Curs III Iris 2013 Eng

COURSE 3Interaction of Ionizing Radiations with Substance

Generation mechanisms of positrons

The positron is the electron’s antiparticle.

Positrons can result from:

(1) β+ disintegration of radioactive nuclides(2) electron-positron pair generation.

β+ disintegration is explained by the transform of a proton into aneutron,

(1)This process takes place only inside of the nucleus.

Oct. 14-th, 2013IIRS - Course 3

2

ep n e ν+→ + +

Generation mechanisms of positrons

The electron-positron pair generation process,(2)

can not take place in vacuum (the momentum conservation lawwould be violated).

The process occurs in the electrostatic field of a nucleus or of anatomic electron. The photon energy muss exceed a certainthreshold energy.

The threshold energy values range from1,022 MeV, when theprocess occurs in the field of a heavy particle (nucleus) and2,044 MeV when it occurs in the field of an atomic electron.

Positrons can exist only in motion (property of any antiparticle).Once at rest, they annihilate with the first electron it meets.


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( ) ( )N e e Nγ − ++ → + +

Generation mechanisms of neutrons


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Beside protons, neutrons are the nucleus constituents.Neutrons occurs in nuclear reactions of the following types: (p, n), (d,

n), (α, n), (γ, n) or after fission reactions.An important neutron source is the nuclear fission reactor.

Neutrons were discovered by Chadwick (1932) in the nuclearreaction

4 9 1 122 4 0 6Be n Cα + → +

Generation mechanism of protons and deuterons


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ProtonsProtons beams can be obtained by ionizing hydrogen atoms or by

nuclear reactions (particle, proton).Accelerators can be used for obtaining proton beams of high

energy.

DeuteronsDeuterons are the nuclei of deuterium atoms (one of the stable

isotopes of hydrogen);Deuterons are obtained in nuclear reactions and can be

accelerated to high energies by particle accelerators.

Generation mechanisms of alpha particles


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α radiations

- α particles (helium nuclei, helions).

- are obtained in nuclear reactions or emitted by radioactive nuclei,

with energies ranging to some MeV.

Alpha spectrum is discrete and usually has a fine structure.

For higher energies one may use particle accelerators (ciclotrons).

A A 4 4Z Z 2 2X Y α−

−→ +

Figure 3.1. Disintegration schema of Am-241

Radionuclides as sources of ionizing radiations


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At the beginning of the study of radiation emission phenomena (as associated with nuclei disintegrations) observations were made only on natural radionuclides.

The main part corresponds to elements a the end of the periodic table, with high atomic mass (A>92).

Some natural radionuclides have smaller mass (40K).

Physical properties of radioactive nuclides


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Unstable nuclides disintegrate, being called as "radionuclides".

Disintegration is spontaneous, the nucleus loses the mass/energy excess by emitting particles and/or photons.

The phenomena was discovered by Becquerel in February 1896. the term “radioactivity” was introduced by Marie Curie who

succeeded the separation of the first radioactive elements: polonium (Po) in 1898 and radium (Ra) in 1902.



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Rutherford and Soddy made the first experiments for determining the activity of a radioactive source (denoted by Λ).

The graphical representation of measurements made at equal time intervals led to the dependencies shown in figure 3.2.

The semi-logarithmic representation in figure 3.2.b shows that the decreasing of the source activity is exponential:

0( ) tt e λ− ⋅Λ = Λ



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Fig. 3.2 a Fig. 3.2.b

Properties of the disintegration process


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1. The disintegration process is statistical. Given an unstable nucleus, there is no way to establish the

time moment when it disintegrates. one may speak about the probability of disintegration in the time unit.

2. The disintegration of a nucleus from a source is independent of the other nuclei in the source.

Disintegration constant


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The second conclusion allows establishing a proportionality relation between the activity of the source (Λ) and the number of nuclei (N) from a source:

N0 represents the number of nuclei from the source at the initial time

N(t) represents the number of remaining nuclei after the time t.

The radioactive constant (λ) represents the probability of disintegration of a single unstable nucleus in the time unit.

