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Interaction of radiation with matter - 1

Charged Particle Radiation

Day 2 – Lecture 1

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• To understand the following interactions for particles: Energy transfer mechanisms Range energy relationships Bragg curve Stopping power Shielding

Objective

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Energy transfer mechanism

• Energy transfer from radioactive particles to other materials depends on: the type and energy of radiation the nature of the absorbing medium

• Radiation may interact with either or both the atomic nuclei or electrons

• The interaction results in excitation and ionisation of the absorber atoms

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When a charged particle interacts with an atom of the absorber, it may:

traverse in close proximity to the atom (called a “hard” collision)

traverse at a distance from the atom (called a “soft” collision)

A hard collision will impart more energy to the material

Particle Interactions

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The amount of energy deposited will be the sum of energy deposited from hard and soft collisions

The “stopping power,” S, is the sum of energy deposited for soft and hard collisions

Most of the energy deposited will be from soft collisions since it is less likely that a particle will interact with the nucleus

Stopping Power

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• The stopping power is a function of the charge of the particle, the energy of the particle, and the material in which the charged particle interacts

Stopping Power

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• Stopping power has units of MeV/cm – the amount of energy deposited per centimeter of material as a charged particle traverses the material

• It is the sum of energy deposited for both hard and soft collisions.

S = = +

Stopping Power

dEdx Tot

dEs

dxdEh

dx

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Mass Stopping Power

• Often the stopping power is divided by the density of the material,

• This is called the “mass stopping power”

• The dimensions for mass stopping power are MeV – cm2

g

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Stopping Power

Stopping power is used to determine dose from charged particles by the relationship:

D = in units of MeV/g, where

= the particle fluence, the number of particles striking an object over a specified time interval

dEdx

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Stopping Power

To convert to units of dose ..we do the following manipulation.

D = MeV/g = (1.6 x 10-10) Gy

dEdx

1ev = 1.6 X 10 -19 J

dEdx

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Bragg Curve – Alpha

Alpha Particle

Energy loss curve – increase initially and virtually no

energy deposited at the end of the track.

Bragg Curve - plot of specific energy loss ( ie rate of ionization ) along the track of a charged particle

A typical Bragg curve is depicted in this graphic for an alpha particle of several MeV of initial energy.

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Bragg Curve –Beta

Beta Path

Energy loss curve – virtually no energy deposited at the end of

the track.

The energy deposition of the electron increases more slowly with penetration depth due to the fact that its direction is changed so much more drastically

As the mass of the beta particle is the same as the orbital electrons they undergo several collisions … the torturous path

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Range – Beta particle

• Depends on the energy of the beta particles and the density of the absorber Beta particle energy reduces as density of the absorber increases

• Experimental analysis reveal that ability to absorb beta particle: Depends on the number of absorbing electrons (electrons per cm 2)in

the path of the beta ray – aerial density Lesser on the atomic number of the absorber

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Range - Energy relationship

• Attenuation of beta particles interposing layers of absorbers between beta

sourceThe number of beta particles

oreduce quickly at firstomore slowly as absorber thickness increasesocompletely stops after certain absorber thickness

Range of beta particle - the thickness of absorber material that stops all particles

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Range – Beta particle

• Aerial density is related to the density of the absorber

td g/cm2 = ρ (density of the absorber) g/cm3 X tl

(thickness of the absorber) cm

• beta shields are usually made from low Z materials

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Range – Beta particles

• Calculate density thickness for aluminium of thickness 1cm .

Note: (Density of Al = 2.7g/cm3)

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Range – Beta particles

• Calculate density thickness for aluminium of thickness 1cm .

td g/cm2 = ρ g/cm3 X tl cm

td = 2.7g/cm2

• A graph of beta energy VS density thickness is useful for shielding and identifying beta source

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Range – alpha particles

• Alpha particles least penetrating of the types of radiation• Alpha particles are mono-energetic. Therefore the

number of alpha particles not reduced until totally eliminated at particular thickness of the absorber.

• The thickness of absorber that totally stops alpha particles is the range of the alpha particle in the material.

• The most energetic alpha particle travels few cms in air, while in tissue only few microns.

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Linear Energy Transfer

LET is the rate of energy absorption by the medium

LET = keV per micron

DE = is the average energy imparted by the radiation of specific energy in traversing a distance of dx.

dEdx

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Linear Energy Transfer

• Specific ionisation is the number of ion pairs formed per unit distance travelled by the radiation particle and very useful concept in health physics

• Specific ionisation is very high for low energy beta particles and decreases as the energy increases.

• Specific ionisation is high for alpha particles. • Travelling through air or tissue alpha particle loses on average 35 eV per

ion pair it creates .• The high electrical charge and low velocity means tens of thousands of

ion pair per cm of air travelled.

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Shielding

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Absorbed dose is energy imparted per unit mass of material:

The unit of absorbed dose is the Gray (Gy)

(1 Gray = 1 joule/kg)

To calculate the dose from charged particles, we need to determine the amount of energy deposited per gram of material

Absorbed Dose

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Tissue Equivalent Stopping Power for Electrons

Energy (MeV) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mass Stopping

Power, S/ (MeV-cm2)/g

4.2 2.8 2.4 2.2 2.0 2.0 1.9 1.9 1.8 1.8

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Stopping Power Example

Calculate the dose from a 37,000 Bq source of 32P spread over an area of 1 cm2 on the arm of an individual for 1 hour

D = (1.6 x 10-10) Gy

32P has a 0.690 MeV beta particle (average energy). Assume that 50% of the particles on the skin interact with the skin

dEdx

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= (½)(37,000 Bq)(1 dis/s/Bq)(1 hr)(3600 s/hr) = 6.67 x 107 dis

32P has a 0.690 MeV beta particle (average energy)

For tissue equivalent plastic and a beta particle with an energy of 0.690 MeV, the stopping power is 1.96 MeV-cm2/g

Stopping Power Example

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D = 6.67 x 107 X 1.96 X1.6 x 10-10 J/kg

D = 0.021 Gy

D = MeV-cm2/gdEdx

Stopping Power Example

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Where to Get More Information

Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009)

International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)