Ionizing Radiation

Ho Kyung Kimhokyung@pusan.ac.kr

Pusan National University

Radiation DosimetryAttix 1

References

F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry, Ch. 1, John Wiley and Sons, Inc., 1986

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Types and sources of ionizing radiations

Ionizing radiations

• Characterized by their ability to excite and ionize atoms of matter with which they interact• To ionize an atom (to cause a valence electron to escape), the energy of the order of 4 – 25 eV is

required• How about UV, optical lasers, and RF? Are they ionizing radiations?

𝛾𝛾-rays• Electromagnetic (EM) radiation emitted from a nucleus or in annihilation reactions between

matter and antimatter• Emitted by radioactive atoms

– 2.6 keV (𝐾𝐾𝛼𝛼 characteristic x-rays from electron capture (EC) in 1837Ar)

– 6.1 and 7.1-MeV 𝛾𝛾-rays from 716N

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X-rays• EM radiation emitted by charged particles (usually electrons) in changing atomic energy levels

(called characteristic or fluorescence x-rays) or in slowing down in a Coulomb force field (continuous or bremsstrahlung x-rays)

• An x-ray and a 𝛾𝛾-ray photon of a given quantum energy have identical properties, differing only in mode of origin

Fast electrons• Positrons if positive in charge• 𝛽𝛽-rays (positive or negative) when emitted from a nucleus• 𝛿𝛿-rays if resulted from a charged-particle collision• Continuous electron beams from Van de Graaff generators• Pulsed electron beams from linacs, betatrons and microtrons

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Heavy charged particles (HCPs)• Usually obtained from acceleration by a Coulomb force field in a Van de Graaff, cyclotron, or

heavy-particle linac• Alpha particles are also emitted by some radioactive nuclei

– Proton: the hydrogen nucleus– Deuteron: the deuterium nucleus, consisting of a proton & neutron bound together by nuclear force– Triton: a proton & two neutrons similarly bound– Alpha particle: the helium nucleus, i.e., two protons & two neutrons– Other HCPs: the nuclei of heavier atoms, either fully stripped of electrons or in any case having a different

number of electrons than necessary to produce a neutral atom– Pions: negative 𝜋𝜋-mesons produced by interaction of fast electrons or protons with target nuclei

Neutrons• Neutral particles obtained from nuclear reactions [e.g., (p, n) or fission]

– Cannot be accelerated electrostatistically

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ICRU

International Commission on Radiation Units and Measurements

1. Directly ionizing radiation: Fast charged particles, which deliver their energy to matter directly, through many small Coulomb-force interactions along the particle's track

2. Indirectly ionizing radiation: X- or 𝛾𝛾-ray photons or neutrons (i.e., uncharged particles), which first transfer their energy to charged particles in the matter through which they pass in a relatively few large interactions. The resulting fast charged particles then in turn deliver the energy to the matter as above (1)

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Radiation effects

The expenditure of a relatively trivial amount of energy (~4 J/kg) throughout the human body is likely to cause death, even though that amount of energy can only raise the gross temperature by about 0.001 ℃

The high local concentration of absorbed energy can kill a cell either directly or through the formation of highly reactive chemical species such as free radicals in the water medium

• A free radical is an atom or compound in which there is an unpaired electrons, such as H or CH3

Ionizing radiation can change, either desirable or deleterious, organic compounds by breaking molecular bonds, or crystalline materials by causing defects in the lattice structure

• Even structural steel can be damaged by large enough numbers of fast neutrons, suffering embrittlement and possible fracture under mechanical structure

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Course objectives

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Radiological physics

• Science of ionizing radiation and its interaction with matter, with special interest in (absorbed) energy since;

– x rays by Wilhelm Röntgen– radioactivity by Henri Becquerel– Radium by the Curies

Radiation dosimetry

• Quantitative determination of the energy deposition in matter

Radiation quantities

Exposure 𝑋𝑋• Related to the ability of photons to ionize air

Kerma 𝐾𝐾• Kinetic Energy Released by MAtter• Describing the first step in energy dissipation by indirectly ionizing radiation, that is, energy

transfer to charged particles (per unit mass of the absorber)

