interaction of radiation with matter
DESCRIPTION
This lecture on interaction of radiation with matter has been given to teaching faculty and post graduate students.Some of the material has been downloaded from internet.TRANSCRIPT
Interaction of Radiation with Matter
K.L. Ramakumar
IndiaIndia
Presentation to College Students
KL RamakumarIndia
1
Presentation to College Students
Who has seen the wind?Neither I nor you.But when the leaves hang trembling,The wind is passing through.Who has seen the wind?Neither you nor INeither you nor I.But when the trees bow down their heads,The wind is passing by.
Christina Georgina RossettiHow do you define wind?
Air in motion is called wind
Who has seen the radiations?
Neither I nor you!
---------------------------------------
---------------------------------------
We will have the answer at the end of this presentation
KL RamakumarIndia
2
We will have the answer at the end of this presentation (hopefully!)
The term “radiation” in nuclear sciencerefers to all those particles/electromagnetic radiations emitted as aresult of nuclear reactions includingresult of nuclear reactions includingradioactive decay. These include charged,neutral, and electromagnetic radiations.
We will discuss interaction of radiationemitted from radioactive nuclei
KL RamakumarIndia
3
Interaction of Radiation with MatterInteraction: Process or phenomenon resulting
Radiation
Interaction: Process or phenomenon resulting when Radiation passes through Matter
Radiation
Corpuscular Electromagnetic
Charged Neutral
Li h H Li h HLight Heavy Light Heavy
e.g. electron e.g. proton e.g. neutrino e.g. neutron
KL RamakumarIndia
4
X-rays -raysMatter: Solid Liquid Gas
Why Interaction?Why Interaction?
What is the consequence?
Study of processes of interaction helps in id tif i th t f di ti it identifying the nature of radiation, its energy
Helps in deciding the shielding materials
Effectiveness of the medium
its response to the incident radiationits ability to absorb energy
KL RamakumarIndia
5
Rutherford's alpha scattering experiments During 1909Metal box was evacuated to minimize alpha loss by scattering from air molecules The source M t l bfrom air molecules. The source was 226Ra (to be precise, its decay product 222Rn) at R. Diaphragm placed at D acted as
Metal box
p g pcollimator to direct a beam of particles normally on to the scattering foil F.
Rutherford Gold foil experiment apparatus
By rotating the microscope [M] the alpha particles scattered in different directions could be observed on the screen S. (Possible with dark-adapted eyes.) Two days later there was real excitement.p y ) y
“We have been able to get some of the alpha-particles coming backward … (1 in 8000). It was quite the most incredible event that ever happened to me in my life It was almost as incredible as if you fired a
KL RamakumarIndia
6
happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
Back-scattered alphasBack scattered alphas
Appreciating “back scattering” of alpha particles in Rutherford Gold foil experiment
KL RamakumarIndia
7
p p
Why study interaction?Rutherford’s Gold foil experiment
Through interactions of Through interactions of particles with the matter in the gold foil, elucidation of atomic structure became possible
Alpha
Ernest Rutherford, first baron (1871 - 1937)Rutherford had established a new branch of physics called
Alpha particles
radioactivity. His work on radioactive decay won him the 1908 Nobel Prize in Chemistry.He also established the nuclear theory of the atom. In 1919, he announced his success in the artificially disintegration of
KL RamakumarIndia
8
he announced his success in the artificially disintegration of an atom.
We will understand Interaction of
particles
electronselectrons
rays
neutronsneutrons
fission fragments
in gaseous medium
KL RamakumarIndia
9
Example of particle interaction in gaseous medium
particle : Energy in MeV range
Massive alpha particles travel almost straight paths ( li ibl f i h lli i i h i
4 2+He
(negligible momentum transfer in each collision with tiny electron in the gaseous molecule)
Gaseous atoms along the path will get ionisedGaseous atoms along the path will get ionised
Energy of particle goes on reducing (ultimately it stops and gets neutralized becoming He atom)p g g )
Interactions of all types of radiations ultimately lead to production of ion lead to production of ion pairs through loss of energyIonisation of gaseous
KL RamakumarIndia
10
Particles MediumIonisation of gaseous species along the path
What happens during interaction of radiations?
Interaction results in
Dissociation of molecules of the mediumDissociation of molecules of the medium
Excitation and ionisation of molecules or atoms of the medium
Energy of the radiation is reduced
About 35 eV of energy is spent by the radiation to About 35 eV of energy is spent by the radiation to generate an ion pair in the medium.