0( ) tN t N e λ− ⋅=

0tdN

N e Ndt

λλ λ− ⋅= − ⋅ ⋅ = − ⋅

Activity of a source


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Given that the disintegration process of a nucleus is independent of its neighbors, the product λN represents the probability of disintegration of N nuclei in the time unit.

This is actually equal to the number of nuclei which disintegrate in the time unit, known as activity of the radiation source.

The activity of source (Λ) represents the number of nuclei form the source which disintegrate in the time unit.

The measurement unit in I.S. for the activity is called ”Becquerel” (Bq).

Half-time


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The half-life of a radionuclide is the time after which the number of radioactive nuclei from a source halved in the process of disintegration.

Since the activity of a source is proportional to the number of radioactive nuclei in the source, the relationship can write:

From this relationship it results that:

1/201/2 0( ) 2

TNN T N e λ−= =

1/2

1/2 0( ) TT e λ−Λ = Λ

1/2

1ln2·T

λ=

Natural radionuclides


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Natural radionuclides are radioactive nuclides naturally occurring on earth.

The Earth is about 1010 years, so any radionuclide created during the planet formation is found today only if its half-life time has the same order of magnitude.

Several dozen of these radionuclides have half-life T1/2 of the order of the estimated age of the earth, so that is supposed to be a so-called "dowry" primary.



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These radionuclides can be classified in two groups:

1. radionuclides from radioactive series

2. radionuclides which are not part of radioactive series; these nuclides disintegrate into a stable nuclide.

There are 3 natural radioactive series: thorium’s (Th), uranium’s (U) and actinium’s (Ac) series, and also an artificial series, the neptunium’s (Np).



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Radium (Ra) is part of the uranium series and is one of the radioactive elements which or firstly separated by Curie in the early twentieth century.

Since radium emits α and γ radiation, it has been used a long period as a source of radiations in various applications, including medical ones.

After World War II the scientific community realized the risks involved by the radiation exposure to radium sources and also its “toxicity” (one of its descendants is the radon, a radioactive noble gas).



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Another isotope of interest is 234Th, which can be chemically separated form the uranium series. This radionuclide has a half-time of 24 days and emits only βand γ low energy rays, being used in nuclear medicine.

Radioactive gases are also isotopes from radioactive series. The best known is radon, which has a radioactive isotope (222Rn) and three stable isotopes (219 Rn, 220 Rn, 221Rn). Isotope 222 Rn is produced by 226Ra decay, being part of the uranium series.

Natural radionuclides which are not part of radioactive series


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The most important isotopes in this category are 40K and 87Rb.

Radionuclide 40K is basically β active ( 87%) and γactive (10, 67%) it contributes both to external and internal irradiation of the

body (following intake). fond in nature as constant fraction (0,017%) of the natural

potassium.

Isotope 87Rb is pure β active. found in crystalline rocks, concentrations of about 0, 07Bq/g.

Cosmogenic radionuclides


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Cosmogenic radionuclides form at the interaction of high energy cosmic radiation with stable elements form the atmosphere and the surface of earth.

All the geosphere, atmosphere and parts of the earth which exchange matter with the atmosphere contain such radionuclides.

The production rate at the interaction with cosmic radiation with elements from the surface of the earth is small because the high energy particles are attenuated by the atmosphere.

The most important radionuclide is the carbon isotope with the atomic mass 14 (14C). Other isotopes which may occur are tritium (3H), 23Na or 7Be.

Artificial radionuclides


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are obtained by artificially produced nuclear reactions. are more often used in applications because they can

be 'manufactured' in order to satisfy certain requirements. can be obtained from virtually any element and in a pure

isotopic sate, that is to contain a single radioelement. there is possibility to choose between various half-times, specific activities

and chemical properties.

may be easily incorporated in various materials, including those used as biological or chemical tracers.

accidentally, it may be dispersed into atmosphere and contribute to the radiation background.

Artificial radionuclides


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Artificial radionuclides are created for their use in various applications in domains such as industry, medicine, agriculture etc.

