DOCSLIB.ORG

Passage of Particles Through Matter

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

C4: Particle Physics Major Option Passage of Particles Through Matter Author: William Frass Lecturer: Dr. Roman Walczak Michaelmas 2009 1 Contents 1 Passage of charged particles through matter3 1.1 Energy loss by ionisation.....................................3 1.1.1 Energy loss per unit distance: the Bethe formula...................3 1.1.2 Observations on the Bethe formula...........................5 1.1.3 Behaviour of the Bethe formula as a function of velocity...............5 1.1.4 Particle ranges......................................7 1.1.5 Back-scattering and channelling.............................8 1.1.6 The possibility of particle identification........................9 1.1.7 Final energy dissipation.................................9 1.2 Energy loss by radiation: bremsstrahlung........................... 10 1.2.1 In the E-field of atomic nuclei.............................. 10 1.2.2 In the E-field of Z atomic electrons.......................... 10 1.2.3 Energy loss per unit distance and radiation lengths.................. 11 1.2.4 Particle ranges...................................... 11 1.3 Comparison between energy loss by ionisation and radiation................. 12 1.3.1 The dominant mechanism of energy loss........................ 12 1.3.2 Critical energy, EC .................................... 12 1.4 Energy loss by radiation: Cerenkovˇ radiation......................... 14 2 Passage of photons through matter 15 2.1 Absorption of electromagnetic radiation............................ 15 2.1.1 Linear attenuation coefficient, µ ............................ 15 2.1.2 Partial cross-sections................................... 15 2.2 Photoelectric effect........................................ 15 2.2.1 Summary......................................... 15 2.2.2 Work function...................................... 15 2.2.3 Cross-section....................................... 16 2.3 Compton scattering....................................... 16 2.3.1 Summary......................................... 16 2.3.2 Compton shift formula.................................. 17 2.3.3 Cross-section....................................... 18 2.4 Pair-production.......................................... 18 2.4.1 Summary......................................... 18 2.4.2 Reaction rate....................................... 19 2.4.3 Cross-section....................................... 19 2.5 Overall cross-section for photons................................ 20 2.6 Comparative summary of photon attenuation phenomena.................. 20 3 Passage of hadrons through matter 21 3.1 Hadron-nucleus interactions................................... 21 3.2 Quasi-elastic interactions.................................... 21 3.3 Inelastic interactions....................................... 22 3.3.1 Inelastic cross-section.................................. 22 3.3.2 Absorption length, λ ................................... 22 4 Development of showers in matter 23 4.1 Electromagnetic showers..................................... 23 4.1.1 Modelling an electromagnetic shower.......................... 23 4.1.2 Total shower depth.................................... 24 4.2 Hadronic showers......................................... 24 4.2.1 Modelling a hadronic shower.............................. 24 4.2.2 Total shower depth.................................... 25 2 1 Passage of charged particles through matter 1.1 Energy loss by ionisation A charged particle moving through different types of matter will interact with it in different ways, losing energy in various ways. • Solids, liquids and gases: the charged particle will ionise the material's atoms. • Semiconductors: the charged particle will produce electron-hole pairs. • Scintillator: the charged particle will lead to the production of light. • Superheated liquid: the charged particle will leave a trail of bubbles. In the limit that all electrons in the material's atoms can be modelled as free, the kinetic energy (EKE) loss per unit distance travelled (dx), known as the stopping power is: dE 1 − / (1) dx β2 Here, β = v=c. This relationship can be understood by looking at the Bethe formula1, derived in the following section. 1.1.1 Energy loss per unit distance: the Bethe formula Charged particles like alpha-particles, protons and pions, scatter electrons according to Rutherford scattering. Therefore scattering of the charged particles by free electrons is the same process, just in the rest frame of the electrons. • The Rutherford scattering formula is improved by the Mott scattering formula for electrons of momentum p and velocity v and particles with charge Ze: 2 2 dσ Zα~c 4 θ v 2 θ = cosec 1 − 2 sin (2) dΩ Mott 2pv 2 c 2 • Convert the scattering angle θ into a momentum transfer q: q θ = p sin (3) 2 2 θ q sin = (4) 2 2p θ q 2 sin2 = (5) Figure 1: Momentum triangle. 