Topic 3 
Review of Fundamentals
Interactions of Radiation With Matter



Outline
 Beta Radiation
 Rangeenergy relationship
 Mechanisms of Energy Loss
 Alpha Rays
 RangeEnergy Relationship
 Energy Transfer
 Gamma Rays
 Exponential Absorption
 Interaction Mechanisms
 Neutrons
 Production/Classification/Interaction
Beta Rays (Particles)
RangeEnergy Relationship
Curve of 210Bi 1.17 MeV beta particles with Al absorbers
Determination of range
 End point in absorption curve = range
 Rule of thumb:
 Absorber halfthickness = 1/8 range of beta
 Systematic experiments have established beta range as function of
material, energy:
Rangeenergy Curve for Beta Rays in Various Substances
RangeEnergy Observations
 Required absorber thickness increases with increasing energy (!!)
 Range is largely a function of electron density ( per cm2),
 To a lesser degree range is a function of Z
 Result has practical implications for shielding
 Atomic number neglected
 Areal density is used
Density thickness
 Areal density of electrons
 Proportional to product of absorber density and linear thickness:
*Units can differ from those shown, as long as they are internally consistent
Advantage of density thickness
Range Energy Curve for Beta Particles
Beta Range – Empirical Equations
 R = 412E^{1.265 – 0.0954 ln E}
 for 0.01 E
2.5 MeV
 ln E = 6.63 – 3.2376 (10.2146 – ln R)^{1/2}
 for R 1200
 R = 530 E – 106
 for E > 2.5 MeV, R > 1200
 where
 R = range, mg/cm^{2}
 E = maximum betaray energy, MeV
Beta Particles – Energy Loss Mechanisms
Ionization and Excitation
 Interaction between electric fields of beta and orbital electrons
 inelastic collisions
 energy loss by beta f(distance, KE)
 E_{k} = E_{t}  f
 E_{k} = kinetic energy of ejected electron
 E_{t} = energy lost by beta particle
 f ionization
potential of absorbing medium
 Ejected electron may produce additional ion pairs
(clusters, delta rays)
Ionization Potential vs Energy Expended
Average energy lost by a beta particle in the production of an ion pair
Gas

