Interaction of Charged 

Particles With Matte

r

3/1/2011
Objectives

Qualitative

Quantitative

Introduction

General

Force of the Interaction

Contents

Force of the InteractionFour Types of Charged Particle Interactions

Ionization

GeneralIon PairsDelta Ray
Excitation

General

Bremsstrahlung

GeneralIntensity of Bremsstrahlung – Monoenergetic E

Intensity of Bremsstrahlung Beta Particles

Contents

Intensity of Bremsstrahlung – Beta ParticlesBremsstrahlung Spectra

Cerenkov Radiation

General
Quantitative Measures of Energy Loss

GeneralW ValueSpecific IonizationStopping Power and Linear Energy TransferMass Stopping Power

Contents

Alpha Particles

GeneralAlpha TracksRangeRange in AirApproximate Data for 5 MeV Alphas
Beta Particles

GeneralRangeRange (as a density thickness)Range and PenetrationBremsstrahlung

C k R di ti

Contents

Cerenkov Radiation

Approximate Data for 1 MeV Beta Particles

Summary

Types of InteractionsAlpha ParticlesBeta Particles

References
Objectives
– Ionization

– Excitation

ObjectivesQualitative

– Bremsstrahlung– Cerenkov radiation
To review the following measures of energy loss:

– W Value

– Specific Ionization

ObjectivesQuantitative

Specific Ionization

– Stopping Power/Linear Energy Transfe– Mass Stopping Power
Introduction
• “The interaction of charged particles with matte

concerns the transfer of energy from the chargparticles to the material through which they tra

• The

“charged particles

” considered here are:

IntroductionGeneral

The charged particles considered here are:

- Alpha particles (+2 charge)- Beta particles (+ or -1 charge) or electron

• Photons and neutrons, which have no charge, 

interact very differently.
• Charged particles passing through matter cont

interact with the electrons and nuclei of the suatoms.

• In other words, alpha and beta particles are co

IntroductionGeneral

slowing down as they travel through matter.

• The interactions involve the electromagnetic fo

attraction or repulsion between the alpha or beparticles and the surrounding electrons and nu
• The force associated with these interactions ca

described by Coulomb’s equation:

IntroductionForce of the Interaction

k is a constant = 9 x 10

9 N-m

2/C

2.

q1 is the charge on the incident particle in Cou

q

2 is the charge on the “struck” particle. 

r is the distance between the particles in mete
Things to notice about the equation:

• The force increases as the charge increases• The force increases as the distance decrease

quadruples if the distance is cut in half)

IntroductionForce of the Interaction

qp )

• The force can be positive or negative (attract

repulsive)
Introduction

Four Types of Charged Particle Interactions• The four types of interactions are:

Ionization (alphas and betas)Excitation (alphas and betas)

Bremsstrahlung (primarily betas)Bremsstrahlung (primarily betas)Cerenkov radiation (primarily betas)

• Ionization is almost always the primary mechan

energy loss.
Ionization
• A charged particle (alpha or beta particle) exert

sufficient force of attraction or repulsion to compremove one or more electrons from an atom.

• The energy imparted to the electron must excee

bi di f th l t

IonizationGeneral

bi

nding energy o

f the elec

tron.

• Ionization is most likely to involve atoms near th

charged particle's trajectory.

• Each ionization event reduces the charged part

velocity, i.e., the alpha or beta particles loses kenergy.
• Ionization turns a neutral atom into an ion pair.

• The electron stripped away from the atom is the 

member of the ion pair.It is known as a secondary electron.

IonizationIon Pairs

The secondary electron has some, but not mucenergy - usually less than 100 eV.Sometimes it has enough energy to ionize additatoms. Then it is referred to as a delta ray.

• The atom , now with a vacancy in one of its elec

shells, is the positive member of the ion pair. 
e

-

e

-

e

-

e

-

e

-

+

+

+

+

+

+

+

e

-

e

-

+
e

-

e

-

e

-

e

-

e

-

+ +

+ +

+

+

+

e

-

e

-

e

-

+
e

-

e

-

e

-

e

-

e

-

+ +

+ +

+

+

+

e

-

e

-

+
Negative 

the i

(seconda

e

-

e

-

e

-

e

-

e

-

+ +

+ +

+

+

+

e

-

This is an ion pair 

Positive member of the ion pair

(e.g., N2+)

+
N2

N2

N2

N2 O + 2 -

N2

2 2 eIon pair
+ + + + + + + + + + + + + + + +

---------- -----

IonizationDelta Ray

edelta ray

A delta ray is a secondary electron (negative membion pair) that has sufficient kinetic energy to cause ionization.
Excitation
• The charged particle (alpha or beta particle) ex

just enough force to promote one of the atom’s electrons to a higher energy state (shell).Insufficient energy was transferred to ionize the E it ti ll f th f th

ExcitationGeneral•

Excit

ation usually occurs 

farther away 

from the 

charged particle's trajectory than ionization.