Energy of particle No. ion pairs produced Energy of particle No. ion pairs produced 5 MeV
Energy required per ion pair is independent of energy
6 55x10 1.4x1035
KL RamakumarIndia
11
gy q p p p gyand type of radiation and also of the medium
Interaction of Charged Particles
Interactions with matter are due primarily to coulomb forcesto coulomb forces
The net outcome is the reduction inThe net outcome is the reduction inthe kinetic energy of theparticle/radiation during interactionultimately resulting in eithercomplete absorption of radiation orstopping of the particle and itsstopping of the particle and itscharge neutralization.
KL RamakumarIndia
12
Interaction processes : excitation,ionization, scattering and various types ofradiative losses of energy
On an average, approximately 34 electronlt f i l t f h i ivolts of energy is lost for each primary ion
pair formed in air. This is more or lessindependent of nature of charged particlep g p
Only about half to two-thirds of this energyis actually required to remove the orbitalelectron, the balance being lost inelectronic excitation processes
KL RamakumarIndia
13
Average energy lost by the incident radiation/particle Average energy lost by the incident radiation/particle in a gaseous medium
(W-value: eV/ion pair)(W value: eV/ion pair)
Medium Electron particleAr 27 0 25 9Ar 27.0 25.9He 32.5 31.7H2 38.0 37.02
N2 35.8 36.0O2 32.2 32.2Air 35.0 35.2CH4 30.2 29.0
KL RamakumarIndia
14
The mechanisms by which a charged particle losesit ki ti d fl t d f it i i l thits kinetic energy, or deflected from its original path,involve four principal types of interaction.
Inelastic Collision with Bound Atomic ElectronsInelastic Collision with Bound Atomic ElectronsPredominant mechanism by which a charged particleloses its kinetic energy in an absorber.As a result of each collision, one or more atomicAs a result of each collision, one or more atomicelectrons experience a transition to an excited state(excitation) or to an unbound state (ionization).
Inelastic Collision with a NucleusIn a close encounter with a nucleus, the incidentcharged particle experiences a deflection. In somesuch deflections, if the energy of the particle is nearthe relativistic range, a quantum of radiation(bremsstrahlung) is emitted, and a correspondingamount of kinetic energy is lost by the incident
KL RamakumarIndia
15
amount of kinetic energy is lost by the incidentparticle.
Elastic Collision with a NucleusIn elastic nuclear scattering the incident particle isdeflected but does not radiate, nor does it excite thenucleus. The incident particle loses only the kinetic
i d f ti f tenergy required for conservation of momentumbetween the two particles. Incident electrons have ahigh probability of experiencing nuclear elasticscatteringscattering.
Elastic Collision with Atomic ElectronsAn incident charged particle may be elasticallyAn incident charged particle may be elasticallydeflected in the field of atomic electrons of an atom.Energy and momentum are conserved, and theenergy transfer is less than the lowest excitationgypotential of the electrons, so that the interaction isreally with the atom as a whole. Such interactionsare significant only for the case of very low energy
KL RamakumarIndia
16
(<100 eV) incident electron.
It should be clearly understood that in an absorbingmaterial, a moving charged particle is slowed downmaterial, a moving charged particle is slowed downand finally brought to rest by the combined action ofall four of these elastic and inelastic processes.
Which type of interaction, if any, will occur when acharged particle passes a particular atom isdescribed only by the laws of chance/probability.
The statistical average of the effect of all thecollisions is what is obtained by direct experimentand is more convenience to interpret the grossand is more convenience to interpret the grossresults.
KL RamakumarIndia
17
Interaction of Heavy Charged Particles (e.g. AlphaParticles) with Matter
Less complicated than the interaction of light charged particles e g electrons particles e.g. electrons.
Elastic nuclear scattering and bremsstrahlung are generally negligible. g y g g
Alpha collisions may result in energy transfer by (1) ionization and/or (2) excitation.
Finite amount of energy is required to ionize or excite an atom
Kinetic energy of the alpha particle is gradually dissipated by such interactions until it captures two electrons and settles down to a quiet existence as a
KL RamakumarIndia
18
helium atom.
Important parameters in interaction of radiation with matter
S Stopping power of the mediumSpecific ionisation in the mediumSpecific ionisation in the mediumRate of energy loss in the medium
S = Energy loss/unit lengthdEdx
S (charge)2 of the ion velocity of the ion =
21v 2
1v
1E
N Number density of the medium Z Z Atomic number of the medium
2v 2v E
KL RamakumarIndia
19
Z Z Atomic number of the medium
Bethe’s expression for energy loss (stopping power) i i B is given By
24 2 02m vdE 4πe zS = = NZ ln 02
0S = = NZ ln Idx m v
where I geometric mean of all ionization and excitation potentials of the absorbing atom. When the velocity of the incident particles is in the y prelativistic range (V = c, c is the velocity of light), Bethe’s formula becomes
24 2 2 20
20
2m vdE 4πe zS = = NZ ln ln(1 )Idx m v
KL RamakumarIndia
20
0
Expression for the stopping power of a mediumExpression for the stopping power of a medium
24 2 02
0
2m vdE 4πe zS = = NZ ln Idx m v
Hans Bethe (1906 - 2005)
H h d h h f f h h l d
0
Hans Bethe served as the chief of the theoretical divisionfor the Manhattan Project. At the end of the SecondWorld War, Bethe, along with Edward Teller, worked onthe development of the hydrogen bombthe development of the hydrogen bomb.In 1967 he was awarded the Nobel Prize for Physics forresearch in the nuclear reactions in stars.