Ionization
Potential, eV

w, Mean energy expended per ion
Pair, eV

H_{2}

13.6

36.6

He

24.5

41.5

N_{2}

14.5

34.6

Air



33.7

CH_{4}

14.5

25.7

C_{2}H_{4}

12.2

26.3

Difference is attributed to electronic excitation
Linear Rate of Energy Loss by Beta Particle
 Called specific ionization
 Key
 Understanding biological impacts
 Detector design and response
 Number of ionpairs formed per unit distance traveled.
Specific Ionization
Relationship of beta particle energy to specific ionization of air
Specific Ionization (S.I.)
 Number of ionpairs created per specific distance traveled by the
beta particle
 Where
 dE/dx is the energy loss due to ionization and excitation
per cm traveled (eV/cm)
 W is the mean energy (eV) required to create an ion pair;
 High values for lowenergy betas
 Decreases rapidly as beta energy increases
 Broad minimum around 1 MeV,
 Slowly increases at energies above this point
Specific Ionization  Beta Energy Loss, MeV/cm
 Where
 q = charge on one electron
 N = number of absorber atoms per cm^{3}
 Z = atomic number of the absorber
 NZ = # of absorber electrons per cm^{3}
 E_{m} = energy equivalent of electron mass (0.511
MeV)
 E_{k} = kinetic energy of the beta particle, MeV
 b = v/c = speed of particle relative to c (light)
 I = mean ionization and excitation potential of absorbing
atoms, MeV
Mean Excitation Energies (I)
 Calculated for several elements from quantum principles
 Measured
 Approximate empirical formula:
 I ~ 19.0 eV for Z = 1
 I ~ 11.2 +11.7Z eV for 2 <=Z <= 13
 I ~ 52.8 +8.71Z eV for Z > 13
Mass Stopping Power
 Another way to express energy loss
 If density thickness is used instead of length, then:
 Where S is the Mass Stopping Power ,
 r is
the density of the absorber
Linear Energy Transfer
 Specific Ionization used to describe energy lost by
the radiation
 In radiobiology, focus is on linear rate of energy absorption in
the medium.
 This measure is Linear Energy Transfer
 dE_{l} is the average energy locally imparted to
absorbing medium by particle traversing dl
 "Locally Imparted" refers to either
 maximum distance from the track of the particle, or
 maximum value of discrete energy loss
 Either case, LET refers to energy imparted within a limited volume
of absorber
Energy Transferred vs Absorbed
 The initial b^{}(blue) is losing energy by creation of
ion pairs or delta rays. Not all its lost energy is localized.
 LET is energy deposited within the volume shown by the cylinder
Relative Mass Stopping Power
 Compares energy absorptive power of different media.
 Defined as:
 r_{m} is not a density
 Is relevant to dose measurements……
Bremsstrahlung
 Xrays emitted when highspeed charged particles are rapidly accelerated
 b passes close to nucleus and is deflected from path
 Heavy nuclei are more effective in causing deflections
 Single electron can emit Xray up to its own kinetic energy
 Monoergetic beam of electrons produces a continuous spectrum
Estimating Bremsstrahlung Production
 f_{ b} is
the fraction of incident beta energy converted into photons (Bremmstrahlung)
 Z = atomic number of the absorber
 E_{m} = maximum energy of the beta particle
Importance of Bremsstrahlung
 b particles
can excite and ionize atoms
 Also radiate energy via bremsstrahlung
 Relative contribution important only at high energies
 high energy photons can be created
 additional shielding problem from highenergy beta emitters
Stopping Power Stopping Power for Electrons in water in MeV cm^{2}/g
Radiative to Collisional Losses
Xray Production from Monoenergetic Electrons
 f_{e} is the fraction of energy in electron beam converted
into X –rays
 Z = atomic number of the absorber
 E_{m} = maximum energy of the beta particle
ALPHA RAYS (PARTICLES)
Alpha Particles
 Least penetrating of radiations
 in air, range ~ few cm
 in tissue, ~ microns (10^{4}cm)
 Range
 mean range
 extrapolated range
Alphaparticle Absorption Curve
Alpha Particles – Range
 Empirical equations for Alphas in air
 R = 0.56 E
 R in cm
 E in MeV, E< 4 MeV
 R = 1.24 E –2. 62
 E in MeV, 4 <E< 8 MeV
 For range in air at 0^{0} C and 760 mm pressure
 Empirical equations for Alphas in other media
 R_{m} = 0.56A^{1/3}R
 R_{m} is in mg/cm^{2}
 A = atomic mass number of the medium
 R = range of the alpha particle in air, cm
Alpha Particles, Energy Loss
 Only significant mechanism:
 interaction with electrons in absorbing medium
 at very slow speeds nuclear collisions can occur
 only small energy transfers occur at each interaction