2 2p 4 θ 2 θ • Using (5), the cosec =2 and sin =2 terms in the Mott scattering formula, (2), can be replaced: 2 4 2 2 dσ Zα~c 16p v q = 4 1 − 2 2 (6) dΩ Mott 2pv q c 4p 1The term "Bethe-Bloch formula" actually refers to the modified Bethe formula that includes Bloch's Z4 correction. 3 • Now convert the differential cross-section, dσ=dΩ into dσ=dq2: Replace the differential solid angle, dΩ, in (6) using dΩ = 4π sin(θ)dθ: dσ Zα c2 16p4 v2 q2 = 4π ~ 1 − (7) sin(θ)dθ 2pv q4 c2 4p2 The operator sin(θ)dθ can be obtained by differentiating (5) in the form q2 = 4p2 sin2(θ=2) to give: dq2 θ θ 1 θ θ = 4p2 sin cos = 4p2 sin + = 2p2 sin(θ) (8) dθ 2 2 2 2 2 dq2 sin(θ)dθ = (9) 2p2 Substituting (9) into (7) and cancelling terms yields: dσ Zα c2 v2 q2 = 8π ~ 1 − (10) dq2 q2v c2 4p2 • Now transfer to the frame in which the electron is at rest, with the charged particle moving towards it: pelectron ! pnucleus = mevγ (11) 2 2 2 dσ Zα~c v q 2 = 8π 2 1 − 2 2 (12) dq q v c 4(mevγ) • The momentum transfer squared is the same in both frames and is related to the energy transfer, δ as follows: 2 2 q = 2me δ ! dq = 2me dδ (13) 2 2 dσ Zα~c v 2meδ = 8π 1 − 2 2 (14) 2me dδ 2meδv c 4(mevγ) 2 dσ Zα~c meδ = 16πme 1 − 2 2 2 (15) dδ 2meδv 2mec γ • So the cross-section for energy loss in the range δ ! δ + dδ is: 2 2 dσ 4π Zα~c δ v = 1 − 2 1 − 2 (16) dδ me δv 2mec c • If the charged particle loses energy −dE in a distance dx in a material containing n atoms of atomic number Zmaterial per unit volume then: number of electrons energy loss −dE = × (17) per unit volume per unit volume energy loss −dE = nZ × dx (18) material per unit area dE Z δmax dσ − = nZmaterial δ dδ (19) dx δmin dδ 4 • Substitute (16) into (19) and integrate: Z δmax 2 2 dE 4π Zα~c δ v − = nZmaterial δ 1 − 2 1 − 2 dδ (20) dx δmin me δv 2mec c 2 Z δmax 2 dE 4π Zα~c 1 1 v − = nZmaterial − 2 1 − 2 dδ (21) dx me v δmin δ 2mec c 2 2 dE 4π Zα~c δmax δmax − δmin v − = nZmaterial ln − 2 1 − 2 (22) dx me v δmin 2mec c • At large δ, the electrons can be assumed to be free; kinematics shows that: 2 2 δmax = 2mev γ (23) • However, this is not true at small δ. At low δ the momentum and energy transfer can lead to excitation as well as ionisation: it is therefore necessary to integrate over δ and q with cross- sections that depend on the atomic structure of the material in question. • The Bethe formula avoids this problem by defining a mean excitation potential, I, as follows: 0:9 δmin = I = 16Z (24) • The final result is... 2 2 2 dE 4π Zα~c 2mev v − = nZmaterial ln 2 2 − 2 (25) dx ionisation me v I(1 − v =c ) c Remember: Z is the charge (in units of e) of the charged particle striking the material, which has atomic number or effective charge Zmaterial . 1.1.2 Observations on the Bethe formula The stopping power (dE=dx) has the following general properties: • It is independent of the mass of the incident particle. • It depends on the charge of the incident particle squared (Z2). • Treating the slowly varying logarithmic term as a constant, it can be seen that dE=dx / c2=v2 or dE=dx / 1/β2, as noted above. 1.1.3 Behaviour of the Bethe formula as a function of velocity Low velocity regime: βγ < 3:5 In general the stopping power (dE=dx) falls off as 1=v2 in accordance with (1). Slow moving positively charged particles can capture the material's negative electrons, reducing the inci- dent particle's effective charge, Z, thus reducing dE=dx. Negative incident particles can suffer stripping of their electrons, reducing their value of Z. Minimum ionisation loss: βγ ≈ 3:5 The 1=(1 − β2) term in the logarithm halts the general decrease in stopping power. It stops decreasing somewhere in the range of βγ = 3 ! 4: this is known as the minimum ionisation loss. 5 The relativistic rise: βγ > 3:5 Beyond the minimum ionisation loss dE=dx begins to rise again, in fact the Bethe formula predicts it should rise indefinitely. In addition, as the incident charged particle reaches relativistic energies its transverse electric field in- creases, meaning more of the material's atoms are within range of the particle's electric field, leading to greater ionisation energy loss. This is known as the relativistic rise. Density effect However, the slope actually does shallow out because of the density effect: long distance atomic elec- trons are screened from the electric field of the incident particle by the dielectric effect of the intervening atoms in the material. Stopping Power of H2, He, C, Al, Fe, Sn and Pb 10 8 ) 6 2 H2 liquid cm 5 1 − 4 He gas 3 (MeV g C Al 2 Fe dE/dx Sn − Pb 1 0.1 1.0 10 100 1000 10 000 βγ = p/Mc 0.1 1.0 10 100 1000 Muon momentum (GeV/c) 0.1 1.0 10 100 1000 Pion momentum (GeV/c) 0.1 1.0 10 100 1000 10 000 Proton momentum (GeV/c) Figure 2: Mean energy loss rate divided by density in: liquid (bubble chamber) hydrogen, gaseous helium, carbon, aluminium, iron, tin, and lead.
Recommended publications
  • The African School of Physics

