Interaction of Ionizing Radiation with Matter

Interaction of Ionizing Radiation with Matter
Type of radiation charged particles photonen neutronen Uncharged „particles“ Charged particles electrons (b-) He2+ (a), H+(p) D+ (d) Recoil nuclides Fission fragments Interaction of ionizing radiation with matter can be described at the molecular level (molecular process) or as macroscopic effects ( decrease, absorption, scattering, etc.)

Practical consequences of the interaction with matter Radiation: deceleration, decrease of energy Matter: physical, chemical, and/or biological effects Important parameters: particle mass, charge speed, kinetic energy spin matter atom mass Atom number Z number of e- per volume density ionization potential

Synopsis of interactions with the electron shell charged particles scattering, ionization photons photo effect compton effect

Synopsis of interactions with the atomic nucleus charged particles scattering, Bremsstrahlung, nuclear reaction photons pair formation nuclear reaction

Direct ionizing radiation: a, b-, b+, … Energy is high enough to ionize by collision Indirect ionizing radiation: n, g Ionization as a consequents of nuclear reactions in the absorbing matter In the context of radiation absorption, two definitions are important: linear stopping power also important and linear energy transfer Without Bremsstrahlung SI and LI are equal, otherwise there will be a substantial difference

Charged particles: deceleration by inelastic scattering Ionization and Excitation

By collision with electrons, the incident particle ionizes matter The mean energy to remove an electron is called the W-factor W-factor for air is 33.85eV/IP When the charged particle travels through matter, it makes an energy dependent number of ionization / length this is called specific ionization (SI) The mean energy loss per path length (LET) can determined by: LET = SI∙W LET = Linear Energy Transfer

The lower the energy, the higher the SI since probability of interaction with shell electron increases Bragg Peak

Example 241 Am was in smoke detectors Ea= 5.48 MeV specific ionization (SI) = 3.4104 IP/cm LET = 3.4·104·33.8 = 1.2 MeV/cm Range = = = 4.8 cm This is the maximum range, the SI increases dramatically at the end of the path.

SI is a characteristic feature of a specific material, since the e--density changes. To compare different materials, the relative stopping power is useful. RSP = Rair/Rabs (R = Range) RSP values for some materials and particles

Ranges in air for different particles and energies

Interaction of electrons with matter The most important interaction of electrons with matter is inelastic scattering with electrons from the shells. ionization Since not every collision leads to ionization, the average energy loss for ionization is larger than the minimal Ie of the atoms Bethe and Bloch proposed a „simple“ formula for energy loss along a track, considering the nature of the absorber

Interaction of electrons with matter me = rest mass of an electron e0 = dielectric constant (vacuum) n = velocity of the electron T = mean ionization density of the matterial e- are light particles, relativistic effects have to be considered E = 100 keV v = 0.55 c m = 1.2 ∙ mo E = 1000 keV v = 0.94 c m = 3 ∙ mo for lower energies, the relativistic effects can be neglected

Interaction of electrons with matter dE dx The formula predict a minimum value at a certain energy.... ...depending only on the mass of the particle The slower the particle the more ionization per length.

Interaction of electrons with matter Typical b- decay shows a continuous energy distribution, hence it has many low energy electrons The Bethe-Bloch formula is an exponential formula Empirically, it can be described: Y(x) = Y(0) ∙ e-m∙x with m = konst or N(x) = N0 ∙ e-m∙x with m = linear absorption coefficient (see x-ray crystallography)

Interaction of electrons with matter The absorption of electrons decreases linearly Often, instead of path x one takes mass-equivalent range d = d∙ x then with m/d = mass absorption coefficient m is a function of the electron energy and the material it allows to calculate the maximum range of electrons in a material it allows to calculate the thickness of materials for shielding

Interaction of electrons with matter Example: equivalent range of e- in Al one can easily calculate the path for reducing the e--flux to 50% ln2 m x1/2 = and d1/2 = (ln2)/(m/8) x1/2 can be determined experimentally and m be calculated for a particular material

Interaction of electrons with matter Semiempirical relationship between m, d and Emax Semiempirical relationships for connecting range with electron energy (0.15 < Eβ < 0.8 MeV)

Interaction of electrons with matter Maximum ranges of different β-emitters

Interaction of charged particles with matter How much energy can be lost in a single collision? Of particular interest: collision with a shell electron Maximum energy transfer incoming particle : mass Mi, speed Vi1 electron : mass me speed 0 after collision : Mi, v2, me, ve Energy: ½ Mi·v12 = ½ Mi·v22 + ½ me· ve2 momentum: Mi ·v1 = Mi·v2 + me·ve (non-relativistic)

Maximum energy transfer (MET) speed of reflected particle MET Qmax = nicht relativistisch If Mi = me (electron on electron) then Qmax = E This explains why light particles have a zigzag pass in matter Example: a-particle colliding with an e- me = 9.109∙10-31 kg ma = 6.646∙10-27 kg 5.468 ∙10-4 u u Qmax/E = = = 0.05 % !! heavy particles travel straight