 Result in excitation and ionization of absorber atoms
 On average, alpha loses 35 eV per ion pair
 Because of high charge and low velocity
 (due to mass) specific ionization is very high
 path is almost straight
 energy loss is essentially continuous
Comparison with e^{,+}
 Electrons and positrons
 lose energy almost continuously as they slow
 can lose large fraction of energy in single collision with
atomic electron (equal mass)
 large deflections
 frequently scattered through large angle deflections by nuclei
(result: bremsstrahlung)
 HCPs
Alpha vs Beta –particle tracks
Alpha Particle Bragg Peak
Alpha Particles, Energy Loss
 Where
 Z = atomic number of ionizing particle
 q = unit electrical charge. 1.6 x 10^{19}C
 zq = electrical charge on the ionizing particle
 M = rest mass of the ionizing particle, gms
 V = velocity of the ionizing particle, cm/s
 N = number of absorber atoms per cm^{3}
 Z = atomic number of the absorber
 NZ = # of absorber electrons per cm^{3}
 C= velocity of light, 3 x 10^{10}cm/s
 I = mean ionization and excitation potential of absorbing
atoms, for air= 1.38 x 10 ^{10}erg
Notes re energy transfer equation
 Previous equation appropriate for other heavy charged particles (HCPs)
 derived by Bethe from quantum mechanics
 various versions around
 logarithmic term leads to increase in stopping power at energies
 low energies, lhs of equation dominates
 Bragg peak consequence of ln term decreasing
GAMMA RAYS
Gamma Rays
 Key differences in charged and uncharged particle interactions
 photon electrically neutral
 does not steadily lose energy as it penetrates
 interaction is statistically governed by:
 probability described by coefficient
Photon Interactions
Nature of Photon Interactions
 Absorption with disappearance of photon
 Scatter
 direction change
 energy change
 no energy change
 Principal methods of energy deposition
 photoelectric
 Compton scattering
 pair production
 photonuclear reactions
Describing Photon Behavior
 Exponential Absorption Equation
I = I_{0}e^{mt}
 I_{0_} = photon intensity with no absorbers
 I = photons transmitted through absorber
 t = absorber thickness
 e = base of natural logarithm (~2.71828183…)
 m =
atteunation coeffcient (slope of absorption curve)
Determining Attenuation Coefficients
 Measurements taken under conditions of good geometry
 monoenergetic
 wellcollimated
 narrow beam
 Data plotted as semilog
 straight line
 slope is m
 intercept is I_{0}
Good Geometry Conditions
Attenuation of ^{137}Cs Gamma Rays under conditions of good geometry
Additional Considerations
 e^{}^{m}^{t}
 Exponential term – must be dimensionless,
 m and
t must have reciprocal dimensions
 m or m_{l}
 Linear attenuation coefficient
 Total attenuation coefficient
 m/r (mass attenuation coefficient)
 also identified as mm
 units g/cm^{2}
 paired with t expressed as density thickness
 Atomic attenuation coefficient, m_{a}
Linear, Mass, Electronic, and Atomic Attenuation Coefficients
r is the density; Ne is the number of electrons per g; Z = atomic number
of the material
Miscellaneous Relationships
 Number of atoms per g = N_{A}/A
 N_{A} = atoms per mol
 A = gms per mol
 Number of electrons per g = N_{A}Z/A = N_{e}
 Number of electrons per kg= 1000 N_{e}
Photon Interaction Mechanisms
 Photoelectric effect
 Scattering
 Pair (and triplet) production
 These 3 mechanisms result in electron emission from material
interacting with the photon
 Photonuclear reactions
 This mechanism initiates a nuclear reaction and results in emission
of other radiations
Summary of Photoelectric Effect
 Involves bound electrons
 Probability of ejection is greatest if photon has just enough energy
to knock electron from shell
 Cross section varies with photon energy, approximately 1/hn^{3}
Interaction Mechanism  Photoelectric Effect
Compton Scattering
 Elastic collision between photon & “free” e
 photon transfers some, not all, of its energy
 Scattered photon, and e, result
Probability of Compton interaction
 Decreases with increasing Z
 For lowZ elements, Compton interaction predominates
 every electron acts as a scattering center
 electron density is important
 scatter described wrt solid angle
 KleinNishina equation describes scattering coefficient
Compton relationships
 Energy of scattered photon
KleinNishina
 Scattering into differential solid angle dW at
angle q
 a defined as
 hn/m_{0}c^{2}
 or hn (expressed in MeV)/0.511
Summary for Pair Production
 Interaction between photon and nucleus
 Threshold is 1.02 MeV