In the case of medical applications, the radionuclides can be used as: Radioactive tracers (labeled chemical compounds) in nuclear

medicine (123I, 131I, 99mTc, 18F etc.) Implants in brachyterapy (192Ir, 198Au, 137Cs etc.) External radiation sources in external radiotherapy with γ

rays (137Cs, 60Co).

Artificial radionuclides used in nuclear medicine


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Iodine isotope with mass number123 (123I) is an gamma emitter, with energy of about 159KeV; it also emits X-rays and beta radiations.

The target organ is the thyroid.

Iodine 123 is obtained after bombarding a 123Xe target with protons accelerated in a cyclotron.

Having a short half-time (13h), 123I is preferred because the radiation dose received by the other organs of the patient is low.



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Iodine 131 (131I) was one of the first radionuclides used in medicine.

It is a fission product, obtained in the nuclear reactor.

Iodine 131 emits β and γ rays.

The target organ is thyroid.

With a half-time of about 8 days, it is used in treatment of thyroid cancer or other diseases of this gland.



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Technetium 99m (99mTc) is a gamma active isotope, with energy of 141KeV.

Target organ – thyroid and superior intestinal tract. It has a short half-time (6h), ensuring a small radiation dose at

the patient.

Another great advantage is the capacity of forming chemical compounds with tracers with will fix it in other target organs.

Technetium is obtained in a generator following the disintegration of 99mMb (T1/2 = 66h) from which is extracted as a saline solution before use.



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Fluorine 18 (18F) is a positron emitting isotope. It is obtained after bombarding a target containing 17O with

protons accelerated in a cyclotron. The half-time is very short (109 min) and is used in combination

with tracers which transport it to various target organs.

The positron annihilation is followed by the emission of two gamma rays in opposite directions, having 511MeV each. The detection of the gamma rays is used for superior imaging of organs, technique called Positron Emission Spectroscopy (PET).


Artificial radionuclides used in brachytherapy Iridium 192 (192Ir) is furnished as wires which are introduced

through catheters in the affected organ (containing tumors). 192Ir emits both γ and β radiations It is a product of the nuclear reactor.

It is the most used radioisotope in brachytherapy, because the beta radiation is rapidly absorbed in the vicinity of the source; the risk of irradiating the surrounding tissues is very low.

Iodine 125 (125I) is an isotope emitting low energy photons (27KeV). the emitted photons have lower penetration power than high energy

ones, therefore the risk of irradiating other organs is low.

It is a product of the nuclear reactor.

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Artificial nuclides used in teletherapy

The most used nuclide is the isotope 60 of Cobalt (60Co). It is obtained by irradiating the stable isotope 59Co with

neutrons. The obtained isotope is disintegrating in excited states of 60Ni,

following emission of two γ rays, with energies of 1,17Mev and 1,33 MeV.

The isotope is processed by specialized organizations and is placed into devices projected for medical purposes (radiotherapy or cobaltotherapy).

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Iradiation head of a teletherapy device

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Fig. 3.3

Radiation field. Radiometric quantities

Field of ionizing radiations (RF) ≡ a region in vacuum orin a substance which is crossed by radiationsgenerated by concentrated or distributed sources.

As any physical field, it is described by a series ofquantities (scalar or vectorial) which are dependingon the position (i.e. coordinates in a referencesystem) and time.


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Radiation field. Radiometric quantities

RF represents the agent (cause) of phenomena taking placein the irradiated substance.

RF has a quantified structure, consisting of: corpusclar particles (e-, e+, p, α, n, ions, etc.), quanta of the electromagnetic field (X or γ photons).

The quantum structure of the RF determines its statisticalbehavior at microscopic scale, resulting the need todescribe RF by stochastic quantities (i.e. quantities whichcan vary randomly from point to point).


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RF may be described by stochastic and nonstochastic quantities


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At macroscopic scale, RF may be described by nonstochastic quantities.

At microscopic scale, RF must be described by stochastic quantities.

Fig. 3.4.