    The African School of Physics

    The African School of Physics Lecture : Particle Interactions with Matter Version 2012 ASP2012 - SH Connell 1 Learning Goals, Material 1. Understand the fundamental interactions of high energy particles with matter. 1. High Energy Physics : 1. Understand the HEP detector design and operation. 2. Research in HEP 2. Nuclear Physics 1. Understand detector / shielding design and operation. 3. Medical Physics 1. Understand biological implications 2. Understand radiation therapy 4. Other 1. Environmental radiation 2. Radiation damage for Space applications 3. Semiconductor processing 4. Radiation Damage in Materials 2. The core material is from “Techniques for Nuclear and Particle Physics Experiments” by WR Leo. Supplementary material from ASP2010 and ASP2012 lecture notes. ASP2012 - SH Connell 2 Contents 1. Overview : Energy Loss mechanisms 2. Overview : Reaction Cross section and the probability of an interaction per unit path-length 3. Energy Loss mechanisms. 1. Heavy charged particles 2. Light charged particles 3. Photons 4. (Neutrons) 4. Multiple Coulomb Scattering 5. Energy loss distributions 6. Range of particles. 7. Radiation length 8. Showers 9. Counting Statistics ASP2012 - SH Connell 3 An example from the ATLAS detector Reconstruction of a 2e2μ candidate for the Higgs boson - with m2e2μ= 123.9 GeV We need to understand the interaction of particles with matter in order to understand the design and operation of this detector, and the analysis of the data. ASP2012 - SH Connell Energy Loss Mechanisms Heavy Charged Particles Light Charged
  • 6.2 Transition Radiation