• The excited atom will de-excite and emit a low 

ultraviolet photon.

• Each excitation event reduces the charged par

velocity.
e

-

e

-

e

-

-

+ +

+ +

+

+

e

-
e

-

e

-

e

-

-

+ +

+ +

+

+

alpha

e

-
e

-

e

-

e

-

+ +

+ +

+

+

alpha

e
e

-

e

-

e

-

+ +

+ +

+

+

e
e

-

e

-

e

-

e

+ +

+ +

+

+

e-

Ultra violet photon
Bremsstrahlung
• Bremsstrahlung radiation is electromagnetic ra

that is produced when charged particles are de(decelerated) while traveling near an atomic nu

• Bremsstrahlung is almost exclusively associate

l t (b t ti l ) b th l tt 

BremsstrahlungGeneral

elec

trons (b

e

ta parti

cles

)

because the latter are 

deflected.

• Large particles (e.g., alpha particles) do not pro

significant bremsstrahlung because they travel lines. Since they aren’t deflected to any real exbremsstrahlung production is inconsequential.
• Bremsstrahlung photons may have any energy 

energy of the incident particle.For example, the bremsstrahlung photons prodP-32 betas have a range of energies up to 1.7 maximum energy of the P-32 alphas.

BremsstrahlungGeneral• Bremmstrahlung is most intense when:

- The beta particles or electrons have high - The material has a high atomic number
+ +

+

l

+ +

+

+

+ +

nucleus
+ +

+

e

-

l

+ +

+

+

+ +

nucleus
+ +

+

l

brems

+ +

+

+

+ +

e

-

nucleus
+ +

+

l

brem

+ +

+

+

+ +

e

-

nucleus
+ +

+

l

+ +

+

+

+ +

nucleus
+ +

+

l

+ +

+

+

+ +

nucleus
+ +

+

e

-

l

bremsstra

+ +

+

+

+ +

nucleus

The greater the charge in the nucleus (atomic numbgreater the deflection of the electrons and the greateintensity of the bremsstrahlung
• According to Evans, the fraction of the energy o

monoenergetic electrons that is converted to bremsstrahlung (f) can be calculated as follows

BremsstrahlungIntensity of Bremsstrahlung – Monoenergetic 

Z is the atomic number of the materialE is the kinetic energy of the electron (MeV)
• Turner gives slightly different equation for the f

of the energy of monoenergetic electrons that iconverted to bremsstrahlung:

BremsstrahlungIntensity of Bremsstrahlung – Monoenergetic 

Z is the atomic number of the materialE is the kinetic energy of the electrons (MeV)
• The following equation (Evans) estimates the f

beta particle energy converted to bremsstrahluBeta particles are emitted with a range of energsome maximum value (Emax).

BremsstrahlungIntensity of Bremsstrahlung – Beta Particles

Z is the atomic number of the materialEmax is the maximum energy of the beta particle
• The beta energy rate (MeV/s) is the activity of t

emitter multiplied by the average energy of the particles:

Beta energy rate = Activity x Average beta e

BremsstrahlungIntensity of Bremsstrahlung – Beta Particles

(MeV/s) (dps) (MeV)

• This is multiplied by the fraction (f) to determine 

bremsstrahlung energy emission rate in MeV/sBremsstrahlung energy rate = Beta energy rat

(MeV/s) (MeV/s)
• The following discussion tries to explain the sh

bremsstrahlung spectrum (e.g., that produced itarget of an x-ray tube)

• Bremsstrahlung photons have a range of energ

th i f th l t /b t t

BremsstrahlungBremsstrahlung Spectra

the maximum energy o

f the elec

trons/b

e

ta part

• When monoenergetic electrons lose energy in 

extremely thin target, the bremsstrahlung specflat up to the maximum energy of the electronsImaginary targets like this are not found in the rworld.
Bremsstrahlung spectrum for 

monoenergetic electrons and a

imaginary thin target

BremsstrahlungBremsstrahlung Spectra

imaginary thin target

Photon energy

Number of 

photons

Kinetic 

the ele

beta 
• Monoenergetic electrons losing energy in a thic

world) target can be considered to interact in a thin sections (targets). 

