Interaction of Particles with Matter Alfons Weber STFCRAL

Interaction of Particles with Matter Alfons Weber STFC/RAL & University of Oxford Graduate Lecture 2020

Table of Contents n Bethe-Bloch Formula n n Multiple Scattering n n Light emitted by particles travelling in dielectric materials Transition Radiation n Nov 2020 Change of particle direction in Matter Cerenkov Radiation n n Energy loss of heavy particles by Ionisation Light emitted on traversing matter boundary A. Weber 2

Nov 2020 A. Weber 3

Bethe-Bloch Formula n n Describes how heavy particles (m>>me) loose energy when travelling through material Exact theoretical treatment difficult n n Simplified derivation ala MPhys course n Nov 2020 Atomic excitations Screening Bulk effects Phenomenological description A. Weber 4

Bethe-Bloch (1) n Consider particle of charge ze, passing a stationary charge Ze ze r n Assume n n n θ y x Ze Target is non-relativistic Target does not move Calculate n n Nov 2020 b Momentum transfer Energy transferred to target A. Weber 5

Bethe-Bloch (2) n Force on projectile n Change of momentum of target/projectile n Energy transferred to target Nov 2020 A. Weber 6

Bethe-Bloch (3) n Consider α-particle scattering off Atom n n Nov 2020 Mass of nucleus: Mass of electron: M=A*mp M=me n But energy transfer is n Energy transfer to single electron is A. Weber 7

Bethe-Bloch (4) n n Energy transfer is determined by impact parameter b Integration over all impact parameters b ze Nov 2020 db A. Weber 8

Bethe-Bloch (5) n n n Nov 2020 Calculate average energy loss There must be limits material dependence is in the calculation of the limits A. Weber 9

Bethe-Bloch (6) n n Nov 2020 Simple approximations for n From relativistic kinematics n Inelastic collision Results in the following expression A. Weber 10

Bethe-Bloch (7) n This was just a simplified derivation n Incomplete Just to get an idea how it is done The (approximated) true answer is with n n Nov 2020 ε screening correction of inner electrons δ density correction (polarisation in medium) A. Weber 11

Energy Loss Function Nov 2020 A. Weber 12

Average Ionisation Energy Nov 2020 A. Weber 13

Density Correction n Density Correction does depend on material with n n Nov 2020 x = log 10(p/M) C, δ 0, x 0 material dependant constants A. Weber 14

Different Materials (1) Nov 2020 A. Weber 15

Different Materials (2) Nov 2020 A. Weber 16

Particle Range/Stopping Power Nov 2020 A. Weber 17

Energy-loss in Tracking Chamber Nov 2020 A. Weber 18

Straggling (1) n n n So far we have only discussed the mean energy loss Actual energy loss will scatter around the mean value Difficult to calculate n n Nov 2020 parameterization exist in GEANT and some standalone software libraries From of distribution is important as energy loss distribution is often used for calibrating the detector A. Weber 19

Straggling (2) n Nov 2020 Simple parameterisation n Landau function n Better to use Vavilov distribution A. Weber 20

Straggling (3) Nov 2020 A. Weber 21

δ-Rays n n Energy loss distribution is not Gaussian around mean. In rare cases a lot of energy is transferred to a single electron δ-Ray n n Nov 2020 If one excludes δ-rays, the average energy loss changes Equivalent of changing Emax A. Weber 22

Restricted d. E/dx n Some detector only measure energy loss up to a certain upper limit Ecut n n Nov 2020 Truncated mean measurement δ-rays leaving the detector A. Weber 23

Electrons n Electrons are different light n n Nov 2020 Bremsstrahlung Pair production A. Weber 24

Table of Contents n Bethe-Bloch Formula n n Multiple Scattering n n Light emitted by particles travelling in dielectric materials Transition Radiation n Nov 2020 Change of particle direction in Matter Cerenkov Radiation n n Energy loss of heavy particles by Ionisation Light emitted on traversing matter boundary A. Weber 26

Multiple Scattering n Particles don’t only loose energy … … they also change direction Nov 2020 A. Weber 27