KL RamakumarIndia
21
Usefulness of stopping power equationd d2
2dE dE 1 1- α z - α =dx dx v E
F th l it d h f th For the same velocity and charge of the incident radiation, stopping power is same1H+ 2H+ 3H+ Same charge (z = 1)H H H Same charge (z = 1)
If velocity is also same, then is samedEdx
Alpha particle (He2+), charge z = 2 Proton (H+) z = 1
If velocities of alpha and proton are same then
dE dE dE = (22) = 42dE- α zdx
HαdE dE- -dx dx
4
Alphas lose energy 4 times faster than protons if
KL RamakumarIndia
22
Alphas lose energy 4 times faster than protons if both have same velocity
Usefulness of stopping power equation
22
dE dE 1 1- α z - α =dx dx v E
Combining both
22
2vdE z dE- α - α z2v
v- α - α zdx dx
.
Multiplying both sides by ½ mMultiplying both sides by ½ m
2 21 1m m
2 2vdE- α z
dx. is kinetic energy E21
m2
v2 2dx
21E m
2dE- α zdx
.
2
Particle identifier telescope principle
KL RamakumarIndia
23
2dx p p p
Particle identifier detectors
R di ti Radiation source
TransmissionTotal absorptiondetectordEDetector to measure dE-
dxTotal energy (E) is obtained from sum of the Total energy (E) is obtained from sum of the signals from the two detectors
Can be calculated from the signal obtained dE-d in the transmission detectordx
21E m
dE- α zd
. Particle can be identified
KL RamakumarIndia
24
2dx
Particle identifier detectors
21E m
2dE- α zdx
. 2E
mdE-2 αdx z
.
For the same energy and charge on the ion, the stopping power is proportional to mass of the stopping power is proportional to mass of the incident particle
N
14in aluminium
. MeV.cm / mg
22 49OO
15
16
in aluminium
absorber
g. MeV.cm / mg. MeV.cm / mg
2
23 323 46
80 MeV
Using particle identifier detectors
Isotopes identified up to z < 10
KL RamakumarIndia
25
Elements identified up to z < 50
Range
Inversely related to the stopping power of theabsorber is the range (R) of the charged particle.
The concept of range only has meaning for chargedparticles whose energy is kinetic energy which is lostcontinuously along their path.continuously along their path.
The range of a charged particle in an absorber is theaverage depth of penetration of the charged particleg p p g pinto the absorber before it loses all its kinetic energyand stops.
If a particle has a high range, the absorber has a lowstopping power. If the particle has a short range, theabsorber has a high stopping power.
KL RamakumarIndia
26
Range of alpha particles in a medium
After the complete loss of energy in the medium, the charged particle picks up electrons and gets neutralised
The distance travelled in the medium up to the stopping is called range extrapolated
range Res
Mean range
range Re
. p
art
icle
Alpha particles are monoenergetic ionsDistance
No
.Alpha particles are monoenergetic ions
Collisions in the medium and rate of energy transfer are purely statistical
KL RamakumarIndia
27
Distribution of ranges occur - Straggling
Bragg curve for t f lrate of energy loss.
Bethe’s expression for Bethe s expression for energy loss
24 2 02m vdE 4πe z N l
It can be seen from the above expression that the stopping
4 2 02
0
2m vdE 4πe zS = = NZ ln Idx m vIt can be seen from the above expression that the stoppingpower is greatest for high-density, high-Z materials, and forions in higher charge states. Shown above is a sketch ofBragg Curve for the rate of energy loss. As the chargedgg gy gparticle losses its energy, the stopping power increases. Atthe end of its path, the stopping power is the highest. Thus,along the path, the ion-pair density is the highest at the
KL RamakumarIndia
28
path end.
6600 ion pairs/mmp
2759 ion pairs/mm
proton
Residual range, cm air 03
Relative ionisation due to charged particles
KL RamakumarIndia
29
g p
Sir William Henry Bragg OM KBE (2 July 1862 – 10 March 1942)Sir William Henry Bragg OM, KBE (2 July 1862 10 March 1942)was a British physicist and chemist who uniquely shared the NobelPrize in Physics with his son, William Lawrence Bragg, in 1915 for x-ray diffraction phenomenon.