Absorbed dose 𝐷𝐷• Energy absorbed per unit mass of medium• Describing the energy imparted to matter by all kinds of ionizing radiations, but delivered by the

charged particles

Equivalent dose 𝐻𝐻• Dose multiplied by a radiation weighting factor

Activity 𝒜𝒜• The number of nuclear decays per time 9

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Quantity Definition SI unit Old unit Conversion

Exposure 𝑋𝑋 𝑋𝑋 =∆𝑄𝑄

∆𝑚𝑚𝑎𝑎𝑎𝑎𝑎𝑎2.58 × 10−4

Ckg air 1 R =

1 esucm3 air𝑆𝑆𝑆𝑆𝑆𝑆

1 R

= 2.58 × 10−4C

kg air

Kerma 𝐾𝐾 𝐾𝐾 =∆𝐸𝐸𝑡𝑡𝑎𝑎∆𝑚𝑚

1 Gy = 1J

kg

Dose 𝐷𝐷 𝐷𝐷 =∆𝐸𝐸𝑎𝑎𝑎𝑎∆𝑚𝑚

1 Gy = 1J

kg1 rad = 100

ergg 1 Gy = 1 rad

Equiv. dose 𝐻𝐻 𝐻𝐻 = 𝐷𝐷𝑤𝑤𝑅𝑅 1 Sv 1 rem 1 Sv = 100 rem

Activity 𝒜𝒜 = 𝜆𝜆𝑁𝑁 1 Bq = 1 s−1 1 Ci= 3.7 × 1010 s−1 1 Bq =

1 Ci3.7 × 1010

∆𝐸𝐸𝑡𝑡𝑎𝑎 is energy transferred from indirectly ionizing particles to charged particles in absorber

Description of ionizing radiation fields

Stochastic quantities

• Not be predicted• Discontinuous in space & time (no gradient & rate of changes)• Defined for finite domains• The probability of their values are determined by probability distributions• �𝑁𝑁 (mean of measured values 𝑁𝑁) → 𝑁𝑁𝑒𝑒 (expectation) as 𝑛𝑛 (observations) → ∞

Nonstochastic (or deterministic) quantities

• Can be predicted by calculation• Point functions for infinitesimal volumes• Continuous & differentiable functions of space (spatial gradient) & time (rate of change)

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12Attix Fig. 1.1

Fluence Φ = d𝑁𝑁d𝑎𝑎

[cm−2]

Flux density 𝜑𝜑 = dΦd𝑡𝑡

= dd𝑡𝑡

d𝑁𝑁d𝑎𝑎

[cm−2 s−1]

• Fluence rate

Note that Φ & 𝜑𝜑 express the sum of rays incident from all directions, and irrespective of their quantum or kinetic energies

Energy fluence Ψ = d𝑅𝑅d𝑎𝑎

[keV cm−2]• 𝑅𝑅 = 𝐸𝐸𝑁𝑁 for monoenergetic rays of energy 𝐸𝐸, thus Ψ = 𝐸𝐸Φ

Energy flux density 𝜓𝜓 = dΨd𝑡𝑡

= dd𝑡𝑡

d𝑅𝑅d𝑎𝑎

[erg cm−2 s−1]• Energy fluence rate• 𝜓𝜓 = 𝐸𝐸𝜑𝜑 for monoenergetic rays

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Differential description

Differential flux density 𝜑𝜑′(Ω,𝐸𝐸) [cm−2 s−1 sr−1 keV−1]