• The deeper into the target a given section is, th

the energy of the electrons and the lower the m

BremsstrahlungBremsstrahlung Spectra

the energy of the electrons, and the lower the m

energy of the bremsstrahlung produced there. The bremsstrahlung produced in the deeper sethe lower energy electrons contributes to the loend of the overall bremsstrahlung spectrum:

• Bremsstrahlung produced in the shallow sectio

target where the electron energies are higher cto the high energy portion of the spectrum.
Target consisting of 

six thin sections

e- Bremsst

Spect

BremsstrahlungBremsstrahlung Spectra

Lower energy e1 2 3 4 5 6

Photon en

Spect

Higher energy bremsstrahlung

Lower energy

bremsstrahlung e- eee12 3 4 5 6
• As a result, the bremsstrahlung spectrum produ

a real world (thick) target looks something like 

BremsstrahlungBremsstrahlung Spectra

Bremsstrahlung photon energy

Number of 

photons
• There is always some shielding/filtration betwe

source of the bremsstrahlung and the point of i

• For example, the glass wall of an x-ray tube wi

the bremsstrahlung generated in the target (an

ld filt i t ti ll l d i f t f th 

BremsstrahlungBremsstrahlung Spectra

would a filter in

tentionally place

d in 

fron

t o

f the 

• This shielding primarily reduces the intensity of 

energy bremsstrahlung.

• As such, a “real world” bremsstrahlung spectru

more like that on the next slide.
Number of Bremsstrahlung spectrum with f

photons

BremsstrahlungBremsstrahlung Spectra

Bremsstrahlung photon energy
Cerenkov Radiation
• Cerenkov radiation is the blue light emitted by 

charged particles that travel through a transparmedium (e.g., water) faster than the speed of liin that medium.J t l i f t th d d

Cerenkov Radiation ProductionGeneral•

Jus

t as a plane going 

fas

ter than soun

d pro

duc

a cone of sound (a sonic boom), a charged particle going faster than light produces a cone light (Cerenkov radiation)

• The production of Cerenkov radiation is essent

limited to high energy (i.e., fast) beta particles aelectrons.
• Cerenkov radiation is often associated with rea

pools or nuclear criticality accidents.

• It is possible to quantify beta emitters by measu

intensity of their Cerenkov radiation (Cerenkov 

Cerenkov Radiation ProductionGeneral

counting)
Quantitative Measure

of Energy Lossof Energy Loss
The four most common measures of energy loss 

charged particles:

1. W Value

2 S ifi I i ti

Quantitative Measures of Energy LossGeneral

2. 

Specific Ionization

3. Stopping power or Linear Energy Transf4. Mass Stopping Power
• W is the average energy lost by a charged part

ion pair produced.

• It depends on: the type of charged particle

material that is being ionized

Quantitative Measures of Energy LossW Value

material that is being ionized

• W doesn’t change much with the energy of the 

particle, but it does increase at low energies (< MeV) for protons and alpha particles.
• Beta particles lose an average of 34 eV per ion 

produced in air.

• Alpha particles lose an average of 36 eV per io

produced in air.

Quantitative Measures of Energy LossW Value• Alpha particles and beta particles (or electrons

an average of approximately 22 eV per ion pair produced in water (Turner p. 140, 161)
• Specific ionization is the average number of ion 

produced per unit distance traveled in a matericharged particle. 

• It depends on: the type of charged particle, Quantitative Measures of Energy LossSpecific Ionization

the energy of the charged pathe material through which it 

• Alpha particles produce 20,000 to 60,000 ion p

centimeter (cm) in air.

• Beta particles might produce 100 ion pairs per 

air.
• There is no practical difference between stoppin

and linear energy transfer.

• The stopping power or the linear energy transfe

average energy lost by a charged particle per u

Quantitative Measures of Energy LossStopping Power and Linear Energy Transfer

distance traveled.

• Typical units: MeV/cm or eV/um
• When a distinction is made:

Stopping power is used to describe the total eby the charged particle.Linear energy transfer 

(LET

) is used to descr

Quantitative Measures of Energy LossStopping Power and Linear Energy Transfer

gy ( )

energy lost by the charged particle that is locabsorbed in the material the particle is traveli

• In this sense, stopping power is akin to kerma w

akin to absorbed dose
• LET is sometimes referred to as the restricted st

power.It describes the energy lost by charged particles energy interactions. 

