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Fundamentals of Interactions of Particles in Matter

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Fundamentals of Interactions of Particles in Matter Fundamentals of interactions of particles in matter Paulo Martins1,2 1 DKFZ, Division of Biomedical Physics in Radiation Oncology, Heidelberg, Germany 2 IBEB, Faculty of Sciences of the University of Lisbon, Portugal Physics of Charged Particle Therapy Author DivisionBibliography 7/5/20 | Page2 • Techniques for Nuclear and Particle Physics: A How-to Approach, William R. Leo, Springer-Verlag, 2nd Ed., Ch. 2, pp. 17-53 • Principles of Radiation Interaction in Matter and Detection, Claude Leroy and Pier-Giorgio Rancoita, World Scientific, Ch. 1-2, pp. 19-135 • Physics of Proton Interactions in Matter, Bernhard Gottschalk, in: Proton Therapy Physics, Harald Paganetti, Ch. 2, pp. 20-59 Physics of Charged Particle Therapy | Paulo M. Martins Author DivisionBibliography 7/5/20 | Page3 • Radiation Detection and Measurement, Glenn F. Knoll, Wiley, 4th Ed., Ch. 2, pp. 29-42 • Passage of Particles Through Matter, M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 0300001 (2018) pp. 2-17 Physics of Charged Particle Therapy | Paulo M. Martins Author DivisionGoal 7/5/20 | Page4 Two physics problems in particle radiotherapy: • Designing beam lines • Predicting the dose distribution in the patient We need to understand the interactions of particles with matter Physics of Charged Particle Therapy | Paulo M. Martins Author Division 7/5/20 | Page5 Proton and a photon posterior-oblique beam M. Goitein 2008 Physics of Charged Particle Therapy | Paulo M. Martins Author DivisionAccelerator and beam delivery (passive scattering) 7/5/20 | Page6 M. Goitein 2008 Physics of Charged Particle Therapy | Paulo M. Martins Author DivisionAccelerator and beam delivery (passive scattering) 7/5/20 | Page7 IBA Nozzle (Burr Center Gantry) B. Gottschalk 2007 Physics of Charged Particle Therapy | Paulo M. Martins Author DivisionOutline 7/5/20 | Page8 • Preliminary notions and definitions • Energy loss of heavy charged particles by atomic collisions • The Bethe-Bloch formula (stopping power) • Fluence, stopping power and dose • Range Physics of Charged Particle Therapy | Paulo M. Martins January 9, 2009 10:21 World Scientific Book - 9.75in x 6.5in ws-book975x65˙n˙2nd˙Ed Introduction 9 January 9, 2009 10:21 World Scientific Book - 9.75in x 6.5in ws-book975x65˙n˙2nd˙Ed 1.3.1 The Two-Body Scattering Radiation processes, like the ones resultingIntroduction in energy losses by9 collision, take place January 9, 2009 10:21 World Scientific Book - 9.75in x 6.5in ws-book975x65˙n˙2nd˙Ed in matter and can1.3.1 beThe consideredTwo-Body Scattering (see following chapters) as two-body scatterings January 9, 2009 10:21 World Scientific Book - 9.75in x 6.5in ws-book975x65˙n˙2nd˙Ed in which the targetRadiation particle processes, like theis ones almost resulting atin energy rest. losses In by collision, this section,take place we will study the in matter and can be considered (see following chapters) as two-body scatterings kinematics of thesein which the processes target particle and, is almost in at rest. particular, In this section, derive we will study equations the regarding the kinematics of these processes and, in particular, derive equations regarding the maximum energymaximum transfer. energy transfer. Let us considerLet anus consider incident an incident particleIntroduction particle [e.g., [e.g., a proton a (p), proton pion (º), kaon (p), (K), pion etc.] (º), kaon9 (K), etc.] of mass m and momentum p~, and a target particle of mass me [Rossi (1964)] at of mass m andrest. momentum For collision energy-lossp~, and processes, atarget the target particle particle in matter of is usuallymass anme [Rossi (1964)]Introduction at 9 1.3.1 The Two-Bodyatomic electron (see Scattering Fig. 1.1). After the interaction, two scattered particles emerge: rest. For collisionthe former energy-loss with mass m processes,and momentum p~ the00 and target the latter with particle mass me inand matter is usually an momentum p~ . The latter one has the direction of motion (i.e., the direction of the Radiation processes, like0 the ones resulting in energy1.3.1 losses byThe collision, Two-Body take place Scattering atomic electronthree-vector (see Fig.p~ 0) forming 1.1). an After angle µ with the the interaction, incoming particle direction. two scatteredµ is the particles emerge: in matter andangle can at be which considered the target particle (see is followingscattered. The chapters)kinetic energy [see as Eq. two-body (1.12)] of scatterings the former with mass m and momentum p~ 00 Radiationand the processes, latter with like the mass onesm resultinge and in energy