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Interaction of Charged Particles with Matter

Interaction of Charged Particles with Matter. Survey: Interactions of Radiation with Matter : Massive Particles. Literature/Tutorials. James Ziegler. Atomic excitation ionization fluorescence phosphorescence. Dominant type of interaction: inelastic collisions with electrons.

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Interaction of Charged Particles with Matter

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  1. Interaction of Charged Particles with Matter Survey:Interactions of Radiation with Matter : Massive Particles Surv Part Int. with Matter

  2. Literature/Tutorials James Ziegler Surv Part Int. with Matter

  3. Atomic excitation ionization fluorescence phosphorescence Dominant type of interaction: inelastic collisions with electrons Main Interactions of Charged Particles Less important (CP) collisions with nuclei : Surv Part Int. with Matter Most interactions of charged particles with material components are collisions with atomic electrons. Nuclear collisions are noticeable only at low kinetic energies.

  4. Stochastic Multiple Scattering and Straggling U ions, 60 keV, straggling in range and angle Target of layers (“absorbers” Be, Au, Si) Surv Part Int. with Matter Range is diffuse: “Range straggling” Probability Range (Å)

  5. electron shell Zp, r dx dr Phenomenological Model of Energy Loss in Matter Bethe et al. (1930-1953), Lindhardt’s electron theory Describes energy loss through ionization, incoming ions are fully stripped Estimate of trends/Order of magnitudeE=particle kinetic energy, e- at rest Surv Part Int. with Matter

  6. electron shell Zp, r dx dr Phenomenological Model of Energy Loss in Matter Integrate over radial coordinate: Estimate of radial limits: Ne = e- density le = electronic wave length, IE=ionization energy Surv Part Int. with Matter

  7. Phenomenological Model of Energy Loss in Matter Further: Insert: r = number density of atoms (#atoms/volume), ZT= atomic number of target  Ne= ZT ·r Surv Part Int. with Matter Remember: This is only a rough estimate! Calibrate real detectors

  8. (Zp, Ap, E) ZT AT r E-dE dx Bethe-Bloch Equation Quantum mechanical calculation (for heavy particles M»me): • = matter density ZT = atomic number of target AT = mass number of target Surv Part Int. with Matter

  9. Specific Energy Loss of Protons in Silicon Minimum Ionizing Particles Bethe-Bloch Formula • At high (relativistic energies, the b terms become dominant. • In addition, radiation losses (bremsstrahlung) and r-dependent plasma effects become important. • dE/dx(E) has minimum • “minimum-ionizing particles (mip)” examples: e±, m± Surv Part Int. with Matter

  10. Units MeV/Nucleon Loss:MeV/A per mg/cm2 Bragg maximum Semi-quantitative only: Expt values smaller both at small and large energies  recharging effects for projectile Theoretical E-Loss Curves Mg Surv Part Int. with Matter He MathCad Program

  11. Theory and Practice for Heavy Ions Theoretical energy loss in material of finite thickness is obtained from integration of the Bethe-Bloch formula or equivalent. Actual data may differ: Calibration required Surv Part Int. with Matter Energy lost by various ions in a 15.9 mm Si transmission detector vs. ion energy per nucleon (mass number A). Curves represent different theories.

  12. Path length of trajectory ds qs qs Probability Range (Å) Range and Stopping Power Scattering angle qs path variable s Stochastic multiple scattering process produces straggling in range, energy loss, angle Range Surv Part Int. with Matter Stopping power

  13. 6600 ip/mm a a p 2750 ip/mm Range and Specific Ionization E-loss in Air: 1atm, 150C Stopping power dE/dx (specific energy loss) depends on energy E and therefore on x Bragg Curve Highest E loss close to end of path  Bragg maximum Main E-loss mechanism: ionization, production of d electrons, electron-ion pairs Surv Part Int. with Matter

  14. Stopping Power Isotopic Scaling Laws Describes well the difference of R for different isotopes of a given element, but: Surv Part Int. with Matter R(Be)/R(Ar)=2.97 expt 4.67 theo Zeff ŧ Zp effective charge

  15. Interactions of Neutrons via Secondaries No electric charge  no direct atomic ionization  only collisions and reactions with nuclei  10-6 x weaker absorption than charged particles Processes depend on available n energy En: En ~ 1/40 eV (= kBT) Slow diffusion, capture by nuclei En < 10 MeV Elastic scattering, capture, nucl. excitation En > 10 MeV Elastic+inel. scattering, various nuclear reactions, secondary charged reaction products • Characteristic secondary nuclear radiation/products: • charged particles (n,p), (n, a),… • neutrons (n,n’), (n,2n’),… • fission fragments (n,f) • g-rays (n, g) Surv Part Int. with Matter

  16. Neutron Cross Sections 1b=10-24cm2=100fm2 Surv Part Int. with Matter

  17. Neutron Mean Free Path Mean Free Path of Neutrons in Water r: atomic density s: cross section l = average path length in medium between 2 collisions Surv Part Int. with Matter

  18. Data: Neutron-mfp-Water Neutron mean free path data (H2O): http://t2.lanl.gov/data/ Surv Part Int. with Matter

  19. The End Surv Part Int. with Matter

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