Quantitative Measures of Energy LossStopping Power and Linear Energy Transfer

The assumption is that the secondary electrons in these low energy interactions don’t travel outsvolume of interest and deposit their energy localThis would exclude interactions producing delta bremsstrahlung.
• The maximum energy that can be transferred in 

interactions is sometimes indicated with a subsLET1 keV, LET5 keV

• The 

greater the energy cutoff, the lar

ger the LE

Quantitative Measures of Energy LossStopping Power and Linear Energy Transfer

g gy , g 

e.g., LET5 keV > LET1 keV 

• If no restriction is placed on the energy of the 

interactions, the unrestricted LET is indicated a

• LET

∞ is the same as stopping power.
• The mass stopping power can be more conveni

than the stopping power. 

• It is the stopping power (e.g., MeV/cm) divided b

density (g/cm

3) of the material.

Quantitative Measures of Energy LossMass Stopping Power • The units of the mass stopping power are usual

cm

2

g-1 (MeV per g/cm

2

)

• It is the average energy lost by a charged partic

distance traveled where the distance is expressaerial density (g/cm

2

)
Alpha Particles
• The principal types of interactions for alpha part

- Ionization- Excitation 

Alpha ParticlesGeneral• Usually have energies from 4 to 8 MeV • High specific ionization 

(because of their +2 charge and low velocity)

• High LET radiation - lose their energy very quic

they travel through matter. 
Alpha Particles

General• Easy to shield – can be stopped by a piece of p• Not an external hazard – cannot penetrate the d

of skin on the surface of the body

• Potential internal hazard – the large radiation w

factor for alpha particles (20) means that the consequence of a given alpha particle dose is gthan that for other types of radiation.
Alpha Particles

Alpha Tracks

Alpha particle tracks are short and straigh

From Turner, James. Atoms, Radiation, and Radiation Protection

1986, pg. 74.
• The range of an alpha particle is short:

- approximately 5 cm in air. - 20 to 70 um in tissue (one, two or three c

Alpha ParticlesRange• The survey instrument must be close (e.g., < 1 c

contaminated surface if alpha emitting radionucto be detected. It is best if the contaminated surface is dry and cdust or moisture could attenuate the alphas. 
• Alphas with energies of 4 to 8 MeV (almost all 

emitters):

R (cm) = 1.24 E - 2.62

Alpha ParticlesRange in Air• Alphas with energies below 4 MeV:

R (cm) = 0.56 E

E is the alpha energy in MeV
Air 

(D=0.001293 g/cm3)

(D

W (eV/ip) 36 

Stopping Power/LET 

(M V/ )

1.23 

Alpha ParticlesApproximate Data for 5 MeV Alphas

(MeV/cm)

Mass Stopping Power 

(MeV cm2 g-1)

950 

Specific Ionization 

(Ion pairs per cm)

34,000 4

Range (g/cm2) 5 x 10-3 3 

Range (cm) 4 3 x 1
Beta Particles
• Beta particles (or electrons) interact by all of th

following mechanisms:

– Ionization

– Excitation

Beta ParticlesGeneral

– Bremsstrahlung– Cerenkov radiation (relatively unimportan

For betas above 150 eV, roughly 95% of the paenergy loss in water is due to ionization. 
• Not as intensely ionizing as alphas (because the

higher velocities and one half the charge). 

• Low specific ionization (ca. 100 ion pairs per cm 

Beta ParticlesGeneral• Low stopping powers (low LET radiation)• Betas might produce (the specific ionization) in 
• Much greater range than alphas (except for the 

energy betas):

- Approximately 3 meters in air for a 1 MeV - A few millimeters in tissue (water)

Beta ParticlesRange

A few millimeters in tissue (water)

• The atomic number of the material is not a majo

fact, the range of beta particles under 20 MeV is lead than in water!

• The next slide shows two empirical equations re

range of a beta particle to its energy.
• The range of a beta particle can be determined 

energy is known:

Beta ParticlesRange (as a density thickness)

• The energy of a beta particle can be determined 

range is known:

R is the range in mg/cm

2

E is the maximum beta energy in MeV
• The easiest way to determine the range of a bet

is to use a curve similar to that on the next slideA more readable version can be found on page PTP’s Rad Health Handbook.

