Lecture 2. Interaction of Radiation with Matter

Transcription

1 Lctur Intraction of Radiation with Mattr

2 Dats Vorlsung 1 T.Stockmanns Vorlsung J.Ritman Vorlsung 3 J.Ritman Vorlsung 4 J.Ritman Vorlsung 5 J.Ritman Vorlsung 6 J. Ritman (Akad. Fir?) Vorlsung 7 M.Mrtns 0.1. Vorlsung 8 T.Stockmanns 09.1 Vorlsung 9 T.Stockmanns fällt aus 3.1. Vorlsung 10 J.Ritman Vorlsung 11 T.Stockmanns Vorlsung 1 T.Stockmanns Vorlsung 13 J.Ritman 03.0 Vorlsung 14 J.Ritman Bsuch von COSY:

3 Introduction Ovrviw of dtctor systms Sourcs of radiation Radioactiv dcay Cosmic Radiation Acclrators Contnt Intraction of Radiation with Mattr Gnral principls Chargd particls havy chargd particls lctrons Nutral particls Photons Nutrons Nutrinos Dtctors for Ionizing Particls Principls of ionizing dtctors Gas dtctors Principls Dtctor concpts

4 Contnt Intraction of shll lctrons of atoms causs a dclration of particls à nrgy loss Elastic hits with atomic nuclus causs a scattring of particls à multipl scattring Light particls (lctrons) suffr a high acclration during th scattring at th nuclus. Part of this kintic nrgy is mittd as radiation à brmsstrahlung High nrgtic particls (> ~ 1 GV) can crat nw lmntary particls via inlastic procsss. This is not covrd hr. Also not part of th lctur ar inlastic intractions with a nuclus or nuclons

5 Crnkov and transition radiation Crnkov radiation is mittd if th vlocity of a particl in a mdium is highr than th spd of light in th mdium à lctromagntic shock wav à radiation in con form Transition radiation appars if a chargd particl crosss th boundary btwn two mdia with diffrnt dilctric constant γ Both will b covrd latr

6 Enrgy loss of havy chargd particls Why havy? Bcaus th chang in th flight path can b nglctd For th total nrgy loss rat ( nrgy pr track lngth de/dx) all procsss hav to b takn into account Enrgy loss is a statistical procss Elctromagntic intraction is dominant procss Classical dviation from Bohr dscribs th nrgy loss of havy particls (p, α-particls, ) via ionization and xcitation Quantum-mchanically corrct tratmnt à Bth-Bloch-Formula Furthr corrctions à corrct tratmnt O(%) and bttr

7 de/dx history N. Bohr ( ) classical dviation Bth ( ), Bloch ( ) quantum mchanical L. Landau ( ) distribution E. Frmi ( ) dnsity corrctions

8 Ionization: classical drivation (Bohr) Enrgy loss mainly du to inlastic collisions with th lctrons of th targt atoms à ionization and xcitation Assumptions: M(projctil) >> m, lctrons at rst Projctil: v βc, charg z, targt charg Z z r θ b Z b: impact paramtr x Momntum loss: Δp F Coulomb Longitudinal forcs cancl: Only transvrsal forcs play a rol: dt F Coulomb 1 4πε F ( x) F ( x) l l 0 zz / r b F t F! F cos(θ) r

9 Ionization: classical drivation (Bohr) Transvrsal forc on projctil: 1 zz F Ct cosθ 4πε r 0 1 4πε 0 zz b cos 3 θ Momntum transfr of targt: Δp ( b) F dt F dx Ct Ct v 1 4πε θ cos θ 1 zz cosθ dθ 4πε bv 0 zz b cos 3 dx θ v dx b d / π 1 0 π 4πε 0 zz bv Enrgy transfr to targt with mass m t ΔE( b) Δp m t Z 1( lctron ) 1 4πε 0 4 z m c β b

10 Ionization: classical drivation (Bohr) Enrgy loss at lctrons in th ring btwn b and db in layr dx: Numbr of lctrons: πb db dx N Elctron dnsity: N N A Z/A ρ de( b) ΔE( b) N dv 4 4π z m c β db b Intgration ovr all impact paramtrs from b min to b max : N dx de dx ( b) 4 4π z m c β ρn A Z 1 A b db de dx 4 4π z m c β ρn A Z A ln b b max min Maximum momntum transfr at cntral collision: Δp max Δp mcβ ΔE( b) m Minimum nrgy transfr: Ionization nrgy I b min z m c β b max z cβ m I 4 z m c β b

11 de/dx classical drivation (Bohr) Classical formula for nrgy loss via ionization: de dx K z ρ Z β A 1 c m ln β I with K π c m 4 4 N A 0.31 MV cm / g Unit [de/dx] MV/cm oftn de/dx is dividd by ρ è Unit[dE/dX] MV cm /g!

