neutron interactions part i - uthgsbsmedphys.org neutron lecture 01 200… · neutron interactions...

Neutron Interactions Part I

Rebecca M. Howell, Ph.D.Radiation Physics

[email protected]

mailto:[email protected]

November 2007 November 2007 Rebecca M. Howell, Ph.D.Rebecca M. Howell, Ph.D.

Why do we as Medical Physicists care about neutrons?

• Neutrons in Radiation Therapy• Neutron Therapy• Contamination Neutrons on X-Ray Therapy• Contamination Neutrons in Proton Therapy

• The above will be discussed in lecture #2.

• Today’s focus will be general neutron interactions

• Unwanted patient dose

• Shielding Considerations

• Neutron Dose


Outline – Neutron Interactions

• General properties• Neutron Reaction Cross Sections• Neutron Interactions


General Properties

• Neutrons are Neutral• Can Not interact by coulomb forces• Can travel through several cm of material without

interacting.• Neutrons interact with nucleus of absorbing

material (do not interact with orbital electrons).

Reaction Cross SectionsUsed to describe neutron interaction probabilities.


Reaction Cross Sections• Reaction cross sections are used to quantitatively

describe the probability of interactions between neutrons and matter.

• Microscopic cross section, σ

is defined per nucleus for each type of interaction.

• Units of area.• Common unit for reaction neutron cross sections is the

barn (10-24cm2). • Energy Dependent - tabulated as a function of

energy.


Reaction Cross Sections• Macroscopic cross section, Σ, probability per unit path

length that a particular type of interaction will occur.

• σ

= microscopic cross section, cm2

• N = number of nuclei per unit volume, nuclei/cm3

• All processes can be combined to calculate Σtotal , probability per unit path length that any type of interaction will occur.

σN=Σ

...... +Σ+Σ=Σ captureradscatterTotal


to

totaleII Σ−=

Exponential Attenuation

• Neutrons are removed exponentially from a collimated neutron beam by absorbing material.

Io I

whereN = number of absorber atoms

per cm3 (atomic density)σ

= the microscopic cross

section for the absorber, cm2

t = the absorber thickness, cm

σtotal N


Exponential Attenuation Example

• In an experiment designed to measure the total cross section of lead for 10 MeV neutrons, it was found that a 1 cm thick lead absorber attenuated the neutron flux to 84.5% of its initial value. The atomic weight of lead is 207.21, and its density is 11.3 g cm-3.

• Calculate the total cross section from these data.


Exponential Attenuation Example

• Rearrange/Solve the general attenuation equation for σ:

=⎥⎦⎤

⎢⎣⎡

=Nt

IILn 0

σ

[ ]( )

barn 1.5101.51atoms1029.3

18.1log 224

322

=×=×

− cmcm

cm

Calculate N, the atomic density of lead:

322

23

3

atoms1029.3

207.21gmole 1

moleatoms1003.63.11

cm

cmg

×

=×

×


Neutron Mean Free Path, λ

• Slow neutrons• λ

is on the order of 1cm or less

• For fast neutrons• λ

may be tens of centimeters

TotalΣ=

1λ


Neutron Mean Free Path, λ Example

• Calculate the mean free path for the previous example.

322 atoms1029.3

cmN ×=224101.5 cm−×=σ

95.5168.0111

===Σ

=NTotal σ

λ

A few background concepts…..


Compound Nucleus Model Multi-step Reaction

• Projectile and target fuse together, then by successive nucleon-nucleon collisions within the combined system, the reaction energy becomes shared among many nucleons.

• Once equilibrium occurs, the compound nucleus can exist in an excited state for a long period of time (10-16-10-18).

• Eventually deexcitation occurs, and by chance a single nucleon or group of nucleons acquires enough energy to escape

Resonance• At higher energies x-section may have large peaks.

• Peaks = resonances• Occur at neutron energies where reactions with nuclei

are enhanced

Rinard, Fig. 12.3

• A resonance will occur if the energy of the incident neutron is close to the energy of an excited state of the compound nucleus


Resonance• In this example, at ≈

250 keV, the neutron energy is such that

the compound nucleus 7Li is formed at an excitation energy which corresponds exactly to one of its higher states or natural frequencies.

Peak is due to “resonance” in initial fusion process of the neutron with 6Li target.

• Energy is drawn from incident neutron into the reaction channel for the compound nucleus excited state.

Cross section for 6Li(n,α)t

Lilly, fig 1.14

Resonance General Trends

• Heavy nuclei• Large and narrow resonances appear for

neutron energies in eV range.• For energies in keV region, resonances can be

too close together to be resolved.• Light nuclei

• Resonances appear only in MeV region and are broad and relatively small.

Classification of Neutrons by Energy

November 2007 November 2007 Rebecca M. Howell, Rebecca M. Howell, Ph.D.Ph.D.