Maximum energy transfer (MET) Examples for protons H Proton Kinetic Energy E (MeV) 0.1 1 10 100 103 104 105 106 107 Maximum percentage energy transfer 100Qmax/E 0.22 0.23 0.33 1.4 10.6 53.8 92.1 Qmax (MeV) 0.0022 0.0219 0.229 3.33 136 1.06 x 104 5.38 x 105 9.21 x 106

Bremsstrahlung Besides inelastic scattering at the electron shell, inelasting scattering at the nucleus is the most important interaction. Which results in the emission of Bremsstrahlung

Bremsstrahlung The stopping power of atoms or materials does not only depend on ionization but also on direct electron-target nucleus interactions This energy loss generates photons, so called Bremsstrahlung total stopping power From Bethe-Formula, the ratio between collision and radiation is The higher the energy, the more Bremsstrahlung The higher the atomic number, the more Bremsstrahlung

Bremsstrahlung The stopping efficiency by Bremsstrahlung increases by z2, but the stopping by ionization only by z. The formation of Bremsstrahlung increases with the energy of the electron The following formula gives this ratio Example: Pb shielded source of 90Y(Emax = 2.28MeV) produces 10% Bremsstrahlung

Bremsstrahlung

Bremsstrahlung Example: Pb shielded source of 90Y(Emax = 2.28MeV) produces 10% Bremsstrahlung Don‘t shield b-emitters with lead !!

Bremsstrahlung The Bremsstrahlung is used to produce synchrotron radiation Synchrotron Lichtquelle Schweiz SLS

Interaction of g-radiation and x-rays with matter Photons do not steadily lose energy as they penetrate matter The distance the photons can travel before they interact with an atom is governed statistically by a probability, which depends on the specific medium and on the photon energy Photo Effect Three principle modes of interaction Compton Effect Pair Formation

Photo effect interaction between  - quanta and electrons of the inner shells emission of a photoelectron (ionization) dominates with low photon energies incoming g-quant absorption of the  -quant photoelectron Electron of the shell higher energy level radiation electron gap filled by an outer-sphere electron (X-ray fluorescence, secondary radiation) lower energy level g-quant

Photo effect The photoelectron contains the complete energy of the g – quant minus an energy  that the electron expends in escaping the atom Every g-rays emitting nucleus emits g-quanta with a distinct energies (fingerprint) g – spectroscopy

Photo effect The photo effect depends strongly on the atomic number Z and the energy hn of the photons

Compton effect Incoming g-quant scattered g-quant compton electron interaction between  -quanta and e- of the outer electron shells (Compton electrons) emission of a Compton electron (ionization)  -quant loses energy (shift to longer wavelengths, Compton shift) the Compton shift only depends on the scattered angle, not on the wave length of the incident-photon resulting quant can undergo more Compton reaction or finally photo reactions

Compton effect Compton continuum The emitted Compton electrons have no defined energy (Compton continuum)

Pair formation Never forget: A photon with an energy of at least MeV can be converted into an e+ / e- pair in the field of an atomic nucleus Excess energy is kinetic energy of the products The distribution of the excess energy is continuous incoming g-quant

Pair formation Pair production becomes more likely with increasing photon energy The probability also increases with the atomic number

Annihilation of positrons The produced positron immediately reacts with an electron Since the total momentum before the decay is zero, two photons must be produced in order to conserve momentum The produced photons going off in opposite directions Due to the photon energy is 511 keV (1.022 MeV/2)

Pair formation Disadvantage: The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard Advantages: Pair Formation helps to convert high energy photons (> MeV) into photons with less energy (511 keV)  easier to shield Question: How would you shield a g-emitter ?

Interaction of g-radiation and x-rays with matter

Interaction of neutrons with matter Neutrons have no charge and don‘t interact with the shell electron (no direct ionization) Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes) Classification of Neutrons Thermal Neutrons: Energy distribution according to the Maxwell – Boltzmann equation Energy ≈ eV (most probable energy in the distribution at 20°C) Slow Neutrons: Also called “intermediate” of “resonance” neutrons. Energy ≤ 0.1 MeV Fast Neutrons: Energy ≤ 20 MeV Relativistic Neutrons: Energy > 20 MeV

Interaction of neutrons with matter Elastic scattering Inelastic scattering slow neutron W2 slow neutron W2 Backscattered nucleus W3 fast neutron W1 fast neutron W1 Backscattered nucleus W3 g-quant energy range: 10 keV - 1 MeV energy range: MeV emission of excess energy as -quants

Interaction of neutrons with matter M = Mass of a neutron m = Mass of the recoil nucleus En = Kinetic energy of the neutron Elastic scattering slow neutron W2 Maximum Fraction of Energy Lost, Qmax / En Backscattered nucleus W3 fast neutron W1 energy range: 10 keV - 1 MeV

Interaction of neutrons with matter Slowing-down neutrons is called neutron moderation If a neutron reaches thermal energies, it will move about randomly by elastic scattering until absorbed by a nucleus Nuclear reaction: (n,p), (n, 2n), (n, a), (n, g) Neutron Activation Analysis

Interaction of Ionizing Radiation with Matter

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