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Quantities for Describing Radiation Interactions Ho Kyung Kim [email protected] Pusan National University Radiation Dosimetry Attix 2
Quantities for Describing Radiation Interactions
Ho Kyung [email protected]
Pusan National University
Radiation DosimetryAttix 2
References
F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry, John Wiley and Sons, Inc., 1986
G. F. Knoll, Radiation Detection and Measurement, 4th ed., John Wiley and Sons, Inc., 2010
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Nonstochastic quantities for describing the interactions of the radiation field with matter (in terms of expectation values for the infinitesimal sphere at the point of interest)
1. Kerma πΎπΎβ The first step in energy dissipation by indirectly ionizing radiation (i.e., energy transfer to charged particles)
2. Absorbed dose π·π·β The energy imparted to matter by all kinds of ionization radiations, but delivered by the charged particles
3. Exposure ππβ X- & πΎπΎ-ray fields in terms of their ability to ionize air
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Kerma
Relevant only forβ’ Fields of indirectly ionizing radiations (e.g., photons or neutrons)β’ Any ionizing radiation source distributed within the absorbing medium
Energy transferred
πππ‘π‘π‘π‘ = (π π ππππ)π’π’β π π πππ’π’π‘π‘ π’π’πππππππ‘π‘ + οΏ½ππ
β πππ‘π‘π‘π‘ = energy transferred (stochastic quantity)β (π π ππππ)π’π’ = radiant energyβ of uncharged particles entering ππβ π π πππ’π’π‘π‘ π’π’
πππππππ‘π‘= radiant energy of uncharged particles leaving ππ, except that which originated from radiative lossesβ‘ of KE by charged particles while in ππ
β βππ = net energy derived from rest mass in ππβ’ positive when Ξππ β (ππ β πΈπΈ)β’ negative when Ξππ β (πΈπΈ β ππ)
4β‘ Conversion of charged-particle KE to photon energy through either bremsstrahlung or in-flight annihilation of positrons
β The energy of particles (excluding rest energy) emitted, transferred, or received
πΎπΎ β‘dπππ‘π‘π‘π‘dππ
β’ The expectation value of the energy transferred to charged particles per unit mass at a point of interest, including radiative-loss energy but excluding energy passed from one charged particle to another
β’ Simply, the KE received by charged particles in the specified finite volume ππβ’ The kerma for x- or πΎπΎ-rays consists of the energy transferred to electrons & positrons per unit
mass of mediumβ’ 1 Gy = 1 J/kg = 102 rad = 104 erg/g
For monoenergetic photons
πΎπΎ = Ξ¨πππ‘π‘π‘π‘ππ πΈπΈ,ππ
β πππ‘π‘π‘π‘ππ
= mass energy-transfer coefficient (depending on πΈπΈ & ππ)
β πππ‘π‘π‘π‘ = linear energy-transfer coefficient
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For spectral photons
πΎπΎ = οΏ½0
πΈπΈππππππΞ¨β²(πΈπΈ)
πππ‘π‘π‘π‘ππ πΈπΈ,ππ
dπΈπΈ
An average value of mass energy-transfer coefficient for the spectrum Ξ¨β²(πΈπΈ) is given by
πππ‘π‘π‘π‘ππ Ξ¨β² πΈπΈ ,ππ
=πΎπΎΞ¨
=β«0πΈπΈππππππ Ξ¨β²(πΈπΈ) πππ‘π‘π‘π‘
ππ πΈπΈ,ππdπΈπΈ
β«0πΈπΈππππππ Ξ¨β²(πΈπΈ) dπΈπΈ
