Rare Pion Decays in the PIONEER experiment | year=2022 | class=hep-ex | display-authors=1 }}
- Lead tungstate crystals: 2.2 cm{{cite book|last1=The CMS Collaboration|year=2006|chapter=Chapter 1. Introduction|title=CMS Physics : Technical Design Report Volume 1: Detector Performance and Software|chapter-url=https://cds.cern.ch/record/922757|publisher=CERN|page=14|isbn=9789290832683|quote=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).}}
- Caesium iodide: 3.5 cm[http://pdg.lbl.gov/2014/AtomicNuclearProperties/HTML/cesium_iodide_CsI.html Atomic and nuclear properties of cesium iodide (CsI)]
- Liquid krypton: 4.7 cm{{cite journal |last1=Fanti |first1=V. |last2=Barr |first2=G.D. |last3=Buchholz |first3=P. |last4=Cundy |first4=D. |last5=Doble |first5=N. |last6=Gatignon |first6=L. |last7=Gonidec |first7=A. |last8=Hallgren |first8=B. |last9=Kesseler |first9=G. |last10=Lacourt |first10=A. |last11=Laverrière |first11=G. |last12=Linser |first12=G. |last13=Norton |first13=A. |last14=Schinzel |first14=D. |last15=Seidl |first15=W. |last16=Stemmler |first16=T. |last17=Taureg |first17=H. |last18=Viehhauser |first18=G. |last19=Wahl |first19=H. |last20=Duclos |first20=J. |last21=Gianoli |first21=A. |last22=Martini |first22=M. |last23=Piemontese |first23=L. |last24=Savrié |first24=M. |last25=Kalinin |first25=A. |last26=Kekelidze |first26=J. |last27=Kozhevnikov |first27=Y. |last28=Coward |first28=D. |last29=Leber |first29=F. |last30=Cenci |first30=P. |last31=Lariccia |first31=P. |last32=Lubrano |first32=P. |last33=Pepe |first33=M. |last34=Calafiura |first34=P. |last35=Cerri |first35=C. |last36=Fantechi |first36=R. |last37=Gorini |first37=B. |last38=Laico |first38=F. |last39=Mannelli |first39=I. |last40=Marzulli |first40=V. |last41=Schiuma |first41=D. |last42=Debu |first42=P. |last43=Mazzucato |first43=E. |last44=Migliori |first44=A. |last45=Peyaud |first45=B. |last46=Turlay |first46=R. |last47=Kreutz |first47=A. |last48=Biino |first48=C. |last49=Ceccucci |first49=A. |last50=Palestini |first50=S. |last51=Griesmayer |first51=E. |last52=Markytan |first52=M. |last53=Neuhofer |first53=G. |last54=Pernicka |first54=M. |last55=Taurok |first55=T. |last56=Wulz |first56=C.-E. |title=Performance of an electromagnetic liquid krypton calorimeter |journal=Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment |date=May 1994 |volume=344 |issue=3 |pages=507–520 |doi=10.1016/0168-9002(94)90871-0 |url=https://cds.cern.ch/record/256569/files/P00019924.pdf |access-date=1 December 2022}}
- Liquid argon: 9.04 cm[http://pdg.lbl.gov/2012/AtomicNuclearProperties/HTML_PAGES/289.html Atomic and nuclear properties of materials: Liquid argon (Ar) (Ar)]
- Earth's atmosphere at sea level: 79 m
{{cite journal
|last= Greisen
|first= Kenneth
|date= 1960
|title= Cosmic Ray Showers
|journal= Annual Review of Nuclear Science
|volume= 10
|location= Laboratory of Nuclear Studies, Cornell University, Ithaca, N. Y.
|page= 71
|doi= 10.1146/annurev.ns.10.120160.000431
|bibcode= 1960ARNPS..10...63G
|author-link=
}}