Chapter 2. Radiation

Chapter 2. Radiation • Radioactivity 2.Radiation interaction with Matter 3.Radiation Doses and hazard Assessment

2.1 Radioactivity • Overview • Types of Radioactive Decay • Energetics of Radioactive Decay • Characteristics of Radioactive Decay • Decay Dynamics • Naturally Occurring Radionuclides

2.2Radiation interaction with Matter overview Photon Interactions Neutron Interactions Interaction of Heavy Charged Particles with Matter Scattering of Electrons in a Medium

Radiation is everywhere 1) overview Cosmic Inhaled Radon Bodies Plants Radioactive Elements Rocks We live in a sea of radiation…

Discovery of Ionization by Radiation X-rays and radioactivity discharged a charged electroscope. Curie and Rutherford attributed the discharge to the ionization of air by these rays. An electroscope consists of two gold leaves suspended from a metallic conductor in a glass jar

Ionization Energy of Gases The minimum energy required to remove an outer electron from atoms or molecules is called ionization potential. Ionizing radiation also remove electrons in atomic inner shell, and the average energy per ion pair is considered ionization energy High energy particles and photons that ionise atoms and molecules along their tracks in a medium are called ionizing radiation He + 25 eV He+ + e- He+ + 54 eV He2+ + e- Ionization energy (IE eV) per ion pair of some substancesMaterial Air Xe He NH3 Ge-crystalAverage IE 35 22 43 39 2.9

1) overview

directly ionizing radiation indirectly ionizing radiation

Interaction of Photons with Matter Photon Energies Visible red light 1.5 eVvisible blue light 3.0 eV UV few eV-hundreds eV X-rays 1 to 60 keV Gamma rays keV - some MeV Interactions of gamma rays with matter: photoelectric effect Compton effect Pair productions

Photoelectric process KE=h-EB a very crude approximation

Compton Effect of Gamma Rays When a photon transfers part of its energy to an electron, and the photon becomes less energetic is called Compton effect. re is the classical electron radius

Pair Production of Gamma Rays Gamma photons with energy greater than 1.02 MeV produce a electron-positron pair is called pair production. The fate of the positron?

Gamma-ray Three Modes of Interaction with Matter Photoelectric effect Compton scattering pair production

Attenuation of Gamma Rays by Matter Gamma-ray intensity decreases exponentially as the thickness of the absorber increases. I = Io e–μx I: Intensity at distance xμ: absorption constantx: thickness

Average Travel Distance Before An Interaction the interaction probability P(x) that a particle interacts somewhere along a path of length x is The probability th that a particle does not interact while traveling a distance x p(x)dx be the probability that a particle interacts for the first time between x and x + dx.

the average distance: the average distance such a particle travels before it interacts. mean-free-path length Half-Thickness: the thickness of a medium required for half of the incident radiation to undergo an interaction

What is the thickness of a water shield and of a lead shield needed to reduce a normally incident beam of 1 MeV photons to one-tenth of the incident intensity? For water μx(1 MeV) = 0.07066 cm-1 and for lead μx(1 MeV) = 0.7721 cm-1 for water x1/10 = 32.59 cm, for lead x1/10 = 2.98 cm x1/2 = 0.898 cm x1/100 = 5.96 cm

Absorption of neutrons Elastic scattering • neutron collides with proton (e.g. hydrogen nucleus) and shares its kinetic energy • dominant process with fast neutrons of energy < 6 MeVin tissue

Absorption of neutrons Inelastic scattering • fast neutron (~ 6 MeV and above) interacts with nucleus and causes disintegration with the atomic nuclei

Neutrons lose very little energy per collision when they collide with heavy nuclei. Nuclei of hydrogen and neutrons have approximately the same mass. In collisions with hydrogen nuclei, neutrons can transfer almost all their kinetic energy to the hydrogen nuclei. Thus, hydrogen‑containing compounds such as H2O, paraffin wax, and hydrocarbons (oil and grease) slow down neutrons rapidly.

