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Charged particle energy loss in matter

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Taken from RPP2008; pdg.lbl.gov

- At very low βγ, large energy loss due to atomic effects
- For large (and relevant) range of relativistic βγ, energy loss is small (minimium ionizing particle – “mip”)
- Ultra-relativistic particles lose energy mostly via gamma radiation

Phys 521A

- Thickness of material (x) is usually measured in gm/cm2
- Related to distance (y) traversed via density: x = y ρ
- Used because relevant issue in determining interaction in matter is how many scattering centres are traversed
- Benchmark values for traversing 1 cm of material:
- Lead: x = 11.4 gm/cm2
- Iron: x = 7.9 gm/cm2
- Water: x = 1.0 gm/cm2
- Liquid H2x = 0.07 gm/cm2
- Air: x ~ 0.001 gm/cm2

Phys 521A

- Energy loss is small (~few MeV cm2/gm) except for βγ<1
- At very low βγ binding effects become important (keep curves finite); dE/dx magnitude peaks at a few hundred MeV cm2/gm near β ~ 0.01
- Relativistic charged particles traverse large amounts of material; 1 GeV muon penetrates ~500 gm/cm2; for water this corresponds to a length of 500 cm.

Phys 521A

- Slow particles lose most of their energy in a short distance, since kinetic energy T ~ β2
- For 30 MeV protons in water, T0 = 10 MeV <dE/dx> ~ 50 MeV cm2/gm, soΔy ~0.1cm (Bragg peak)

Phys 521A

- Monoenergetic proton beam loses energy more rapidly as it slows down; gives sharp Bragg peak in ionization versus depth (used in proton radiation therapy)
- Using a range of protonenergies allows a variedprofile versus depth
- Photon beam (x-rays)deposits most energy near entrance into tissue

Phys 521A

- Curves scale reasonably well
- Scaling with medium ~Z/A, but I rises with Z
- Note larger relativistic rise in Helium gas; less rise in liquids and solids (screening due to density)
- Recall that linear distance yrelated to x via mass density: x = ρ y

Phys 521A

- Measured values indicate non-trivial structure vs Z (note suppressed zero)
- Crude approximation at large Z is I= 10Z, accurate to about 10%

Phys 521A

- With small probability some collisions can give atomic electrons enough energy to cause further ionization; these are called δ-rays.
- Result is a high-energy asymmetric tail in the energy-loss PDF
- Peak position (most probable energy loss) is not affected; therefore it is used when sampling dE/dx loss
- Width is large (does not fallas √x)

Phys 521A

- Combination of dE/dx (measures βγ) and momentum (βγm) allows determination of m, identification of particle type (but μ/π difficult)
- OPAL dE/dx measurements; since each measurement has large width, need lots of them (OPAL had up to 160/track)

Phys 521A

From Mauricio Barbi, TSI’07 lectures

Interactions of Particles with Matter

Interactions of Electrons

For electrons and positrons,the rate of energy loss is similar to that for “heavy” charged particles, but the calculations are more complicated:

Small electron/positron mass

Identical particles in the initial and final state

Spin ½ particles in the initial and final states

k = Ek/mec2: reduced electron (positron) kinetic energy

F(k,β,)is a complicated equation

However, at high incident energies (β1)F(k) constant

Phys 521A