Report

NE 301 - Introduction to Nuclear Science Spring 2012 Classroom Session 8: •Radiation • • Interaction with Matter Non-Charged Radiation Mass Attenuation Tables and Use Absorbed Dose (D), Kerma (K) Gray (Gy) = 100 rad Dose Calculations •Analysis of Gamma Information (NAA) •Chemical Effects of Nuclear Reactions Reminder Load TurningPoint Reset slides Load List Homework #2 due February 9 Next Tuesday February 14 – 1st Demo Session MCA Gamma Spectroscopy identification of isotopes NAA of samples 2 Ionizing Radiation: Electromagnetic Spectrum Ionizing Radiation Ionizing Each radiation have a characteristic , i.e.: Infrared: Chemical bond vibrations (Raman, IR spectroscopy) Visible: external electron orbitals, plasmas, surface interactions UV: chemical bonds, fluorecense, organic compounds (conjugated bonds) X-rays: internal electron transitions (K-shell) Gamma-rays: nuclear transitions Neutrons (@ mK, can be used to test metal lattices for example) Radiation Interaction with Matter Five Basic Ways: 1. 2. 3. 4. 5. Ionization Kinetic energy transfer Molecular and atomic excitation Nuclear reactions Radiative processes 4 Radiation from Decay Processes Charged Directly ionizing (interaction with e-’s) β’s, α’s, p+’s, fission fragments, etc. Coulomb interaction – short range of travel Fast moving charged particles It can be completely stopped R Uncharged Indirectly ionizing (low prob. of interaction – more penetrating) , X-Rays, UV, neutrons No coulomb interaction – long range of travel Exponential shielding, it cannot be completely stopped 5 Neutral Interactions Stochastic (Probabilistic) With an electron or a nucleus Can be scattering – elastic or inelastic Can be absorptive It is still a collision: Flux of particles is important 6 Flux or Intensity Flux is usually for neutrons (n) Intensity is usually for photons (’s) Target Beam I n . v Density of particles in the beam Velocity of beam particles 7 Attenuation of Uncollided Radiation How do we calculate the change in the flux of (uncollided) particles as it moves through the slab? I0 I ( x) ( x) 0 x Uncollided radiation is a simplification. In reality not every collided photon/neutron is lost and there are buildup factors (Bi) Attenuation of Uncollided Radiation Beam with intensity I, interacting with shield (1-D) I0 I ( x) ( x) 0 x Change in Prod. (i.e. fission/multiplication) - Loss (collisions) Flux with x d 0 N dx d N dx integrating Ln N x c ( x) 0 e t calling (t=0)=0 and calling N t x 9 Microscopic and Macroscopic Cross Sections Sigma-N = Linear Attenuation Coefficient or Macroscopic Cross Section ( or ) i i N i Constant of Proportionality or Microscopic Cross-Section Na A Notice Different Units: is measured in cm-1 is measured in barns 1 barn = 10-24 cm2 10 A beam of neutrons is normally incident on a slab 20 cm thick. The intensity of neutrons transmitted through the slab without interactions is found to be 13% of the incident intensity. What is the total interaction coefficient t for the slab material? 93% t x ( x) 0e 7% 0% 10 cm -1 -1 m cm 1c -1 0% 0. 1 4. -1 3. cm 2. 0.01 cm-1 0.1 cm-1 1 cm-1 10 cm-1 0. 01 1. 