Beta ParticlesRange (as a density thickness)

• Beta particles (and electrons) travel in convolute

• They do not travel in a straight line.• The “range” of a beta particle usually refers to th

th l th

Beta ParticlesRange and Penetration

path length.

• The range is greater than the distance between 

beginning and the end of the path followed by thparticle (the penetration thickness).In other words, the range of a beta particle is grthan the thickness of a material that can be pen
• The following slide shows the predicted paths of 

beta particles in water.

The average penetration thickness: 1500 uThe average range (path length): 3500 u

Beta ParticlesRange and Penetration
Beta Particles

Range and Penetration

Beta particle tracks are convoluted.

From Turner, James. Atoms, Radiation, and Radiation Pro

edition. 1995, pg. 151.
Beta Particles

Range and Penetration

From Turner, James. Atoms, Radiation, and Radiation Prot

edition. 1995, pg. 151.
• Bremsstrahlung is most significant for high ener

emitters such as P-32 and Sr-90. 

• The presence of bremsstrahlung is often interpr

indication that high energy beta emitters are pre

Beta ParticlesBremsstrahlung• Nevertheless, bremsstrahlung can be detected 

energy beta emitters (e.g., tritium) are present in enough activities (e.g., a tritium exit sign).
• To minimize the 

production of unwanted bremsstrahlung, beta sources should be shielded with a low 

t i b t il

Beta ParticlesBremsstrahlung

a

tomic num

ber ma

terial.

For example, high energy beta emitters are commonly shielded with plastic.
• Shielding a high energy beta source with lead c

increase the production of bremsstrahlung.Nevertheless, if the lead is thick enough, it will athe bremsstrahlung.

Beta ParticlesBremsstrahlung• Sometimes a beta shield has two layers: 

- plastic nearest the source to stop any beta- lead outside the plastic to stop any bremss
• The emission of Cerenkov radiation is an intere

relatively unimportant, type of beta particle (or einteraction.

• Cerenkov radiation is the blue glow that often se

Beta ParticlesCerenkov Radiation

reactor’s spent fuel pool. 

• The Cerenkov radiation primarily is due to the h

energy Compton scattered electrons produced bgamma emissions from the fuel.
Fuel assemblies 

being removed from the reactor vessel at TMI’s operating unit

Beta ParticlesCerenkov Radiation

operating unit.
Air 

(D=0.001293 g/cm3)

(

W (eV/ip) 34 

Stopping Power/LET 

(M V/ ) 3.3 x 10-3 

Beta ParticlesApproximate Data for 1 MeV Beta Particles

(MeV/cm) 3.3 x 10 

Mass Stopping Power 

(MeV cm2 g-1) 2.6 

Specific Ionization (Ion 

pairs per cm) 100 

Range (g/cm2) 0.4 

Range (cm) 300 
Summary
• Charged particles continuously interact as they 

through matter - it is not a matter of probability

• The major type of interactions: ionization

SummaryTypes of Interactions• The other types of interactions: excitation

bremsstrahlungCerenkov radia

• Bremsstrahlung production is sometimes an imp

concern with beta particles.

• Cerenkov radiation is interesting but rarely imp
• High specific ionization

• High LET (aka stopping power)• Travel in straight lines SummaryAlpha Particles• Short range: a few cm in air

a couple of cells in the body

• Potential internal hazard but not an external haz
• Low specific ionization

• Low LET radiation (i.e., low stopping power)• Convoluted pathSummaryBeta Particles• Large range: a few hundred cm in air

several mm in the body 

• Penetration distance is less than the range
• Produce bremsstrahlung photons when they cha

direction. 

• Maximum energy of the bremsstrahung photons 

same as the maximum energy of the beta particl

SummaryBeta Particles

• The higher the atomic number of the material, th

the fraction of the beta particle energy that will bas bremsstrahlung

• The higher the energy of the beta particle (or ele

the greater the fraction of the energy that will be as bremsstrahlung.
• Bremsstrahlung complicates radiation protection

counting, shielding, and dosimetry. 

• Bremsstrahlung production can be minimized by 

beta sources with a low Z material such as plas

SummaryBeta Particles
References
• Evans, R. The Atomic Nucleus. McGraw-Hill. 19

• Turner, James. Atoms, Radiation, and Radiation 

Protection, 2nd edition. John Wiley and Sons, In

1995.

References