12 classical vs. quantum mchanical cas classical: de dx K z 1 Z 1 c β m ln β A I qm: de dx K z 1 Z 1 ln β A c β mγ T I max T max mc β γ 1+ γ m / M + ( m / M ) mc γ Mc β γ for γ m << for γ M T max is th maximum transfrabl kintic nrgy pr collision for low nrgis and particl with big masss qual up to a factor indpndnt of mass of projctil (for γm << M) unit MV/(g/cm ) de/dx almost indpndnt of matrial proprtis

13 de/dx Bth Bloch Formula Complt quantum mchanical dviation + corrctions: de dx K z K Z A 1 c β mγ T ln I 1 max δ β β π c m 4 4 N A 0.31MV cm / g C Z valid btwn 6 MV < E < 6 GV (π), or in gnral 0.0 < β < 0.99 (1% prcision) Corrctions: β - atomic transitions δ(β) - dnsity function du to polarization (at high nrgis) C/Z - shll corrctions (at low nrgis)

14 man xcitation nrgy de dx K z Z 1 ln A c β mγ T I 1 max δ β β C Z I / Z [V] I 10 V Z for Z > 0 I charactristic for matrial I 16 Z 0.9 V for Z > 1 for xampl Argon Z 18, I 15 V, masurd V I/Z abov

15 de dx K z z-dpndnc Z 1 ln A c β mγ T I 1 max δ β β C Z Tracs of ions in an mulsion Iron Z 6 Thorium Z 90

16 de/dx discussion lctronic stopping powr ~ β non-ionizing intractions brmsstrahlung ~ 1/β (Frmi-)Platau Ris: T max ~ β γ const ~ ln βγ Minimum at βγ è minimum ionizing particl (MIP) de dx K z Z 1 c ln β A β mγ T I 1 max δ β C Z

17 de/dx min for various matrials βγ 3.5 broad minimum à minimum ionizing particl (MIP) H Z/A 1 de/dx min 4 MV/(g/cm ) oth. Z/A 0.5 de/dx min MV/(g/cm ) de/dx min MV/(g/cm ) only wak matrial dpndnc de/dx curvs shiftd horizontally by ln(m 1 /M )

18 de/dx min rul of thumb: de/dx mip ~ 1.5 MV/ g cm -

19 Rlativistic ris at rst E-fild Lorntz contraction of fild lins è transvrsal componnt of E fild riss with ln(γ) è largr collision distancs Saturation for high nrgis è Frmi platau Solids (de/dx) βà de/dx mip Gass (de/dx) βà de/dx mip gasous mdia solid mdia δ corrction, dnsity ffct: for high dnsitis th E fild is partly shildd by polarization Lss collisions with furthr away lctrons Effct strongr in solids without corrctions with corrctions

20 de dx K z Particl Idntification Z c ln A β mγ I 1 δ β β C Z de/dx only dpndnt of vlocity and not from mass è particl idntification Havy particls: de/dx wll dscribd by Bth- Bloch-Formula Ionization and xcitation of targt lctrons Elctrons do not oby th Bth-Bloch-Formula

21 Rang in mattr Man rang R/M, projctil mass M Intgration of Bth-Bloch: R 0 E dx de de Statistical procss à man pntration dpth For xampl 1 GV particl in lad: K+ M MV βγ.0 R/M 800 g cm - GV -1 ds R/ρ 35 cm in lad Muons R/M 7000 g cm - GV -1 ds 64 cm Protons R/M 0 g cm - GV -1 ds 18 cm

22 Rang: Bragg curv Bragg curv: nrgy loss of a particl in dpndnc of pntration dpth Pntration in mattr: à projctil gts slowr à nrgy loss riss Bragg-pak: most nrgy lost at th nd intnsity as a function of th way nrgy loss pr unit lngth è Bragg-Pak

23 Rang Tracs from α-particls from th dcay of Radium in a cloud chambr Mono nrgtic, sam rang (8.6 cm) Th singl track is from a dcay of an xcitd nuclus

24 Rang Particl Enrgy [MV] Rang in air [m] Rang in watr [m] lctron proton α-particl

25 Mdical application tumor thrapy Ionization profil of 1 C ions in watr

26 Enrgy loss - summary Bth-Bloch formula dscribs th man nrgy loss -<de/dx> of (havy) chargd particls in mattr: by ionization and xcitation à dominant Crnkov radiation and transition radiation (includd in BBF) NOT brmsstrahlung (important for lctrons and high nrgy µ or π) de dx K z Z 1 c ln A β mγ T I 1 max δ β β C Z at low β: <de/dx> ~ 1/β down to Bragg pak minimum at βγ p/m (v96%c) MIP rlativistic ris ~ ln(βγ) du to rlativistic xtnsion of transv. E-fild dnsity ffct à saturation à platau (polarization ffcts) only wak dpndnc on mdium (Z/A, ln(i)) hight of th platau~ 1.1 (solid) 1.7 (gas) x minimum rmmbr: <de/dx> mip ~ 1.5 MV/g cm plotting against p à possibility to distinguish particls by mass!