11 Log[0.13] -1 t 0.102 cm 20 12 Attenuation of Uncollided Radiation Beams of particles: with intensity I0, interacting with shield (1-D) Point sources: Isotropic source emitting Sp particles per unit time I (r ) (r ) I0 I ( x) ( x) 0 A0 r e 4 r 2 r x I ( x) I 0e t x ( x) 0 e t x A0 r I (r ) (r ) e 2 4 r 13 Related Concepts Mean Free Path (mfp or x ): Average distance a particle travels before an interaction x= 1 t Half-thickness (x1/2) of the slab? Thickness of slab that will decrease uncollided flux by half x= Ln 2 t Similar concepts to mean-life and half-life 14 It is found that 35% of a beam of neutrons undergo collisions as they travel across a 50 cm slab. What is the mfp and x1/2 for the slab? 69 3c 10 00 an d 80 cm cm .. . 0% an d t 13 .8 x1/2 = Ln 2 0% 11 6 t an d I ( x) I0e t x 3% 20 x= 1 cm 4. 6. 9 3. an d 2. 10 and 6.9 cm 20 and 13.8 cm 116 and 80 cm 1000 and 693 cm 10 1. 97% 15 Clicker solution Log 0.65 In[6]:= Out[6]= 50 0.00861566 1 In[7]:= Out[7]= , Log 2 116.068, 80.452 16 Photon Interactions - tables Photon energies: 10 eV < E < 20 MeV IMPORTANT radiation shielding design For this energy range, 1. Photoelectric Effect 2. Pair Production 3. Compton Scattering 19 Pair Production Compton Scattering The Photoelectric Effect 20 Example: Photon Interactions for Pb Energy Low Photoelectric Effect Intermediate Compton Scattering High Pair Production : Gammas 22 Problem with Photons 100 mCi source of 38Cl is placed at the center of a tank of water 50 cm in diameter What is the uncollided -flux at the surface of the tank? Problem with Photons 100 mCi 38Cl, water tank 50 cm dia. What is the uncollided -flux at the surface of the tank? I (r ) (r ) Sp 4 r 2 e r r 25 26 Linear Coefficients – Macroscopic Cross Sections Linear Absorption Coefficient μt Linear Scattering Coefficient μs Macroscopic Fission Cross-section Σf, μf for neutrons t i s f etc i 27 Neutrons: 28 29 For homogeneous mixes of any type mix i i Valid for any cross section type (fission, total, etc) Valid for chemical compounds as well DO NOT add microscopic cross-sections 30 In natural uranium (=19.21 g/cm3), 0.720% of the atoms are 235U, 0.0055% are 234U, and the remainder 238U. From the data in Table C.1. What is the total linear interaction coefficient (macroscopic cross section) for a thermal neutron in natural uranium? t Nat U t 234 U .N 234 U t 235 U .N 235 U t 238 U .N 238 U atoms atoms 2.67 e 18 cm3 cm3 atoms atoms 0.0072 4.86e22 3.50 e 20 cm3 cm3 atoms atoms 0.992745 4.86e22 4.82 e 22 cm3 cm3 N ( 234U ) 0.000055 4.86e22 N ( 235U ) N ( 238U ) t Nat U t 234 U .N 234 U t 235 U .N 235 U t 238 U .N 238 U 0.24 cm-1 1024 cm 2 atoms 1024 cm 2 atoms t NatU 116 b 2.67e18 700 b 3.50 e 20 1b cm3 1b cm3 1024 cm 2 atoms 12.2 b 4.82 e 22 0.83 cm -1 -1 3 0.0003 cm 1b cm Who dominates? 238U: 0.59 cm-1 31 Absorbed Dose, D (Gray, rad) Energy absorbed per kilogram of matter (J/kg) Gray: 1 Gy = 1 J/kg The traditional unit: Rad: 100 rad = 1 Gy rad = Radiation Absorbed Man Dose rate = dose/time Dose = dose rate time Kerma (Approx. dose for neutrons) Kerma Kinetic Energy of Radiation absorbed per unit MAss For uncharged radiation Kerma is easier to calculate than dose for neutrons Kerma and Dose: same for low energy Kerma over-estimates dose at high energy No account for “Bremsstrahlung” radiation loses. Calculating Dose Rate and Kerma Rate D[Gy / s] 1.602 10 10 en ( E ) 2 2 1 E[ MeV ] [cm / g ] [cm s ] en(E)/ =mass interaction coefficient (table C3) E = particle energy [MeV] Notice Difference = flux [particles/cm2 s] K[Gy / s] 1.602 10 10 tr ( E ) 2 2 1 E[ MeV ] [ cm / g ] [ cm s ] tr(E)/ =mass interaction coefficient (table C3) E = particle energy [MeV] = flux [particles/cm2 s] Engineering Equations – PLEASE Watch out for units!