Prior to this he was also involved in the study of energy loss ofionising radiation. The Bragg curve plots the energy loss of ionizingradiation during its travel through matter. For protons, α-rays, andg g p , y ,other , there is a pronounced peak in the curve immediately before theparticles come to rest. This is called Bragg peak, for William HenryBragg who discovered it in 1903.
Sir William Sir William Henry Bragg 1862 - 1942
KL RamakumarIndia
30
For a given energy E of the charged particle, rangeb dcan be expressed as
22
ER amz
a is a constant depends on the mediumm and z are mass and charge of the charged particle.
Range is usually expressed in centimeters or cm x density = g.cm-2.
In air, for example, the range (Ra) is empirically given as
R 0 318 E3/2Ra = 0.318 E3/2
at 1 atmosphere and 150C and E = Energy in MeV.
KL RamakumarIndia
31
p gy
KL RamakumarIndia
32
Interaction of Light Charged P ti l ( El t )
End of path
Particles (e.g. Electrons) with Matter
Mass of an electron or beta Mass of an electron or beta particle is about 1/1800 that of a proton.
Absorber
Incidentelectron
Particles with mass comparable to those of electrons arelight charged particles Newtonian physics applied to
R
light charged particles. Newtonian physics applied toestimate the velocity of high-energy electrons givesvelocities larger than that of light, the limiting speed. Thus,Einstein’s theory of relativity must be applied A simpleEinstein s theory of relativity must be applied. A simplemethod in agreement with the theory of relativity is toconsider the relative mass as the sum of rest mass andkinetic energy, (0.51 + Ek) MeV,m = (0.51 + Ek) MeV. The
KL RamakumarIndia
33
gy, ( ) , ( )velocity of the electron is then v = (1 - 0.51/m)1/2c.
For a given kinetic energy, the velocity of an electron will be l t 2000 ti th t f t d b t 8000 ti almost 2000 times that of a proton and about 8000 times
that of an alpha particle. For non-relativistic velocities of electrons, Bethe’s formula for energy loss for electrons is given bygiven by
24 2 02
0
m vdE 4πe zS = = NZ lndx m v 2I
Rate of energy loss or specific ionization caused by the passage of electrons in a medium is therefore substantially less The number of ion pairs produced per unit distance
0
less. The number of ion pairs produced per unit distance traveled is also less.There is another important consideration. The mass of the electron is same as that of the atomic electrons in the electron is same as that of the atomic electrons in the medium. Further unlike the mono-energetic nature of alpha particles being emitted from a source, the energy spectrum of beta particles is continuous with a maximum limiting
KL RamakumarIndia
34
p gvalue.
Hence, the interaction of electrons in a medium is characterised by characterised by
(1) non-linear or tortuous paths unlike in the case of alpha particles, particles, (2) Larger deviations from the path, (3) Larger fraction of energy transfer per interaction, (4) sever straggling, ( ) gg g(5) enormous scattering, and (6) even back scattering from the incident surface of the medium.
Because of these larger deviations and larger scattering the ranges for beta particles are poorly defined due to enormous range straggling low intensities for a given enormous range straggling, low intensities for a given thickness in the medium.
KL RamakumarIndia
35
Path length = S
(Entry to end of Path)(Entry to end of Path)
Range = R Linear distance
Path length > RangePath length > Range
KL RamakumarIndia
36
M h i f I t ti B t El tMechanisms of Interaction Between Electronsand Matter
Ionization, bremsstrahlung radiation, and annihilation with positrons are the three mechanisms by which electrons lose energy in a medium.energy in a medium.
Coulomb interactions between fast moving electrons and molecular electrons excite and ionize the molecule, ,producing ion pairs like in the case of heavy charged particles. In the case of positrons, the annihilation with electrons is another mechanism of interaction which results in conversion of the total mass of the electron positron pair into energy in the form of photons.
KL RamakumarIndia
37
BremsstrahlungWhen a fast-moving electron is accelerated ordecelerated when passing through the field ofatomic nuclei, a photon is emitted, and suchphotons are called bremsstrahlung radiation.
Acceleration produced by a nucleus of charge Zeand mass M on a particle of charge ze and mass mp gis proportional to MZze2/m.
Intensity is proportional to (acceleration)2 x (ze)2 =(MZze2/m)2 x (ze)2 = M2Z2z4e6/m2(MZze /m) x (ze) M Z z e /m
2 2 4 62
M Z z eBremsstrahlung intensitym
Energy emitted by an accelerated particle is proportional to 1/m2. Bremsstrahlung is therefore significant for light particles such
KL RamakumarIndia
38
g g pas electrons.