    6.2 Transition Radiation

    Contents I General introduction 9 1Preamble 11 2 Relevant publications 15 3 A first look at the formation length 21 4 Formation length 23 4.1Classicalformationlength..................... 24 4.1.1 A reduced wavelength distance from the electron to the photon ........................... 25 4.1.2 Ignorance of the exact location of emission . ....... 25 4.1.3 ‘Semi-bare’ electron . ................... 26 4.1.4 Field line picture of radiation . ............... 26 4.2Quantumformationlength..................... 28 II Interactions in amorphous targets 31 5 Bremsstrahlung 33 5.1Incoherentbremsstrahlung..................... 33 5.2Genericexperimentalsetup..................... 35 5.2.1 Detectors employed . ................... 35 5.3Expandedexperimentalsetup.................... 39 6 Landau-Pomeranchuk-Migdal (LPM) effect 47 6.1 Formation length and LPM effect.................. 48 6.2 Transition radiation . ....................... 52 6.3 Dielectric suppression - the Ter-Mikaelian effect.......... 54 6.4CERNLPMExperiment...................... 55 6.5Resultsanddiscussion....................... 55 3 4 CONTENTS 6.5.1 Determination of ELPM ................... 56 6.5.2 Suppression and possible compensation . ........ 59 7 Very thin targets 61 7.1Theory................................ 62 7.1.1 Multiple scattering dominated transition radiation . .... 62 7.2MSDTRExperiment........................ 63 7.3Results................................ 64 8 Ternovskii-Shul’ga-Fomin (TSF) effect 67 8.1Theory................................ 67 8.1.1 Logarithmic thickness dependence
  • Interaction of Radiation with Matter

    Interaction of Radiation with Matter

    INTERACTION OF RADIATION WITH MATTER OBJECTIVES Aims From this chapter you should develop your understanding of the various ways that photons, charged particles and neutrons can interact with matter and the concepts, such as mass attenuation coefficient, stopping power and range, that have been invented in order to aid that understanding. These ideas are the basis for the later study of the effects of x rays, gamma radiation and other ionising radiations on living things. Minimum learning goals When you have finished studying this chapter you should be able to do all of the following. 1. Explain, use and interpret the terms linear attenuation coefficient, mass attenuation coefficient, attenuation length, mean free path, half thickness, density-thickness, build-up, secondary particles, photoelectric effect, atomic photoelectric effect, photoelectrons, photoionisation, absorption edges, Compton effect [Compton scattering], Compton edge, pair production, rate of energy loss, linear stopping power, mass stopping power, minimum ionisation, range, straggling, bremsstrahlung [braking radiation], Cherenkov radiation, elastic scattering. 2. State, explain and apply the exponential attenuation law for a beam of particles suffering all-or- nothing interactions. 3. State, explain and apply the relations among linear attenuation coefficient, mass attenuation coefficient, density and composition of materials. 4. Distinguish between absorption of energy and the attenuation of a beam of photons and describe the build-up of secondary particles. 5. (a) Describe and compare the processes (photoelectric effect, Compton effect, Rayleigh scattering, pair production) by which photons interact with matter. (b) Describe and explain in general terms how attenuation coefficients and the relative importance of those processes vary with photon energy and explain the origin of absorption edges.
  • Neutrino Mixing

    Neutrino Mixing

    Citation: M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) Neutrino Mixing With the exception of the short-baseline anomalies such as LSND, current neutrino data can be described within the framework of a 3×3 mixing matrix between the flavor eigen- states νe, νµ, and ντ and the mass eigenstates ν1, ν2, and ν3. (See Eq. (14.6) of the review “Neutrino Mass, Mixing, and Oscillations” by K. Nakamura and S.T. Petcov.) The Listings are divided into the following sections: (A) Neutrino fluxes and event ratios: shows measurements which correspond to various oscillation tests for Accelerator, Re- actor, Atmospheric, and Solar neutrino experiments. Typically ratios involve a measurement in a realm sensitive to oscillations compared to one for which no oscillation effect is expected. (B) Three neutrino mixing parameters: shows measure- 2 2 2 2 2 ments of sin (θ12), sin (θ23), ∆m21, ∆m32, sin (θ13) and δCP which are all interpretations of data based on the three neu- trino mixing scheme described in the review “Neutrino Mass, Mixing, and Oscillations.” by K. Nakamura and S.T. Petcov. Many parameters have been calculated in the two-neutrino approximation. (C) Other neutrino mixing results: shows measurements and limits for the probability of oscillation for experiments which might be relevant to the LSND oscillation claim. In- cluded are experiments which are sensitive to νµ → νe,ν ¯µ → ν¯e, eV sterile neutrinos, and CPT tests. HTTP://PDG.LBL.GOV Page 1 Created: 6/5/2018 19:00 Citation: M. Tanabashi et al. (Particle Data Group), Phys.
  • 33. Passage of Particles Through Matter 1