Nonstochastic quantities

In the physics of ionizing radiations, the nonstochastic quantities are defined using the mean value of a fundamental stochastic quantity.

It is about the number of radiations N passing near the interest point P (through the volume dv) (Fig. 3. 5).

The mean value (for a very large number of measurements) is considered to be Ne – the expected value:


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N

( )lim enN N

→∞=

Nonstochastic quantities


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Fig. 3.5: The elementary volumecentered in the interest point Pused for defining the quantitiescharacterizing the radiation field(radiometric quantities).

Using a sphere gives theadvantage that the sametransversal surface (da) is crossedby all radiations, whatever theirdirection is.

Describing the radiation field by nonstochastic quantitiesThe RF model operates with average values. It may be

described by continuous functions depending on coordinates and time. For this purpose, the time intervals and spatial regions taken into consideration must fulfill two conditions: (1) They are large enough for determining that the statistical

fluctuations of RF quantities not to be predominant. (2) They are small enough so that the values of these quantities

to be determined (must be considered “punctual” and “instantaneous”).


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Describing the radiation field by nonstochastic quantities

A complete characterization of the RF must specify: The particles nature (photons, electrons etc.), The spatial distribution of particles, The energy of particles, The direction of propagation of particles.


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Radiometric quantities based on the number of particles Let Ne be the expected value of the number of radiations

passing through the sphere S centered in P in a time interval ∆t = t1 –t0.

(1) The flux of particles represents the number of particles entering the sphere S (of a volume dv) in the time unit:


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edNN

dt≡ 1

SIN s− =

Radiometric quantities based on the number of particles

Knowing one can calculate Ne. Therefore, from the definingrelation of the flux of particles it results .

If is constant, one obtains:

If is not constant in time, therefore

And one must know the function (variation in time of the fluxof particles).


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NedN Ndt=

( )1 0e edN N N dt N t t N t= = = − = ∆∫ ∫

( )eN N t dt= ∫

N

N

( )N t


(2) Fluence of particles ≡ number of particles traversing in thetime unit, from any direction, the sphere having the area of itsdiametrically section da, any particle having the trajectoryperpendicular to a diametrically section (see Fig. 3.5):

For a target with the area A and Φ = constant, Ne can becalculated as:


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edNda

Φ ≡ [ ] 2SI

m−Φ =

0

A

eN da A= Φ = Φ ⋅∫


(3) Fluence rate (or flux density)

Knowing the flux density of particles one can calculate theparticle fluence in a certain time interval Δt:


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e e edN dN dNd d ddt dt da da dt da

φ Φ ≡ = = =

[ ] 2 1SI

m sφ − −= ⋅

( ) ( )1

0

0 1,t

t

t t t dtφΦ = ∫

( ) ( )0 1 1 0,t t t t tφ φΦ = ⋅ − = ⋅ ∆

Radiometric quantities based on particles energy

Let E be the energy of a particle (for corpuscular radiations,only kinetic energy). The “e” index will not be used in thefollowing, but N still represents the expected value Ne.

The total radiant energy of the N particles is denoted by R.

(1) The energy flux is defined as:


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dRR

dt≡

SI

JR

s =


(2) Energy fluence is defined in a time interval ∆t as:

In the special case when all N particles have energy E, it

results

and


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dRda

Ψ ≡ [ ] 2SI

Jm

Ψ =

R E N= ⋅

( )d dNE N E E

da daΨ = ⋅ = ⋅ = ⋅ Φ


(3) Rate of energy fluence (density of energy flux)

By definition:

For “mono-energetic” radiations,


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d d dR d dR dRdt dt da da dt da

ψ Ψ = = = =

[ ] 2SI

Jm s

Ψ =⋅

( )d d dE E E

dt dt dtψ φΨ Φ

= = ⋅ Φ = = ⋅


(3) Rate of energy fluence (density of energy flux)

By integrating it results:

And for = constant, it results


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( )1

0

t

t

t dtψΨ = ∫

( )tψ

( )1 0t t tψ ψΨ = − = ⋅ ∆

Curs III Iris 2013 Eng

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