Energy loss in electron interaction
Total energy loss in the case of electron interactionin the medium mainly consists of two componentscoulombic and radiative due to bremsstrahlung:coulombic and radiative due to bremsstrahlung:
dE dE dEdx dx dx
In any medium, it can be assumed
c rdx dx dx
(dE/dx) EZ
E is in MeV and Z is the atomic number of the
r
c
(dE/dx) EZ800(dE/dx)
medium. Radiative losses are more for a given energy of an electron in high Z elements (e.g. lead) than in low Z elements (e.g. Al). For attenuation of electrons therefore lead is not suitable
KL RamakumarIndia
39
electrons therefore lead is not suitable.
Bremsstrahlung radiationBremsstrahlung radiationBremsstrahlung radiation is a German word for breaking radiation. Inthe vicinity of an electric field being generated by the atomic nuclei, theacceleration of passing electrons changes substantially, which results inf p g g y,change in the kinetic energy of the electrons. This change (break) inkinetic energy is manifested as electromagnetic radiation calledBremsstrahlung radiation.
Synchrotron radiationIf the change in the acceleration of electrons is due to the presence of
f ld h l l d d Thmagnetic field, then also electromagnetic radiation is emitted. This iscalled synchrotron radiation.
KL RamakumarIndia
40
Bremsstrahlung radiation and discovery of μ meson
μ meson owes its discovery due to clear understanding of Bremsstrahlungradiation observed in cosmic ray interactions. As mentioned, totalBremsstrahlung intensity varies inversely as the square of the mass of thei id i l H i i l h f h l li iblincident particle. Heavier particles therefore show almost negligibleBremsstrahlung. The μ meson was at first thought to be an electron in cosmicrays. But the radiative losses of its energy were far too small for an electron.Subsequently μ meson was found to have a rest mass about 207m ThisSubsequently μ meson was found to have a rest mass about 207m0. Thiswould mean its radiative losses are about 40,000 times smaller than the lossesof an electron of the same velocity. This was indeed the case.
KL RamakumarIndia
41
Range-Energy Relations for Mono-energeticElectronsElectrons
Exact calculation of the range of electrons is not possibledue to multiple scattering. Straggling is predominant in thedue to multiple scattering. Straggling is predominant in thecase of electrons due to very low mass as shown in Fig. 5.Important observations are:1. Final portion of the curve is because of stragglingp gg g2. Transmission dose not become zero due to rays3. Shape of the curve depends on the experimental arrangement
Concave shape toward the origin results if (1) detection isby electron counting, (2) low-Z elements are used asabsorbers, and (3) collimating slit system allows electrons, ( ) g ywhich have been deflected by 30o or less to be counted
Convex shape toward the origin results if (1) detection is by an ionization chamber (2) high-Z elements are used as
KL RamakumarIndia
42
an ionization chamber, (2) high Z elements are used as absorbers, and (3) narrow collimation is employed.
Transmission curve for Absorption of electronsa s ss o cu e o bso pt o o e ect o selectrons of continuous energy
KL RamakumarIndia
43
Unlike in the case of heavy charged particles, thedetermination of Rm for particles is not easy. Feather’sdetermination of Rm for particles is not easy. Feather smethod of evaluating the maximum range for particles iswidely used. This can easily be adopted for laboratoryexperiments.
KL RamakumarIndia
44
See the next slide for explanation
Feather’s method for evaluating the maximum range Rm of rays-rays
In this method, one compares the absorption curve whoseend point Rm is to be determined with that of a well-mestablished standard (Bi-210 or better P-32). The twocurves are normalized to the same initial value on a plot oflogarithmic transmission against absorber thickness. Therange of the standard curve is divided into N equal partsrange of the standard curve is divided into N equal parts.These parts are designated as Rn
s and the end point whichhas been well established is marked Rm
0. The fractionaltransmission corresponding to these absorber thicknessesis marked on the standard curve. Points corresponding tothe same relative transmission are now marked on theunknown curve. The absorber thickness corresponding tothese transmission values is now marked on the scale ofthese transmission values is now marked on the scale ofabsorber thickness for the unknown and is designated asRn
u .A graph of (N/n) Rnx as a function of n is plotted and
the extrapolated intercept of the curve with n = N axisi R
KL RamakumarIndia
45
gives Rm.
Interaction of Electromagnetic radiations withMatterMatter
Gamma or X-rays do not carry an electric charge andpass through a large number of atoms without anyinteraction taking place.
Kinds of interaction Types of interaction
Interaction with atomic C l b i1 Interaction with atomic electrons A Complete absorption
2 Interaction with nucleons B Elastic scattering (coherent)(coherent)
3Interaction with the electric field surrounding the nuclei or electrons
C Inelastic scattering (incoherent)or electrons ( )
4 Interaction with the meson field surrounding nucleons
KL RamakumarIndia
46
Thus there are 12 different processes by which rays caninteract with matter. But there are only three majorprocesses on interaction (see previous slide). These are thephotoelectric effect (1A), the Compton effect (1C), and pair
d ti (3A)production (3A).