    33. Passage of Particles Through Matter 1

    33. Passage of particles through matter 1 33. PASSAGE OF PARTICLES THROUGH MATTER ...................... 2 33.1.Notation . .. .. .. .. .. .. .. 2 33.2. Electronic energy loss by heavy particles . 2 33.2.1. Momentsandcrosssections . 2 33.2.2. Maximum energy transfer in a single collision..................... 4 33.2.3. Stopping power at intermediate ener- gies ...................... 5 33.2.4. Meanexcitationenergy. 7 33.2.5.Densityeffect . 7 33.2.6. Energylossatlowenergies . 9 33.2.7. Energetic knock-on electrons (δ rays) ..... 10 33.2.8. Restricted energy loss rates for relativisticionizing particles . 10 33.2.9. Fluctuationsinenergyloss . 11 33.2.10. Energy loss in mixtures and com- pounds ..................... 14 33.2.11.Ionizationyields . 15 33.3. Multiple scattering through small angles . 15 33.4. Photon and electron interactions in mat- ter ........................ 17 33.4.1. Collision energy losses by e± ......... 17 33.4.2.Radiationlength . 18 33.4.3. Bremsstrahlung energy loss by e± ....... 19 33.4.4.Criticalenergy . 21 33.4.5. Energylossbyphotons. 23 33.4.6. Bremsstrahlung and pair production atveryhighenergies . 25 33.4.7. Photonuclear and electronuclear in- teractionsatstillhigherenergies . 26 33.5. Electromagneticcascades . 27 33.6. Muonenergy lossathighenergy . 30 33.7. Cherenkovandtransitionradiation . 33 33.7.1. OpticalCherenkovradiation . 33 33.7.2. Coherent radio Cherenkov radiation . 34 33.7.3. Transitionradiation . 35 C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016) October 1, 2016 19:59 2 33. Passage of particles through matter 33. PASSAGE OF PARTICLES THROUGH MATTER Revised August 2015 by H. Bichsel (University of Washington), D.E. Groom (LBNL), and S.R. Klein (LBNL). This review covers the interactions of photons and electrically charged particles in matter, concentrating on energies of interest for high-energy physics and astrophysics and processes of interest for particle detectors (ionization, Cherenkov radiation, transition radiation).
  • Gauge and Higgs Bosons