Kerma rate
οΏ½ΜοΏ½πΎ =dπΎπΎdπ‘π‘
=ddπ‘π‘
dπππ‘π‘π‘π‘dππ
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Components of kermaπΎπΎ = πΎπΎππ + πΎπΎπ‘π‘
β πΎπΎππ = kerma due to collision interactions (local or nearby the charged-particle track)β’ Coulomb-force interactions with atomic electrons (ionization & excitation)
β πΎπΎπ‘π‘ = kerma due to radiative interactions (remote or far away from the charged-particle track)β’ radiative interactions with the Coulomb force field of atomic nucleiβ’ bremsstrahlung, in-flight annihilation
Net energy transferred
πππ‘π‘π‘π‘ππ = (π π ππππ)π’π’β π π πππ’π’π‘π‘ π’π’πππππππ‘π‘ β π π π’π’π‘π‘ + οΏ½ππ = πππ‘π‘π‘π‘ β π π π’π’π‘π‘
β π π π’π’π‘π‘ = radiant energy emitted as radiative losses by the charged particles (which themselves originated in ππ)
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Collision kerma
πΎπΎππ =dπππ‘π‘π‘π‘ππ
dππ
β’ The expectation value of the net energy transferred to charged particles per unit mass at a point of interest, excluding both radiative-loss energy and energy passed from one charged particle to another
Radiative kerma
πΎπΎπ‘π‘ =dπ π π’π’π‘π‘
dππ
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For monoenergetic photons
πΎπΎππ = Ξ¨ππππππππ πΈπΈ,ππ
β ππππππππ
= mass energy-absorption coefficient (depending on πΈπΈ & ππ)
β’ ππππππππβ πππ‘π‘π‘π‘
ππfor low ππ and πΈπΈ (where radiative losses are small)
β ππππππ = linear energy-absorption coefficient
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πΈπΈπΎπΎ (MeV)
πππ‘π‘π‘π‘ β πππππππππ‘π‘π‘π‘
Γ 100
ππ = 6 29 82
0.1 0 0 0
1 0 1.1 4.8
10 3.5 13.3 26
Absorbed dose
Relevant forβ’ All types of ionizing radiation fieldsβ’ Any ionizing radiation source distributed within the absorbing medium
Energy imparted
ππ = (π π ππππ)π’π’β π π πππ’π’π‘π‘ π’π’ + π π ππππ ππ β (π π πππ’π’π‘π‘)ππ+οΏ½ππ
β ππ = energy imparted (stochastic quantity)β π π πππ’π’π‘π‘ π’π’ = radiant energy of all the uncharged radiation leaving ππβ π π ππππ ππ = radiant energy of the charged particles entering ππβ π π πππ’π’π‘π‘ ππ = radiant energy of the charged particles leaving ππβ βππ = net energy derived from rest mass in ππ
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π·π· =dππdππ
β’ The expectation value of the energy imparted to matter per unit mass at a pointβ’ The same dimension & units with πΎπΎβ’ Simply, the energy per unit mass to produce any effects attributable to the radiation (the most
important quantity in radiological physics)β’ Impossible to write a relationship π·π· and Ξ¨ of indirect radiationβ’ 1 Gy = 1 J/kg = 102 rad = 104 erg/g
Absorbed dose rate
οΏ½ΜοΏ½π· =dπ·π·dπ‘π‘
=ddπ‘π‘
dππdππ
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Comparative example 1 of ππ, πππ‘π‘π‘π‘, & πππ‘π‘π‘π‘ππ
12Attix Fig. 2.1a
Ex
Comparative example 2 of ππ, πππ‘π‘π‘π‘, & πππ‘π‘π‘π‘ππ
13Attix Fig. 2.1b
Ex
Ex
If the positron in Attix Fig. 2.1b had been annihilated in flight when its remaining KE was ππ3 , what are the values of ππ, πππ‘π‘π‘π‘, & πππ‘π‘π‘π‘ππ ?