𝜑𝜑 = ∫Ω ∫𝐸𝐸 𝜑𝜑′ Ω,𝐸𝐸 dΩd𝐸𝐸 = ∫𝜃𝜃=0𝜋𝜋 ∫𝛽𝛽=0

2𝜋𝜋 ∫𝐸𝐸 𝜑𝜑′ 𝜃𝜃,𝛽𝛽,𝐸𝐸 sin𝜃𝜃 d𝜃𝜃d𝛽𝛽d𝐸𝐸

14Attix Fig. 1.2

polar angle

azimuthal angle

Energy spectrum• Quantities with 𝐸𝐸 as a variable

• e.g. 𝜑𝜑′(𝐸𝐸) = ∫𝜃𝜃=0𝜋𝜋 ∫𝛽𝛽=0

2𝜋𝜋 𝜑𝜑′ 𝜃𝜃,𝛽𝛽,𝐸𝐸 sin 𝜃𝜃 d𝜃𝜃d𝛽𝛽

15Attix Figs. 1.3a & b

The corresponding spectrum of energy flux density𝜓𝜓′ 𝐸𝐸 = 𝐸𝐸𝜑𝜑′(𝐸𝐸)

A "flat" spectrum of flux density 𝜑𝜑′(𝐸𝐸)

Angular distributions• Flux density per the polar angle

𝜑𝜑 𝜃𝜃1,𝜃𝜃2 = �𝜃𝜃1

𝜃𝜃2𝜑𝜑′ 𝜃𝜃 d𝜃𝜃 = �

𝜃𝜃1

𝜃𝜃2�𝛽𝛽=0

2𝜋𝜋�𝐸𝐸=0

𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚𝜑𝜑′ 𝜃𝜃,𝛽𝛽,𝐸𝐸 sin 𝜃𝜃 d𝜃𝜃d𝛽𝛽d𝐸𝐸

• Flux density per unit solid angle

𝜑𝜑′ 𝜃𝜃,𝛽𝛽 = �𝐸𝐸=0

𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚𝜑𝜑′ 𝜃𝜃,𝛽𝛽,𝐸𝐸 d𝐸𝐸

• For a symmetrical field about 𝑧𝑧 (or independent of 𝛽𝛽)

𝜑𝜑′ 𝜃𝜃 = 2𝜋𝜋 sin 𝜃𝜃 𝜑𝜑′ 𝜃𝜃,𝛽𝛽

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17Attix Fig. 1.4

Note the validated statement as follows:

• Chilton definition: "The fluence at a point 𝑃𝑃 is numerically equal to the expectation value of the sum of the particle track lengths (assumed to be straight) that occur in an infinitesimal volume d𝑉𝑉at 𝑃𝑃, divided by d𝑉𝑉"

• Used to the Monte Carlo methods

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Planar fluence

• The number of particles crossing a fixed plane in either direction (i.e., summed by scalar addition) per unit area of the plane

Net flow• The number of particles per unit time passing through unit area of the plane in one sense (i.e.,

summed by vector addition)• Also called the "planar flux density"• Not relevant to dosimetry

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20Attix Fig. 1.5

Fluence = planar fluencePlanar fluence

Planar fluence

Fluence = Planar fluence × cos𝜃𝜃 −1

Dose

1. Penetrated radiation through detectors– The energy imparted is proportional to the total track length of the rays crossing the detector, or to the

fluence– Dose both in the spherical and flat detectors placed below is increased by a factor of cos𝜃𝜃 −1

2. Stopped radiation within detectors– The energy deposited is related to the planar fluence– Dose only in the spherical detector placed below is increased by a factor of cos𝜃𝜃 −1

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Planar flux density through the x-y plane

𝜑𝜑𝑝𝑝 = �𝜃𝜃=0

𝜋𝜋�𝛽𝛽=0

2𝜋𝜋�𝐸𝐸=0

𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚𝜑𝜑′ 𝜃𝜃,𝛽𝛽,𝐸𝐸 cos𝜃𝜃 sin 𝜃𝜃 d𝜃𝜃d𝛽𝛽d𝐸𝐸

• For an isotropic field

𝜑𝜑𝑝𝑝𝜑𝜑

=∫𝜃𝜃=0𝜋𝜋 cos𝜃𝜃 sin 𝜃𝜃 d𝜃𝜃

∫𝜃𝜃=0𝜋𝜋 sin 𝜃𝜃 d𝜃𝜃

=12

Net flow through the x-y plane = 0

�𝜃𝜃=0

𝜋𝜋cos𝜃𝜃 sin 𝜃𝜃 d𝜃𝜃 = 0

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