Photoelectric Effect (Photoelectric absorption)
In this interaction the energy of the x-ray or gamma rayis completely transferred to an atomic electron which isejected from its atom The x ray or gamma ray no longerejected from its atom. The x-ray or gamma-ray no longerexists after the collision. The process of photoelectricabsorption.
E
e-
KL RamakumarIndia
47
The process of photoelectric absorption
Photoelectric absorption
Incident photon is completely absorbed by an atom inthe absorber material, and one of the atomic electrons isejected. This ejected electron is known as a photoelectron.ejected. This ejected electron is known as a photoelectron.
The electron must be bound to the atom, to conserveenergy and momentum. The kinetic energy of thephotoelectron is given byp g y
Te = E - Be
where Be is the binding energy of the atomic electron.
The vacancy left in the atomic structure by the ejectedelectron is filled by one of the electrons from a higher shell.y gThis transition is accompanied by an emission of an X-ray.These X-rays are also absorbed by the detector
KL RamakumarIndia
48
Photoelectric absorption
Photoelectric absorption is the most favourable processfor the -ray spectroscopist, since the incident photondeposits all of its energy into the detector but it is onlydeposits all of its energy into the detector, but it is onlydominant for low energy photons (≤ 200 keV). Theinteraction is again dependent upon Z, and anapproximate expression for the absorption probability ()approximate expression for the absorption probability ()is
n3.5Z
E
Here n is normally between 4 and 5 depending on theabsorber material. This dependence on Z explains the
choice of high-Z materials such as lead for shieldingpurposes.
KL RamakumarIndia
49
Compton Effect (Compton scattering)
The x-ray or gamma-ray loses only part of its energy in itsinteraction with an atomic electron. The electron is ejectedfrom its atom. The x-ray or gamma-ray of reduced energyand the electron fly off in different directionsand the electron fly off in different directions.
ĒE
The process of Compton scattering
An incident ray scatters from an outer shell electron inthe absorber material at an angle , and some of the rayenergy is imparted to the electron Conservation of energy
p p g
energy is imparted to the electron. Conservation of energyand momentum leads us to the following expression for theenergy of the scattered photon:
_ EE
KL RamakumarIndia
50
20
EE
1 (E /m c )(1 cos )
Compton started a study of X-ray scattering. This led, in 1922, tohis discovery of the increase of wavelength of X-rays due to
i f h i id di i b f l hi hscattering of the incident radiation by free electrons, whichimplies that the scattered quanta have less energy than thequanta of the original beam. This effect, nowadays known as theCompton effect clearly illustrates the particle concept ofCompton effect clearly illustrates the particle concept ofelectromagnetic radiation., For this discovery, Compton wasawarded the Nobel Prize in Physics for 1927 (sharing this withC. T. R. Wilson who received the Prize for his discovery of theArthur Holly
C t C. T. R. Wilson who received the Prize for his discovery of thecloud chamber method).
Compton (1892 - 1962)
KL RamakumarIndia
51
Compton scattering
The kinetic energy of the electron after the collision isgiven by
E (1 cos )T E E
•All scattering angles are possible.
e 20
E (1 cos )T E E
m c E (1 cos )
g g p•Scattered electron energy ranges from zero for = 00 to2Ē /(m0c2
+ 2E) for = 1800
•The photon never loses the whole of its energy in any onellcollision.
The scattered photon can then continue through theabsorber and interact again or scatter out of the absorberabsorber and interact again or scatter out of the absorbermaterial completely. This process, where the scatteredphoton escapes, is very important for the -rayspectroscopist
KL RamakumarIndia
52
spectroscopist
Compton scattering
If the full energy of the incident photon is notabsorbed in the detector, then there is a continuousb k d i th t k thbackground in the energy spectrum, known as theCompton continuum. This continuum extends up toan energy corresponding to the maximum energytransfer where there is a sharp cut off point knowntransfer, where there is a sharp cut-off point, knownas the Compton edge. Compton scattering is themost probable process for photons in theintermediate energy range and the probabilityintermediate energy range and the probabilitydecreases rapidly with increasing energy. Theprobability is also dependent on the number ofelectrons available for the photon to scatter from,p ,and hence increases with increasing Z.
An approximate expression for the Compton
KL RamakumarIndia
53
scattering probability is given by Z/E
Pair production
The third important -ray interaction
511 KeV511 KeV
511 KeVe+
E
e-
The process of pair production /annihilation
If the incident photon energy is greater than 1.022 MeV(twice the electron rest mass) in the presence of an atomicnucleus an electron/positron pair can be produced.
The presence of atomic nucleus is necessary for momentumconservation
KL RamakumarIndia
54
conservation.