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Ex
Exposure
Nonstochastic quantity defined only for x-ray & πΎπΎ-ray photons
ππ =dππdππ
β The absolute value of the total charge dππ of the ions (of one sign) produced in air when all the electrons (negatrons & positrons) liberated by photons in air of mass dππ are completely stopped in air
β The ICRU says that "the ionization arising from the absorption of bremsstrahlung emitted by the electrons is not to be included in dππ"
β’ Also, the radiative losses through in-flight annihilation positronsβ Simply, the ionization equivalent of the πΎπΎππ in air for x- & πΎπΎ-rays
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W-value οΏ½ππ
β’ See Attix 12 for more detailsβ’ The mean energy expended in a gas per ion pair formed
οΏ½ππ =βππππ(1 β ππππ)βππππ(1 β ππππβ²)
β ππππ = initial KE of the ππth electron (or positron)β ππππ = fraction of ππππ that is spent by the particle in radiative interactions along its full path in airβ 1 β ππππ = fraction spent in collision interactionsβ ππππ = total number of ion pairs that are produced in air by the ππth electron of energy ππππβ ππππβ² = fraction of the ion pairs that are generated by the photons resulting from radiative loss interactionsβ 1 β ππππβ² = fraction of the ion pairs produced by collision interactions that occur along the particle track
β’ Not count the energy going into radiative losses, nor the ionization produced by the resulting photons
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All the KE spent by electrons in collision interactions
All the ion pairs produced in collision interactions by electrons
β’ eV/ion pairβ 33.97 eV/ip for x- & πΎπΎ-rays in air
β’οΏ½πππππππ‘π‘ππ
=33.97 eV
ip (or electron)
1.602Γ10β19 C/electronΓ 1.602 Γ 10β19 J
eV= 33.97 J
eV
β’ Constant values for each gas, independent of photon E, for x- & πΎπΎ-ray energies above a few keVβ’ Convenient for relating (πΎπΎππ)πππππ‘π‘ and ππ
Exposure rate
οΏ½ΜοΏ½π =dππdπ‘π‘
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ππ to Ξ¨β’ For monoenergetic photons
ππ = Ξ¨ππππππππ πΈπΈ,πππππ‘π‘
πποΏ½ππ πππππ‘π‘
= (πΎπΎππ)πππππ‘π‘πποΏ½ππ πππππ‘π‘
=(πΎπΎππ)πππππ‘π‘33.97
β 1 R = 1 esu0.001293 g
Γ 1 C2.998Γ109 esu
Γ 103 g1 kg
= 2.580 Γ 10β4 C/kg
β Conversion factorsβ’ ππ (in C/kg) = 2.58 Γ 10-4ππ (in R)β’ ππ (in R) = 3876 ππ (in C/kg)
β’ For spectral photons
ππ = οΏ½0
πΈπΈππππππΞ¨β²(πΈπΈ)
ππππππππ πΈπΈ,πππππ‘π‘
πποΏ½ππ πππππ‘π‘
dπΈπΈ βπποΏ½ππ πππππ‘π‘
οΏ½0
πΈπΈππππππΞ¨β²(πΈπΈ)
ππππππππ πΈπΈ,πππππ‘π‘
dπΈπΈ
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Significance of exposure
1. Ξ¨ is proportional to ππ for any given photon energy or spectrum2. The measurement of ππ may estimate the effects of x- or πΎπΎ-ray in tissue because air is an
approximately "tissue-equivalent" material (πππππππ‘π‘ β πππππ’π’ππππππππ)3. The value of πΎπΎππ in muscle, per unit ππ, is nearly independent of photon E4. One can characterize a photon field at a point
19Attix Figs. 2.2a & b
Other quantities for radiation protection
Quality factor ππβ’ Weighting factor to provide an estimate of the relative human hazard of different types &
energies of ionizing radiationsβ’ Dimensionlessβ’ Determined from the experimental relative biological effectiveness (RBE) & the unrestricted linear
energy transfer (πΏπΏβ) or the collision stopping power
20Attix Fig. 2.3
Dose equivalent π»π»π»π» β‘ π·π·ππ
β Defined at a point (i.e., a point quantity)β Sievert, 1 Sv = 1 J/kgβ 1 rem = 10-2 J/kg (equivalently to "rad")β Not strictly a physical quantity
Equivalent dose π»π»ππ,π π π»π»ππ,π π = π·π·ππ,π π π€π€π π
β Equivalent dose in an organ or in tissue ππ due to radiation π π β Not a point quantity but an average over a tissue or organβ π»π»ππ = βπ π π»π»ππ,π π = βπ π π·π·ππ,π π π€π€π π β Not a measurable quantity
Effective dose
πΈπΈ = οΏ½ππ
π»π»πππ€π€ππ
β Not a measurable quantity
21Knoll 2