    Gauge and Higgs Bosons

    Citation: P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020) GAUGE AND HIGGS BOSONS PC γ (photon) I (J ) = 0,1(1 − −) Mass m < 1 10−18 eV × Charge q < 1 10−46 e (mixed charge) × Charge q < 1 10−35 e (single charge) × Mean life τ = Stable g I (JP ) = 0(1 ) or gluon − Mass m = 0 [a] SU(3) color octet graviton J = 2 Mass m < 6 10−32 eV × W J = 1 Charge = 1 e ± Mass m = 80.379 0.012 GeV ± W Z mass ratio = 0.88147 0.00013 ± m m = 10.809 0.012 GeV Z − W ± m + m = 0.029 0.028 GeV W − W − − ± Full width Γ = 2.085 0.042 GeV ± N = 15.70 0.35 π± ± N = 2.20 0.19 K ± ± N = 0.92 0.14 p ± N = 19.39 0.08 charged ± HTTP://PDG.LBL.GOV Page1 Created: 6/1/2020 08:28 Citation: P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020) W − modes are charge conjugates of the modes below. p + W DECAY MODES Fraction (Γi /Γ) Confidence level (MeV/c) ℓ+ ν [b] (10.86± 0.09) % – e+ ν (10.71± 0.16) % 40189 µ+ ν (10.63± 0.15) % 40189 τ + ν (11.38± 0.21) % 40170 hadrons (67.41± 0.27) % – π+ γ < 7 × 10−6 95% 40189 + −3 Ds γ < 1.3 × 10 95% 40165 c X (33.3 ± 2.6 )% – +13 c s (31 −11 )% – invisible [c] ( 1.4 ± 2.9 )% – − π+ π+ π < 1.01 × 10−6 95% 40189 Z J = 1 Charge = 0 Mass m = 91.1876 0.0021 GeV [d] ± Full width Γ = 2.4952 0.0023 GeV ± Γℓ+ ℓ− = 83.984 0.086 MeV [b] ± Γinvisible = 499.0 1.5 MeV [e] ± Γhadrons = 1744.4 2.0 MeV ± Γµ+ µ−/Γe+ e− = 1.0001 0.0024 ± Γτ + τ −/Γe+ e− = 1.0020 0.0032 [f ] ± Average charged multiplicity N = 20.76 0.16 (S=2.1) charged ± Couplings to quarks and leptons ℓ g V = 0.03783 0.00041 u − ± g V = 0.266 0.034 d ±+0.04 g V = 0.38−0.05 ℓ − g A = 0.50123 0.00026 u − +0.028± g A = 0.519−0.033 g d = 0.527+0.040 A − −0.028 g νℓ = 0.5008 0.0008 ± g νe = 0.53 0.09 ± g νµ = 0.502 0.017 ± HTTP://PDG.LBL.GOV Page2 Created: 6/1/2020 08:28 Citation: P.A.
  • Rho(770), Ω(782), Φ(1020) Resonances, and an Addi- Tional Resonance Describing the Total Contribution of the Ρ(1450) and Ω(1420) States

    Rho(770), Ω(782), Φ(1020) Resonances, and an Addi- Tional Resonance Describing the Total Contribution of the Ρ(1450) and Ω(1420) States

    Citation: M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019 update G PC − − ρ(770) I (J ) =1+(1 ) See the related review(s): ρ(770) ρ(770) MASS We no longer list S-wave Breit-Wigner fits, or data with high combinatorial background. + NEUTRAL ONLY, e e− VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT 775..26 0..25 OUR AVERAGE ± 775.02 0.35 1 LEES 12G BABR e+ e π+ π γ ± − → − 775.97 0.46 0.70 900k 2 AKHMETSHIN 07 e+ e π+ π ± ± − → − 774.6 0.4 0.5 800k 3,4 ACHASOV 06 SND e+ e π+ π ± ± − → − 775.65 0.64 0.50 114k 5,6 AKHMETSHIN 04 CMD2 e+ e π+ π ± ± − → − 775.9 0.5 0.5 1.98M 7 ALOISIO 03 KLOE 1.02 e+ e π+ π π0 ± ± − → − 775.8 0.9 2.0 500k 7 ACHASOV 02 SND 1.02 e+ e π+ π π0 ± ± − → − 775.9 1.1 8 BARKOV 85 OLYA e+ e π+ π ± − → − We do not use the following data for averages, fits, limits, etc. ••• ••• 9 + + 763.49 0.53 BARTOS 17 RVUE e e− π π− ± 10 + → + 758.23 0.46 BARTOS 17A RVUE e e− π π− ± 11 +→ + 0 775.8 0.5 0.3 1.98M ALOISIO 03 KLOE 1.02 e e− π π− π ± ± 12 + → + 0 775.9 0.6 0.5 1.98M ALOISIO 03 KLOE 1.02 e e− π π− π ± ± 13 + → + 0 775.0 0.6 1.1 500k ACHASOV 02 SND 1.02 e e− π π− π ± ± 14 + →+ 775.1 0.7 5.3 BENAYOUN 98 RVUE e e− π π−, ± ± + → µ µ− 770.5 1.9 5.1 15 GARDNER 98 RVUE 0.28–0.92 e+ e ± ± + − → π π− 764.1 0.7 16 O’CONNELL 97 RVUE e+ e π+ π ± − → − 757.5 1.5 17 BERNICHA 94 RVUE e+ e π+ π ± − → − 768 1 18 GESHKEN..
  • Quark Masses 1 66