Pair production
Pair production is also possible in the field of an atomicelectron.
For the conservation of momentum however the minimumFor the conservation of momentum, however, the minimumphoton energy should be 4m0c2 = 2.04 MeV.
This is referred to as triplet production (one positron andtwo electrons). Kinetic energy of one of the electrons isusually lower than the other two particles.
The ratio of triplets to pairs strongly depends on the energyof incident photon. Higher the energy, larger is the ratio.
For a given energy of the photon, this ratio decreases asthe atomic number of the absorbing medium increases.the atomic number of the absorbing medium increases.
Thus triple production is rare in natural circumstances butbecomes significant at very high energies of photons (>
KL RamakumarIndia
55
100 MeV) in low Z absorbers.
Pair production
Residual energy beyond 1.02 MeV is distributed evenlybetween the electron and positron as kinetic energy.
As the positron slows to thermal energies throughp g ginteraction with the absorbing medium, it can annihilatewith one of the atomic electrons producing two rays ofenergy 511 keV.
These rays can then either be absorbed or escape thedetector.
This is evidenced by the so called escape peaks observed inThis is evidenced by the so-called escape peaks observed in -ray spectra. If one of the 511 keV photons escapes thedetector, then a peak is observed at E – m0c2 (singleescape peak). If both escape, then a peak is observed at Eescape peak). If both escape, then a peak is observed at E– 2m0c2 (double escape peak).
Pair production only becomes important for high energy rays (5 10 MeV) An approximate expression for the pair
KL RamakumarIndia
56
rays (5 – 10 MeV). An approximate expression for the pairproduction probability is given by Z2 log E.
Gamma ray interactionGamma ray interaction
Three main types of interaction
Photoelectric absorptionPhotoelectric absorption
Compton scattering
Pair productionp
All the three interactions lead to different peaks in a gamma spectrum
h f h h i lThree types of hypothetical gamma ray detectors
Small size (< 2 cm)( )
Large size ( > 10 cm)
Medium size ( >2 cm < 10 cm)
KL RamakumarIndia
57
KL RamakumarIndia
58
KL RamakumarIndia
59
KL RamakumarIndia
60
Gamma ray interaction probability
Photoelectric absorption probability () n
3.5Z
E
n is normally between 4 and 5 depending on the absorber material
C t tt i b bilit
E
Compton scattering probability Z/E
Pair production probability 2 Z2 log E.
Total absorption probability forgamma ray interaction from allthese three processes (++)passes through a minimum becauseof the functional dependence onenergy
KL RamakumarIndia
61
energy.
Unlike charged particles a well-collimated beam of rays shows a
Absorption behaviour of gamma raysUnlike charged particles, a well collimated beam of rays shows atruly exponential absorption in matter. This is because photons areabsorbed or scattered in a single event.
That is, those collimated ,photons which pass through the absorber have no interaction, while the ones absorbed have been
transmission increases with increasing gamma-ray energy and
ones absorbed have been eliminated from the beam in a single event. This leads to exponential
decreases with increasing absorber thickness.
attenuation. I = I0e-μx
where μ is mass absorption coefficient and x is the absorber x is the absorber thickness. I0 is the initial intensity and I is the transmitted intensity of
KL RamakumarIndia
62
gamma rays.
Pair production and Bremsstrahlung
The pair production process is intimately related to the bremsstrahlung processThe pair production process is intimately related to the bremsstrahlung process.In Bremsstrahlung, an electron undergoes a transition between two states, bothof positive energy, and a photon is emitted instead of being absorbed. Theelectron, when it enters the nuclear field, is acted on by the electromagnetic field, w f , y g fof the emitted photon, as well as by the coulomb field of the nucleus. Theintermediate states of the entire system involve the negative energy states whichcharacterize the Dirac electronic theory. The pair production process also takesrecourse to the Dirac electron theory of positive and negative electron states andthe processes involves lifting of an electron from negative state to a positivestate, thereby creating a hole and electron pair. The nuclear cross section is ofh d f ( 2/ )( 2/ 2) f b h h b h hthe order of (Z2/137)(e2/m0c2) for both the processes. In both the processes,
coupling between charged particles and electromagnetic field is necessary for theprocess to occur.
KL RamakumarIndia
63
Interaction of Neutrons with Matter
Neutrons do not carry any electric chargeNeutrons do not carry any electric charge
They do not have any coulombic interactions with electronsin the matter and do not directly produce ionization and are
i l l d dnot continuously slowed down.
They interact with atomic nuclei, only through the nuclearforce which has an extremely short range.
Therefore they must score an almost direct hit on a nucleusbefore an interaction occurs.