losses by collision, take place in which the targetthe scattered particle particle is related almost to its at momentum rest. byIn this section, we will study the 2 2 2 2 4 in matter and can be considered (see following chapters) as two-body scatterings momentumkinematicsp~ of0. these The latterprocesses one and,E hask + m ine thec particular,= directionp0 c + mec derive, of motion equations (i.e.,(1.22) regarding the direction the of the from which we get p in which the target particle is almost at rest. In this section, we will study the three-vectormaximum energyp~ 0) forming transfer. an angle µ with the incoming particle direction. µ is the 2 E + m c2 m2c4 kinematics of these processes and, in particular, derive equations regarding the 2 k e ° e angleLet at which us consider the antarget incident particle particlep0 = is [e.g.,scattered2 a proton. The. (p), kinetic pion (º energy),(1.23) kaon (K), [see etc.] Eq. (1.12)] of ° c ¢ maximum energy transfer. of mass m andThe momentum total energy beforep~, and after a scattering target isparticle conserved. of Thus, mass we havem [Rossi (1964)] at the scattered particle is related to its momentum byLet us considere an incident particle [e.g., a proton (p), pion (º), kaon (K), etc.] 2 2 2 4 2 2 2 2 4 2 rest. ForAuthor collision energy-lossp c + processes,m c + mec = thep00 targetc + m c particle+ Ek + mec in matter is usually an Division 2 2 2of mass2 4m and momentum p~, and a target particle of mass me [Rossi (1964)] at atomic electronPreliminaryand, (see consequently, Fig.p 1.1).E Afterk +notionsm theec interaction,p= andp0 c two definitions+ scatteredm c , particles emerge: (1.22) 7/5/20 | Page9 e 2 2 2 4 2 2 2 4 rest. For collision energy-loss processes, the target particle in matter is usually an the former with mass m andp momentum00 c + m c = pp~c00+andm c theEk, latter with(1.24) mass me and °atomic electron (see Fig. 1.1). After the interaction, two scattered particles emerge: frommomentum which wep~ 0.while get The from latter momentum onepconservation: has the directionp p of motion (i.e., the direction of the Two-body scattering2 2and2 themaximum former with energy mass m andtransfer momentum p~ 00 and the latter with mass me and three-vector p~ 0) formingp~ an00 = anglep~ p~ 0 µ =withp the00 = p incoming+ p0 2 2pp0 cos particleµ. direction.(1.25) µ is the ° ) 2 ° 2 4 angle at which the target particle2 is scatteredEk + m. Theec kineticmomentumm energyec p~ [see0. The Eq. latter (1.12)] one of has the direction of motion (i.e., the direction of the p0 = ° . (1.23) scatteredparticle 2 three-vector p~ 0) forming an angle µ with the incoming particle direction. µ is the the scattered particle is related towithmomentump” its momentumc by ° ¢ angle at which the targetRelation particle kinetic is scattered energy. The momentum kinetic energy [see Eq. (1.12)] of The total energy before andE + afterm c2 scattering= p 2c2 + ism2 conserved.c4, Thus, we(1.22) have k e 0 ethe scattered particle(scattered is related toparticle) its momentum by incomingparticle from which we get2 2 2 4 withmomentump2 p 2 2 2 4 2 p c + m c θ+ mec = p c + m c + Ek + mec 2 2 2 2 4 scatteredelectron 00 Ek + mec = p0 c + mec , (1.22) withmomentump’ 2 2 2 4 2 Ek + mec mec and, consequently,p p0 = p ° from. which we get (1.23) p c2 ° ¢ 2 Fig. 1.1 Incident particle of mass m and momentum p~ emerges with momentum p = p~ ,while 2 2 4 The total energyEnergy before and and momentum2 after2 scattering2 4 are isconserved: conserved.2 2 2 Thus,4 00 | we00| have Ek + mec m c the scattered electronp emergesc + withm momentumc = p0 = p~ 0 .p c + m c E , 2 (1.24) e 00 | | k p = ° . (1.23) ° 0 2 2 2 2 4 2 2 2 2 4 2 c p c + m c + mec = p00 c + m c + Ek + mec ° ¢ while from momentump conservation: p The total energy before and after scattering is conserved. Thus, we have and, consequently,p p 2 2 2 2 2 2 4 2 2 2 2 4 2 p~ 00 = p~ p~ 0 = p00 = p + p0 2pp0pcosc µ+. m c + mec(1.25)= p00 c + m c + Ek + mec 2 2 2 4 2 2 2 4 p°00 c + m c)= p c + m c Ek, ° (1.24) and,° consequently,p p while from momentump conservation:C. Leroy & P.G.p Rancoita, (2009) Radiation Interaction in Matter and Detection, World Scientific 2 2 2 4 2 2 2 4 scatteredparticle2 2 2 p00 c + m c = p c + m c Ek, (1.24) Physicsp~ 00 =of Chargedp~ p~ 0 Particlewithmomentump”= Therapy | Paulop00 =M. Martinsp + p0 2pp0 cos µ. (1.25) ° ° ) while° from momentump conservation: p 2 2 2 scatteredparticle p~ 00 = p~ p~ 0 = p00 = p + p0 2pp0 cos µ. (1.25) withmomentump” ° ) ° incomingparticle withmomentump scatteredparticle θ withmomentump” scatteredelectron incomingparticle withmomentump’ withmomentump scatteredelectron θ withmomentump’ incomingparticle withmomentump scatteredelectron θ Fig.
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