 Increases rapidly above threshold
 Coefficient
 per atom varies ~Z^{2}
 per mass Z^{1}
 Energy transferred to KE_{particle} = hn1.022
 2 annihilation photons, each 0.511 MeV
Photonuclear Reactions
 Photodisintegration
 Nucleus captures photon, typically emits a neutron
 Generally requires high energy photons
 ~ 6 to 8 MeV common
 Exception: ^{9}Be(γ,n)^{8}Be 
threshold is 1.666 MeV
 Significant for electron accelerators
 Betatrons
 Synchrotrons
 Linear accelerators (common in hospitals)
Summary of Photon Interactions
Photon Interactions: Combined Effects
 Attenuation coefficients are probabilities of removal of photons
under good geometry considerations.
 Total attenuation is sum of interaction mechanisms. Principal
components are:
m_{t}= m_{pe} + m_{cs} + m_{pp}
where each has its own probability based on energy and absorbing material – does
not account for fraction carried away via annihilation
 m_{t} gives
fraction of energy of a beam removed per unit distance traveled
in absorber
Photon Interactions: Combined Effects
 Absorption coefficients considers only the fraction of beam energy
that is transferred to the absorber by:
 Photoelectron
 Compton electron
 Electron pair (from pair production)
 Doesn’t consider
 Scattered compton photon
 Annihilation radiation after pair production
 Absorption coefficients:
 _{e}= m_{pe} + m_{cs} + m_{pp}(hn 1.02)/ hn
Relative Importance of Reactions
Energy Transfer and Energy Absorption
 Photon interaction with absorber complex
 scattered photon
 kinetic energy of electron
 collisional losses
 brehmsstrahlung radiation
 Calculate
 E_{tr} average energy transferred
 E_{ab} average energy absorbed
 difference is bremsstrahlung
Summary
 Energy transfer from radiation field to absorbing medium is basis
of radiation effects
 Charged particles
 excite or ionize atoms
 Have definite range in matter
 exhibit Bragg peak
 Photon (x, gamma) differ qualitatively
 indierctly ionizing
 interact with atomic electrons (pe, scatter, pp)
 stochastic events
NEUTRONS
Neutrons
 No ‘natural’ neutron emitters
 Sources of neutrons
 Fission (reactors)
 Spontaneous nuclear fission:
 Photoneutron sources
 Other forms of nuclear bombardment
Fission
 ^{235}U, ^{233}U, Pu
 Neutron absorbed by fissionable nucleus
 Nucleus becomes ‘compound nucleus’
 Nucleus may then fission, or decay by other emission
^{235}Cf
 Emits alphas
 Also spontaneously fissions
 Neutrons emitted with fission
 10 fissions per 313 alpha emissions
 Most probable neutron energy is 1 MeV
 Average neutron energy is 2.3 MeV
 Half life (T_{1/2,sf}) = 2.65 years
 (both decay modes)
 T_{1/2,a}= 2.73 y
 What is T_{1/2,sf}?
Photoneutrons
 Photodisintegration
 photons break up nucleus
 protons, neutrons, and deuterons (a proton and neutron bound
together) are ejected.
 Photoneutrons:
 Photon incident on nucleus contains enough energy to overcome
binding energy of nucleons
 Neutron is emitted
 Photons (gamma rays) are monoenergetic
 Neutrons are monoenergetic
 Low binding energy target atoms used (Be)
 See Table 5.4 on page 151
Table 5.4 a,n Photoneutron Sources
Other Neutron Production Methods
 (a, n) : An alpha
particle is absorbed by a ^{9}Be nucelues
 ^{9}Be + ^{4}He > (^{13}C)^{*} > ^{12}C
+ ^{1}n
 Neutrons are poly energetic
 Alphas lose energy prior to reaching ^{9}Be
 Typically alpha emitter mixed in powder form with alpha source
Table 5.5 a,n Neutron Sources
Other Neutron Production Methods
 Accelerators may also be source of alphas
 Table 5.5 on page 152 has a list of typical a, n sources
 Typically favored over photoneutron sources since they have a significantly
longer half life
 Note that all neutrons are born ‘fast’
 What is a ‘fast’ neutron?
Classification
 Neutrons are classified according to their energy
 Neutron reactions are very dependant on energy
 Only two classifications important at this point
 Fast neutrons
 Generally greater than 0.1 MeV
 Thermal
 Have same KE as gas molecules in their environment:
MaxwellBoltzmann Energy Distribution  As Function of Temperature
Thermal Neutrons
 Also called ‘slow’ neutrons
 Defined more precisely than fast or other types of neutrons:
 At 293°K
 0.025 eV most probable energy
 2200 m/s most probable velocity
MaxwellBoltzmann distribution  gas molecules
Thermal Neutrons
 Calculating most probable energy
 Average Energy:
 Can E = 1/2 mv^{2} be used for neutrons?
 Gives velocity of thermal neutrons
Neutron Interaction
 All neutrons are born fast
 Lose energy by collisions with nuclei