Since atomic nuclei are so much smaller than the atomsSince atomic nuclei are so much smaller than the atoms,the probability of an energetic neutron hitting a nucleus isvery low and neutrons can traverse great thicknesses ofmaterial before being stoppedmaterial before being stopped.
Common neutron reactions are (1) Spallation reactions, (2)Elastic scattering, (3) Inelastic scattering, (4)Transmutation (5) Radiative capture
KL RamakumarIndia
64
Transmutation, (5) Radiative capture.
S ll ti R tiInteraction of Neutrons with Matter
Spallation ReactionsAt very high energies (over 150 MeV) neutrons may strike anucleus producing a shower of secondary particles includingsecondary neutrons and gamma rays These high energysecondary neutrons and gamma rays. These high energysecondary particles would in turn interact within themedium and get detected
El ti S tt iElastic ScatteringThe neutrons simply bounce off atomic nuclei. The elasticinteraction of neutrons with atomic nuclei is most importantat neutron energies below the threshold for nuclearat neutron energies below the threshold for nuclearreactions at a few MeV. The amount of energy which aneutron loses in a collision with a nucleus will be large onlyif the nucleus is relatively light. The most violently recoilingif the nucleus is relatively light. The most violently recoilingatomic nuclei are the lightest, namely those of hydrogenatoms. A neutron can lose all its kinetic energy in a singlecollision with a proton. Thus, light nuclides are effective
KL RamakumarIndia
65
p , gmoderators, but not heavy nuclides.
Interaction of Neutrons with Matter
I l ti S tt iInelastic ScatteringA neutron may strike a nucleus and form a compoundnucleus instead of bouncing off as in elastic scattering. Thisnucleus is unstable and emits a neutron of lower energynucleus is unstable and emits a neutron of lower energytogether with a gamma photon which takes up theremaining energy. This process is most effective at highneutron energies in heavy materials.neutron energies in heavy materials.
TransmutationWhen neutrons, protons, or other secondary particles, p , y pproduced by spallation strike a nucleus and form acompound nucleus which then ejects a different particle, atransmutation is said to have occurred. These nuclearreactions are most likely to occur when the energy of theincident particle is between a few MeV and several tens ofMeV.
Ex : 16O(N P) 16N
KL RamakumarIndia
66
Ex.: 16O(N, P) 16N
Interaction of Neutrons with Matter
Radiative CaptureThis is one of the most common neutron reactions. Theneutron is captured by a nucleus which emits only a gammaneutron is captured by a nucleus which emits only a gammaphoton. This reaction, which occurs in most materials, is themost important one for neutrons with very low energy. Theproduct nuclei of (n, ) reactions are usually radioactive andp ( ) yare beta and gamma emitters.
e.g.: 59Co(n, )60Co 23Na(n, )24Na
Neutrons therefore produce ionization indirectly through theprotons, recoiling nuclei, and other massive particles whichare products of various reactions of neutrons with atomicare products of various reactions of neutrons with atomicnuclei.
KL RamakumarIndia
67
Detection of neutrons
Neutrons are detected indirectly by observing the protonsknocked loose by them or by nuclear reactions induced bythem. For example, the alpha particles are easily detectedin the nuclear reactions
14N + n 11B+ 10B + n 7Li +
Or 6Li + n 7Li + Or 6Li + n 7Li +
Slow neutrons are thus indirectly measured by aproportional counter which is filled with BF gas Theproportional counter, which is filled with BF3 gas. Theproducts, 7Li and ionize the gas in the proportionalcounter and the signals are detected. Fission reactionsinduced by neutrons can also serve for neutron detection.
KL RamakumarIndia
68
y
Suggested Reading
Glenn F. Knoll, Radiation Detection and Measurement, John Wiley & Sons, New York (1989)
G F i dl d J W K d E S M i d J M G. Friedlander, J.W. Kennedy, E.S. Macias and J.M. Miller, Nuclear and Radiochemistry, John Wiley & Sons, New York (1980)
R.D. Evans, The Atomic Nucleus, Mc Graw Hill Inc., New York (1955)
S.S. Kapoor and V.S. Ramamurthy, Radiation S.S. Kapoor and V.S. Ramamurthy, Radiation Detection and Measurements, Wiley (Eastern), New Delhi (1988)
H J Arnikar Essentials of Nuclear Chemistry Wiley H.J. Arnikar, Essentials of Nuclear Chemistry, Wiley (Eastern), New Delhi (1994)
B.G. Harvey, Introduction to Nuclear Physics and
KL RamakumarIndia
69
Chemistry, Prentice Hall of India, New Delhi (1965)
Who has seen the radiations?
Neither I nor you!
But out of interactions
In the matter they traverse
And through tell-tale signsd t oug te ta e s g s
Of electrical signal they leave behind
Their presence is sure-felt!Their presence is sure-felt!
KL RamakumarIndia
70