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