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Interaction of Charged Particles with Matter

Interactions of Charged Particles with Matter

Literature/Tutorials

James Ziegler

Stopping and Range Tables for Charged Particles

J.F. Ziegler (IBMJ.P. Biersack

(HMI)) http//www.srim.org

Older Literature Hubert et al., Ann. De Physique

Suppl.5, 1 (1980)

Main Interactions of Charged Particles

Collisions with nuclei

Most interactions of charged particles with

material components are collisions with atomic

electrons. Nuclear collisions are noticeable only

at low kinetic energies.

Stochastic Multiple Scattering and Straggling

U ions, 60 keV, straggling in range and angle

Target of layers (absorbers Be, Au, Si)

Range is diffuse Range straggling

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

Stopping power

- Path length of trajectory

Phenomenological Model Of Energy Loss in Matter

- Bethe et al. (1930-1953), Lindhardts electron

theory Describes energy loss through ionization,

incoming ions are fully stripped

Estimate of trends/Order of magnitude Eparticle

kinetic energy, e- ? at rest

Important only forces ? to trajectory, others

cancel

Phenomenological Model of Energy Loss in Matter

- Integrate over radial coordinate

Estimate of radial limits Ne e- density le

electronic wave length, IEionization energy

Phenomenological Model Of Energy Loss in Matter

- Further

Insert r atomic density, ZT atomic number of

target Ne ZT r

Bethe-Bloch Equation

- Quantum mechanical calculation (for heavy

particles Mme)

- atomic density
- ZT atomic number of target
- AT mass number of target

Theoretical E-Loss Curves

- Units MeV/Nucleon
- LossMeV/A per mg/cm2
- Bragg maximum
- Semi-quantitative only Expt values smaller both

at small and large energies - ? recharging effects for projectile

Mg

He

MathCad Program

Stopping Power Isotopic Scaling Laws

Describes well the difference of R for different

isotopes of a given element, but

R(Be)/R(Ar)2.97 expt 4.67 theo Zeff t Zp

effective charge

Theory and Practice for Very 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

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.

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

Transmission Functions

Absorber

Transmission T(x) N(x)/N0

Heavy particles (a, p,..HI) have a well defined

range, R(E). Multiple scattering at small angles

only, because of M gtgt me Light particles

(electrons) and photons are scattered off

original path by large angles Range is not well

defined

a2

a1

e1

e2

Energy Loss Distributions

- Absorber of thickness x (r, ZT, AT), many

statistical scattering events - ? Central Limit Theorem Gaussian distribution in

energy loss DE

Thin absorber Asymmetric tail towards higher DE

Angular Straggling

Theory by Moliere, see W.T. Scott, Rev. Mod.

Phys. 35, 231 (1963) HI M. Wong et al., Med.

Phys. 17, 163 (1990)

Non-trivial geometry !

Assume multiple Coulomb scattering Gaussian

angular distribution

End