MS Theory n Average scattering angle is roughly Gaussian for small deflection angles With n Angular distributions are given by n Nov 2020 A. Weber 28

Correlations n n Multiple scattering and d. E/dx are normally treated to be independent from each Not true n n n Detailed calculation is difficult, but possible n Nov 2020 large scatter large energy transfer small scatter small energy transfer Wade Allison & John Cobb are the experts A. Weber 29

Correlations (W. Allison) nuclear small angle scattering (suppressed by screening) electrons at high Q 2 nuclear backward scattering in CM (suppressed by nuclear form factor) whole atoms at low Q 2 (dipole region) Log cross section (30 decades) 17 2 Log p. L or log k. L energy transfer (16 decades) electrons backwards in CM Example: Calculated cross section for 500 Me. V/c in Argon gas. Note that this is a Log-log plot - the cross section varies over 20 and more decades! Nov 2020 A. Weber 18 7 log k. T Log p. T transfer (10 decades) 30

Signals from Particles in Matter n Signals in particle detectors are mainly due to ionisation n n Direct light emission by particles travelling faster than the speed of light in a medium n n Cherenkov radiation Similar, but not identical n Nov 2020 Gas chambers Silicon detectors Scintillators Transition radiation A. Weber 31

Cherenkov Radiation n n Moving charge in dielectric medium Wave front comes out at certain angle slow Nov 2020 fast A. Weber 32

Cherenkov Radiation (2) n Nov 2020 How many Cherenkov photons are detected? A. Weber 33

Different Cherenkov Detectors n Threshold Detectors n n Differential Detectors n n βmax > βmin Ring-Imaging Detectors n Nov 2020 Yes/No on whether the speed is β>1/n Measure β A. Weber 34

Threshold Counter n n Nov 2020 Particle travel through radiator Cherenkov radiation A. Weber 35

Differential Detectors n Nov 2020 Will reflect light onto PMT for certain angles only β Selection A. Weber 36

Ring Imaging Detectors (1) Nov 2020 A. Weber 37

Ring Imaging Detectors (2) Nov 2020 A. Weber 38

Ring Imaging Detectors (3) n More clever geometries are possible n Nov 2020 Two radiators One photon detector A. Weber 39

Transition Radiation n Transition radiation is produced, when a relativistic particle traverses an inhomogeneous medium n n Strange effect n n Nov 2020 Boundary between different materials with different diffractive index n. What is generating the radiation? Accelerated charges A. Weber 40

Transition Radiation (2) Before the charge crosses the surface, apparent charge q 1 with apparent transverse vel v 1 After the charge crosses the surface, apparent charges q 2 and q 3 with apparent transverse vel v 2 and v 3 Nov 2020 A. Weber 41

Transition Radiation (3) n Consider relativistic particle traversing a boundary from material (1) to material (2) n Total energy radiated n Can be used to measure γ Nov 2020 A. Weber 42

Transition Radiation Detector Nov 2020 A. Weber 43

ATLAS TRTracker ATLAS Experiment Inner Detector: pixel, silicon and straw tubes Combination of Central Tracker and TR for electron identification Nov 2020 A. Weber 44

Atlas TRT (II) Nov 2020 A. Weber 45

Atlas TRT (III) n Electrons with radiator n only electron produce TR in radiator e± / π separation Electrons without radiator n TRT senses n n Bod -> J/y. Kos ionisation transition radiation High threshold hits Nov 2020 A. Weber 46

Table of Contents n Bethe-Bloch Formula n n Multiple Scattering n n Light emitted by particles travelling in dielectric materials Transition radiation n Nov 2020 Change of particle direction in Matter Cerenkov Radiation n n Energy loss of heavy particles by Ionisation Light emitted on traversing matter boundary A. Weber 47

Bibliography n This lecture n n https: //www 2. physics. ox. ac. uk/contacts/people/weber PDG online: Experimental Methods n https: //pdg. lbl. gov/2020/reviews/contents_sports. html n n Nov 2020 References therein, especially Rossi Lecture notes of Chris Booth, Sheffield n n Passage of particles through matter Particle detectors … http: //cbooth. staff. shef. ac. uk/phy 6040 det/ Or just it! A. Weber 48