Chapter 5Interactions of Hadrons andHadronic ShowersCalorimetersChapter5
Chapter 5 Interactions of Hadrons and Hadronic Showers Calorimeters Chapter 5
Comparison Electromagnetic Shower - Hadronic ShowerhadronicShowerelm. ShowerCharacterizedbyCharacterized byAAA1/3InteractionLength:An=RadiationLength:XαCpNA2/3LpZ21MeVRM.X.X8cA1/3ZMintCA4/SizeHadronic Showers >> Sizeelm ShowersXoACalorimetersChapter5
Comparison Electromagnetic Shower - Hadronic Shower elm. Shower Characterized by Radiation Length: hadronic Shower Characterized by Interaction Length: int = A pN A 2 / 3 L A 1 / 3 X0 A Z 2 RM 21MeV c • X0 int X0 = A 1 / 3 Z 2 A A 4 / 3 SizeHadronic Showers >> Sizeelm. Showers Calorimeters Chapter 5
Hadronic ShowersHadronic Showers are dominated bystrong interaction!p+Nucleus→元*+元+元+...+NucleusDistribution of Energy1stStep:IntranuclearCascadeExample5GeVprimaryenergy- lonization Energy of1980MeVcharged particles-Electromagnetic760MeVShower (by 元0->Yy)-Neutron Energy520MeV-gby Excitation of310MeVNuclei2ndStep:Highlyexcitednuclei Fissionfollowed-NotmeasurableEvaporationbyEvaporation1430MeVE.g. Binding Energy5000MeVDistributionandlocal depositionofenergyvariesstronglyDifficulttomodelhadronicshowers0e.g. GEANT4 includes O(10)TdifferentModelsFurtherReading:R.Wigmanetal.NIMA252(1986)4CalorimetersChapter5R.WigmanNIMA259(1987)389
Hadronic Showers Hadronic Showers are dominated by strong interaction ! p + Nucleus → + + − + 0 + . + Nucleus* 1st Step: Intranuclear Cascade Distribution of Energy Example 5 GeV primary energy - Ionization Energy of charged particles 1980 MeV - Electromagnetic Shower (by 0 ->) 760 MeV - Neutron Energy 520 MeV - g by Excitation of Nuclei 310 MeV - Not measurable E.g. Binding Energy 1430 MeV 5000 MeV Distribution and local deposition of energy varies strongly Difficult to model hadronic showers e.g. GEANT4 includes O(10) different Models Further Reading: R. Wigman et al. NIM A252 (1986) 4 R. Wigman NIM A259 (1987) 389 2nd Step: Highly excited nuclei Fission followed Evaporation by Evaporation Calorimeters Chapter 5
Detailed look into Hadronic Shower i-the electromagnetic componentSimplified model - only π produced元's areisotriplett元's are produceddemocraticallyin each nuclearinteractionπo -> y electromagnetic component femfem = 0.33 after 1st interactionfem = 0.33x2/3 + 1/3 = 0.55 after 2nd iaAfter b generations of interactions=1-ElectromagneticComponentincreaseswith increasingenergyofprimaryparticleCalorimetersChapter5
Detailed look into Hadronic Shower I -the electromagnetic component Simplified model - only produced ’s are isotriplett ’s are produced democratically in each nuclear interaction 0 -> electromagnetic component fem fem = 0.33 after 1st interaction fem = 0.33x2/3 + 1/3 = 0.55 after 2nd ia After b generations of interactions f 0 = f em =1− 1− 1 3 b Electromagnetic Component increases with increasing energy of primary particle Calorimeters Chapter 5
fem as a function of the energyn(k-1)<m>Averagemultiplicityperinteractionfem =1-(m)Reality:NumberofGenerationsnkSlopeParameter0.9Largeelectromagnetic0.8componentinhighenergeticshowers0.7e.g. Cosmid Air Showers0.60.5108105106102103104107[GeV]Attention-ProductionofoiststatisticalprocessAtsmall energies:Small multiplicityLargestatisticalfluctuationsinproductionof元‘species"Largefluctuationsofeleetioimagnetipteomponentofshower
fem as a function of the energy Large electromagnetic component in high energetic showers e.g. Cosmic Air Showers Reality: f em =1− m n(k−1) <m> Average multiplicity per interaction n Number of Generations k Slope Parameter Attention - Production of 0 ist statistical process At small energies: Small multiplicity Large statistical fluctuations in production of ‘species’ Large fluctuations of electromagnetic component of shower Calorimeters Chapter 5