    Quark Masses 1 66

    66. Quark masses 1 66. Quark Masses Updated August 2019 by A.V. Manohar (UC, San Diego), L.P. Lellouch (CNRS & Aix-Marseille U.), and R.M. Barnett (LBNL). 66.1. Introduction This note discusses some of the theoretical issues relevant for the determination of quark masses, which are fundamental parameters of the Standard Model of particle physics. Unlike the leptons, quarks are confined inside hadrons and are not observed as physical particles. Quark masses therefore cannot be measured directly, but must be determined indirectly through their influence on hadronic properties. Although one often speaks loosely of quark masses as one would of the mass of the electron or muon, any quantitative statement about the value of a quark mass must make careful reference to the particular theoretical framework that is used to define it. It is important to keep this scheme dependence in mind when using the quark mass values tabulated in the data listings. Historically, the first determinations of quark masses were performed using quark models. These are usually called constituent quark masses and are of order 350MeV for the u and d quarks. Constituent quark masses model the effects of dynamical chiral symmetry breaking discussed below, and are not directly related to the quark mass parameters mq of the QCD Lagrangian of Eq. (66.1). The resulting masses only make sense in the limited context of a particular quark model, and cannot be related to the quark mass parameters, mq, of the Standard Model. In order to discuss quark masses at a fundamental level, definitions based on quantum field theory must be used, and the purpose of this note is to discuss these definitions and the corresponding determinations of the values of the masses.
  • QCD, Jets, & Gluons

    QCD, Jets, & Gluons

    QCD, Jets, & Gluons • Quantum Chromodynamics (QCD) • e+ e- → µ+ µ- • e+ e- annihilation to hadrons ( e+ e- → QQ ) J. Brau QCD, Jets and Gluons 1 Quantum Chromodynamics • Another gauge theory, as QED • Interactions described by exchange of massless, spin-1 bosons – so-called “gauge bosons” • Force is long range, due to massless gluons – but long range force is cancelled by combinations of color in mesons and baryons J. Brau QCD, Jets and Gluons 2 The color quantum number • Color was invented to explain: – Δ++ = uuu – e+e- → hadrons – Also explains π0 → γ γ • Color of a quark has three possible values – say red, blue, green • Antiquarks carry anticolor – Anti-red, anti-blue, anti-green • Bosons mediating the quark-quark interaction are called gluons – Gluons are to the strong force what the photon is to the EM force – Gluons carry a color and an anticolor • 9 possible combinations of color and anticolor • rr+gg+bb is color neutral, leaving 8 effective color combinations 4 • Results in potential V = - 3 αs /r + kr J. Brau QCD, Jets and Gluons 3 Color • 3 different color states Hadrons are combinations C – χC = r, g, b of quarks with Y = 0 and C • Color hypercharge I3 = 0 – YC so baryons = r g b & mesons = r anti-r, etc. • Color isospin C – I3 J. Brau QCD, Jets and Gluons 4 Color • In this diagram, the gluon has the color quantum numbers: C C C – I 3 = I 3(r) - I 3(b) = ½ – YC = YC(r) - YC(b) = 1 • So gluon exists in color state J. Brau QCD, Jets and Gluons 5 Quantum Chromodynamics • Important properties of strong interactions distinguishing it from QED: – Color confinement • Observed states have zero color charges.
  • Particle Interactions in Detectors Outline