 Collisions of fast neutrons are typically elastic
 With low Z absorbers
 "billiard ball" type of collision
 KE and momentum conserved
 Low probability for capture
 Thermal neutron collisions may result in elastic collisions or capture
 Elastic scattering and capture are most important for HP
 Capture of a neutron is typically followed by emission of a photon
or other particle from nucleus
 Neutrons are removed exponentially when a material is placed in
a neutron beam
Absorption
 Linear or mass attenuation coefficients are not typically used with
neutrons
 Microscopic cross section or macroscopic cross sections are normally
given for a material
 Microscopic cross section = s =
cm^{2} / atom
 Macroscopic cross section = S = s N
= cm^{1}
Cross Sections
 Absorption cross section may include activation cross section
 Absorption cross section does not include scattering cross section
 Total cross section is the sum of all cross sections, including
scattering, activation and other reactions
 All cross sections are VERY energy dependent
 Typically, only thermal neutron cross sections are listed
 Be very careful in using cross sections; Tables are not always clear
on how to use them properly
 Absorption cross sections are said to be about 1/3 of the total
cross section, but this is only a rough estimate
Removal of Neutrons
 Equation 5.43 is used with the absorption cross section to find
neutron removal from a beam of neutrons
 I = I_{0}e^{}^{sNt}
 I_{0} = initial neutron intensity
 I = final neutron intensity
 N = number atoms absorber per cm3
 t = thickness of material in cm
 s =
microscopic cross section for absorption in cm2/atom
 Note that if more than one method for removal is possible, it should
be included in the cross section
 Equation 5.43 can also be used to find activation quantities
1/v Law
 Although cross sections are temperature dependant, can ‘correct’ cross
sections for 0.001 to 1000 eV
 Use Equation 5.53 to find cross sections at different energies
 Note that there are some atoms that do not follow the 1/v law
 Called ‘not 1/v’ atoms
 Simply multiply by a factor to obtain the desired result
 Compilation of ‘not’ 1/v atoms in “Introduction
to Nuclear Engineering” by John Lamarsh, 2nd Ed. p. 63
Cross Section Notes
 The cross sections used in calculations should be for poly energetic
neutrons if reactor or (a, n) reaction
 Tables normally list cross sections for monoenergetic thermal neutrons
 Beware of extrapolating outside limits of 1/v (> 1000 eV)
 Beware of resonances and competing reactions
 Divide cross section by 1.128 to correct a monoenergetic neutron
beam cross section to a poly energetic beam cross section
 More detail on this in Chapter 12 later
 BNL is generally best source for cross sections
Neutron Absorption
 Neutron absorption may result in:
 Formation of a stable isotope of an atom and emission of a
photon
 Fission
 Emission of an alpha particle
 Activation of an atom
 Other, more exotic reactions
Activation
 When neutron absorption leads to too many neutrons
 Neutron is absorbed
 Gamma emitted (prompt)
 Atom is now radioactive
 Typically beta (negatron) emitter
 Sometimes alpha emitters formed
Activation
 Equation 5.58
 lN
= fsn (1  e^{}^{l}^{t})
 lN
= Activity in Bq
 f =
Flux, neutrons per cm^{2} per sec
 s =
Activation cross section, cm^{2}
 n = Number target atoms
 t = Time of irradiation
 l =
Decay constant, induced activity
Scattering
 Energy lost best through collisions with atoms of same mass as neutron
 "Billiard ball collisions"
 Scattering with ‘heavy’ atoms typically does not result
in much energy loss
 Measure of energy loss = average logarithmic energy decrement per
collision (See p. 155)
Neutron Energy Loss
 Scattering is how a neutron becomes thermal
 Hydrogen has the highest average logarithmic energy decrement per
collision (almost same mass as neutron)
 Median amount of energy transferred from neutron to hydrogen in
one collision is 63%
Neutron Life
 Fast Diffusion Length  average linear distance a fast neutron travels
 Thermal Diffusion length  average linear distance a thermal neutron
travels
 Note that actual neutron paths are very tortuous
 Diffusion lengths are only of concern when absorption cross section
is small
 Typically measured, many assumptions required for calculations
Summary
 Neutrons slowed down by scattering with light nuclei
 Absorption of neutrons more likely with thermal neutrons
 Activation is possible when neutron absorption occurs
 Exercise caution when using cross sections