Thermal Neutrons Cross Sections Uranium for Fission Fuel in Nuclear Reactor 113Cd 233U 235U 238U  c /b 19,820 46 98 2.7 f /b 530 580 2.7×10-6 t1/2/y 1.6×105 7×108 4.5×109

Thermal Neutrons Cross Sections Cross section () a measure of reaction probabilityThermal neutron cross sections (c)Thermal neutron cross section for fission (f) 1H 2H 12C 14N 16O 113Cd  c /b 0.33 0.00052 0.0034 1.82 0.0002 19,820 Moderators: H2O vs. D2O vs. C

Thermal Neutrons Cross Sections The extremely large thermal neutron cross section of 113Cd makes cadmium a good neutron absorber or eliminator. Neutrons Capture Cross Sections of Cadmium Isotopes 106Cd 108Cd 110Cd 111Cd 112Cd 113Cd 114Cd  c / b 1 1 0.1 24 2.2 19,820 0.3 Abundance/% 1.25 0.89 12.45 12.80 24.13 12.22 28.37 the neutron-capture reaction 113Cd (n, ) 114Cd leads to a stable isotope. These properties made cadmium a very desirable material for the nuclear technology industry.

Conclusion:Slow neutrons (0.03 to 0.001 eV) are more effective for inducing fission of 235U Fast neutrons (10 MeV to 10 KeV) favours neutron capture reaction of 238U Light atoms are effective moderators

4) Interaction of Heavy Charged Particles with Matter Fast moving protons, 4He, and other nuclei are heavy charged particles. Coulomb force dominates charge interaction. They ionize and excite(give energy to) molecules on their path. The Born-Bethe Formula for Energy Loss of Charged Particles.

Range of Heavy Charged Particles in a Medium  source Shield Particles lose all their energy at a distance called range.

Scattering of Electrons in a Medium  source Shield Fast moving electrons are light charged particles. They travel at higher speed., but scattered easily by electrons.

Range of Light Charged Particles in a Medium Range of b particles is not as well defined as heavy charged particles, but measured range is still a useful piece of information.

Braking Radiation of b particles Influenced by Atom Bremsstrahlung (braking) radiation refers to photons emitted by moving electrons when they are influence by atoms.

Interaction of Beta particles with Matter Ionization Annihilation Braking radiation Beta particles interact with matter mainly via three modes: Ionization (scattering by electrons) Bremsstrahlung (braking) radiation Annihilation with positrons

Example : At what energy does an electron moving through gold lose as much energy by bremsstrahlung as it does by ionizing and exciting gold atoms? For gold Z = 79 and for equal energy loss by both mechanisms, we have find for electrons M = me that E = 700/79 = 8.9 MeV.

Stopping power (~dE/ds)/p in mass units (MeV cm2/g) for protons and electrons.

Range or path length pR, in mass units (g/cm2), in the continuous slowing down approximation.

αβγioization radiation αβγ ionizing process D D I track Straight Defle Straight ionization Large medium Small Penetration weak medium long 2 MeV range(m) ion pairs/mm α 0.01 6000 β 2-3 60 γ *10 ~1 air

能量损失

2.1 Two-body collisions Formula Tacit assumptions: Well defined Z1 Independent two body collisions Stochastic process, average E.L. 2.2 Collisions with atoms Elastic and inelastic energy loss 2.3 Adiabatic cutoff Momentum approximation free Harmonic model free bounded 2.4 Under which circumstances is classical mechanics applicable

两体碰撞 INCIDENT ION BEAM

入射粒子散射角：Φ（实验室系）和θ（质心系）入射粒子散射角：Φ（实验室系）和θ（质心系）靶粒子散射角：ψ（实验室系）入射粒子能量：靶粒子获得的能量：图1-1 粒子-粒子两体碰撞

速度矢量相加关系 是入射粒子速度是入射粒子速度是质心速度

靶粒子得到的能量 b: collision diameter Closest distance in repulsive potential

两体碰撞

2.2 Collisions with atomsElastic and inelastic energy loss Elastic moving the center of the mass of the atom-- nuclei Inelastic leading to excitation of internal degrees of freedom--electrons

e,m P Z v t 动量变化： electrons feels a constant force during collision time

Chapter 2. Radiation