27 Enrgy loss distribution (straggling) Enrgy loss is a statistical procss Distribution function is asymmtric for small absorbrs For thick absorbrs th distribution bcoms Gaussian Collisions with small de mor probabl larg de rar à lctrons with larg nrgy (kv) ar calld δ-lctrons (or rays) δ-lctrons hav nough nrgy for thir own ionization trac Paramtrizd via asymmtric Landau(-Vavilov) distribution

28 Landau(-Vavilov) Distribution Landau, Vavilov and Gaussian distribution ar valid only in crtain rgions Distinguishing paramtr is κ: κ Δ /T max Landau Thory for vry thin absorbrs (κ < 0.01), max E-trans Vavilov Thory for intrmdiat absobrs (0.01 < κ < 10) Gaussian Distribution abov κ > 10 Δ ξ Z z π Nar mc ρ A β

29 δ - lctrons

30 δ - lctrons: angular distribution 1-1 rlation btwn scattring angl and kin. nrgy T m T T T arctan 1 1 arctan ) ( 1 max Θ γ T kin (MV)

31 δ - lctrons: rat of production d N/dθ dx ρ sin(θ) /cos 3 (θ) d N/dT dx lad lad air air θ(dgrs) T(MV) Rmmbr: 1. rat of δ-lctrons chang rapidly by many powrs. 1-1 rlation btwn kin. nrgy and mission angl 3. most δ-lctrons ar mittd at 90 with low nrgy, low β

32 Problms for Dtctors Q rconstructd position primary δ spac point rconstruction systmatically shiftd du to δ-lctrons

33 Enrgy loss of lctrons and positrons In addition to nrgy loss via ionization/xcitation brmsstrahlung gts important Bcaus th masss of intracting particls ar qual additional hit paramtrs hav to b takn into account à significant dflction For - collisions taks part btwn quantum mchanically indistinguishabl particls brmsstrahlung: Dflction of (high nrgtic) particls in an xtrnal fild (.g. Coulomb fild of a nuclus, shll lctron) nuclus

34 Bth-Bloch for Elctrons Bth Bloch formula for high masss: Has to b modifid for lctrons and positrons bcaus th masss of th intraction particls is qual. Th maximum transfrabl nrgy changs to: Approximatly: Mor accurat calculations of th kinmatic + shilding ffcts givs: NO brmsstrahlung includd! Z C I T m c A Z K z dx de ln 1 1 max δ β γ β β g cm MV N m c K A / π max ) / ( / 1 γ β γ γ β m c M m M m m c T + + ln 1 δ β γ β β I m c A Z K dx de ) (1 1 1 ln 1 δ γ γ γ γ β γ β β I m c A Z K dx de

35 Brmsstrahlung Enrgy loss via intraction with Coulomb fild of nucli Particls ar slowd down è xcitation of photons For high nrgis: de dx 4 Z 183 α N 1 ln 4 0c A 3 Z πε z m A E linar in E 1/m const. indpndnt of matrial and particl matrial constants of th absorbr particl charg z particl mass m particl nrgy E

36 Th radiation lngth X 0 is a masur for th absorption of nrgy in mattr Handy for dimnsioning of dtctors: full nrgy absorption (X0 at maximum) è calorimtr low distortion of othr masurmnts (X0 at minimum) è tracking Radiation lngth cm Air Watr 36.1 Silicon 9.36 NaJ.59 Pb 0.56 Radiation Lngth de dx 4 Z 183 z α N 1 ln 4 0c A 3 Z πε m A de dx : 1/X 0 E X 0 E( x) E0 xp( x X 0) Aftr th distanc X 0 th radiation nrgy of an lctron has droppd to 1/ 37 % Aftr 7 X 0 is th nrgy only 0.1 % E

37 Critical Enrgy Ionization ln(β γ )/ β ln E Brmsstrahlung E critical nrgy: losss from ionization and brmsstrahlung ar qual OR losss from ionization/x 0 and lctron nrgy ar qual

38 Critical Enrgy Critical nrgy [MV] Hydrogn 340 Hlium 0 Carbon 103 Aluminum 47 Iron 4 Lad 6.9 approximatly: E c 610 MV / (Z+1.4) for solids and liquids E c 710 MV / (Z+0.9) for gasss

39 Enrgy Loss of Muons Enrgy loss via brmsstrahlung (m µ /m ) much smallr, 45,000 x lss E c scals with (m µ /m ),E c svral hundrd GV In addition to brmsstrahlung also dirct pair cration µ à µ de/dx of muons in havy targts

40 Multipl (Coulomb) Scattring Moliér thory dscribs multipl Coulomb scattring (mainly Ruthrford scattring) Roughly Gaussian distribution with long tails For most applications sufficint to us th Gaussian approximation for th cntral 98 % For Exampl: lctron with p 5 MV flis through 3 m of air à θ 0 16 θ θ rms rms spac 13.6MV 0 θ plan z x X 0 + ln βcp [ ( x X )] 0 1/p è larg for low momntum particls x/x 0 è us only thin matrials with larg X 0 for tracking