    Particle Interactions in Detectors Outline

    Particle Interactions in Detectors Dr Peter R Hobson C.Phys M.Inst.P. Department of Electronic and Computer Engineering Brunel University, Uxbridge [email protected] http://www.brunel.ac.uk/~eestprh/ Dr P R Hobson, Brunel Outline • Introduction • Energy Loss of Heavy Particles • Energy Loss of Electrons and Positrons • Interactions of Photons • Scattering • Cherenkov Radiation • Interaction of Neutrons Dr P R Hobson, Brunel 1 Sources of Information Quite a large number of books on elementary particle physics contain a description of the fundamental interactions of particles with matter. I quite like these two general texts: •Leo W R Techniques for Nuclear and Particle Physics Experiments, Springer-Verlag • Ferbel T Experimental Techniques in High Energy Physics, Addison-Wesley There are specialised ones for individual detector systems which often go into even more detail (probably more than you need or want!). However … Dr P R Hobson, Brunel The Best Source? Chapter 26 of the Particle Data Group tables has everything! It is available (along with all the other chapters of course) at http://pdg.lbl.gov/ Dr P R Hobson, Brunel 2 Introduction • My aims are simple! – To give you an understanding of particle-matter interactions – To draw out the basic effects – To give you an “order of magnitude” feel for processes – To provide a background to my lectures on detectors. Dr P R Hobson, Brunel Cross-section • Measures the probability of an interaction • Assume that on average Ns particles are scattered per unit time from a beam (of flux
  • Generation and Modeling of Radiation for Clinical and Research Applications Bishwambhar Sengupta Clemson University, Bishwambharsengupta@Gmail.Com

    Generation and Modeling of Radiation for Clinical and Research Applications Bishwambhar Sengupta Clemson University, [email protected]

    Clemson University TigerPrints All Dissertations Dissertations 8-2019 Generation and Modeling of Radiation for Clinical and Research Applications Bishwambhar Sengupta Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations Recommended Citation Sengupta, Bishwambhar, "Generation and Modeling of Radiation for Clinical and Research Applications" (2019). All Dissertations. 2440. https://tigerprints.clemson.edu/all_dissertations/2440 This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints. For more information, please contact [email protected]. Generation and Modeling of Radiation for Clinical and Research Applications A Dissertation Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Physics by Bishwambhar Sengupta August 2019 Accepted by: Dr. Endre Takacs, Committee Chair Dr. Delphine Dean Dr. Brian Dean Dr. Jian He Abstract Cancer is one of the leading causes of death in todays world and also accounts for a major share of healthcare expenses for any country. Our research goals are to help create a device which has improved accuracy and treatment times that will alleviate the resource strain currently faced by the healthcare community and to shed some light on the elementary nature of the interaction between ionizing radiation and living cells. Stereotactic radiosurgery is the treatment of cases in intracranial locations using external radiation beams. There are several devices that can perform radiosurgery, but the Rotating Gamma System is relatively new and has not been extensively studied.
  • Bremsstrahlung 1

    Bremsstrahlung 1

    Bremsstrahlung 1 ' $ Bremsstrahlung Geant4 &Tutorial December 6, 2006% Bremsstrahlung 2 'Bremsstrahlung $ A fast moving charged particle is decelerated in the Coulomb field of atoms. A fraction of its kinetic energy is emitted in form of real photons. The probability of this process is / 1=M 2 (M: masse of the particle) and / Z2 (atomic number of the matter). Above a few tens MeV, bremsstrahlung is the dominant process for e- and e+ in most materials. It becomes important for muons (and pions) at few hundred GeV. γ e- Geant4 &Tutorial December 6, 2006% Bremsstrahlung 3 ' $ differential cross section The differential cross section is given by the Bethe-Heitler formula [Heitl57], corrected and extended for various effects: • the screening of the field of the nucleus • the contribution to the brems from the atomic electrons • the correction to the Born approximation • the polarisation of the matter (dielectric suppression) • the so-called LPM suppression mechanism • ... See Seltzer and Berger for a synthesis of the theories [Sel85]. Geant4 &Tutorial December 6, 2006% Bremsstrahlung 4 ' $ screening effect Depending of the energy of the projectile, the Coulomb field of the nucleus can be more on less screened by the electron cloud. A screening parameter measures the ratio of an 'impact parameter' of the projectile to the radius of an atom, for instance given by a Thomas-Fermi approximation or a Hartree-Fock calculation. Then, screening functions are introduced in the Bethe-Heitler formula. Qualitatively: • at low energy ! no screening effect • at ultra relativistic electron energy ! full screening effect Geant4 &Tutorial December 6, 2006% Bremsstrahlung 5 ' $ electron-electron bremsstrahlung The projectile feels not only the Coulomb field of the nucleus (charge Ze), but also the fields of the atomic electrons (Z electrons of charge e).