Classification of Neutrons by Energy There are three energy categories of neutrons (NCRP-38):

1. Thermal neutrons are in thermal equilibrium with the medium they are in. The average energy of thermal neutrons is typically below 1eV, depending on temperature. The most probable velocity for thermal neutrons is 2200 meters per second at 20.44oC. This velocity corresponds to an energy of 0.0253eV.

2. Intermediate Energy Neutrons are classified as having intermediate energy range from above 1eV to tens of keV and typically result from elastic collisions of fast neutrons.

3. Fast Neutrons are classified as having energies above the intermediate neutrons.


Classification of Neutrons by Energy

The classification of neutrons by energy is somewhat dependent on the reference text. Some sources may include an epithermal category while others only include fast and slow (thermal).

Category Energy RangeFast > 500 keVIntermediate 10 keV – 500 keVEpithermal 0.5 eV – 10 keVThermal < 0.5 eV

Cd-cutoff energy: sharp drop occurs in Cd absorption cross section at 0.5 eV

0.5 eV


Overview of Neutron Interactions Scattering and Absorption

Total

Scatter AbsorptionInelastic Scatter (n,n’)

Elastic Scatter (n,n)

Electro-magnetic

(n,γ)

Neutral (n,2n) (n,3n) (n,4n) (n,xn)

Charged (n,p) (n,α) (n,d)

(n,etc)

Fission (n,f)

Sometimes called

“radiative”capture

Sometimes called “transmutation”

Sometimes shown as (n,nγ)

Non-elastic

Processes

(n,n’3a)

(n,n’4a)

(n,n’etc)

Also called “neutron capture”

Boxes shaded in light blue follow the compound nucleus model.


General Neutron Interactions Scattering and AbsorptionScatter

• When neutron is elastically or inelastically scattered by nucleus speed and direction change, but nucleus is left with same number of p+ and no as before the interaction.

• Elastic Scatter (n,n)• Inelastic Scatter (n,n’)

• Nonelastic Processes

Absorption• When neutron is absorbed by

nucleus, a wide range of radiations can be emitted or fission can be induced.

Neutral• (n,2n)• (n,3n)• (n,4n)• (n,etc)Fission• (n,f)

Electromagnetic • (n,γ)Charged• (n,p)• (n,α)• (n,d)• (n,etc)

Neutron Interactions are Energy Dependent



• Fast neutrons lose energy through scatter interactions with atoms in their environment.• At higher energies inelastic scatter dominates, while at

lower energies elastic scatter dominates.

• After being slowed down to thermal or near thermal energies, they are absorbed (captured) by nuclei of the absorbing material.

• absorption is often followed by emission of a photon (n,γ) or another particle from the absorber nucleus e.g. (n,p), (n,α), (n,etc).


Scatter of Fast Neutrons• Elastic Scatter – Kinetic Energy AND Momentum

Conserved• More likely in low Z materials• More likely at lower energies, < 1MeV• Maximum amount of energy that can be lost is function of target

nuclei mass.• Larger cross sections

• Inelastic Scatter – Reaction kinematics more complicated than for elastic scatter • More likely in high Z materials• More likely at higher energies E > 1MeV• Can loose large amounts of energy in one collision• Smaller cross sections• Threshold Energy


Elastic Scatter of Fast Neutrons (n,n)

• Elastic scattering is the most likely interaction between (lower energy) fast neutrons and low Z absorbers.

• Billiard ball type collision• Direct collision – More energy transferred• Indirect Collision – Less Energy transferred

• Kinetic energy and momentum are conserved

• Light recoiling nucleus can cause high LET tracks


Kinematics of Neutron Elastic Scattering

• Equation demonstrates that energy given to recoil nucleus is determined by scattering angle:

( )( ) nR E

AAE θ2

2 cos1

4+

=

Knoll, fig 15-12

Where A is the mass of the target nucleus

En - energy of incident neutron

θ

= angle of scatter of recoil nucleus


Elastic Scatter Grazing Angle Encounter

• For grazing angle encounter, recoil is emitted almost perpendicular to incoming neutron (θ≈90).

• Calculate energy of recoil nucleus :

( )( ) nR E

AAE 90cos

1)(4 2

2+=

0

• For a grazing hit almost no energy goes to recoil nucleus, regardless of mass of the target nuclei.


Elastic Scatter Direct Head-on Collision

• For direct head-on collision, recoil is emitted at almost same angle as incoming neutron (θ≈0).

• Calculate energy of recoil nucleus :

( )( ) nR E

AAE 0cos

1)(4 2

2+=

1

• For a direct head-on collision, the energy of recoil nucleus increases with increasing mass of the target nuclei.

( ) nR EAAE 21

)(4+

=


Maximum Fractional Energy Transfer in Neutron Elastic Scattering

Target Nucleus1H 12H 8/9=0.8893He 3/4=0.7504He 16/25=0.64012C 48/169=0.28416O 64/289=0.221

( )21)(4

AA

EE

n

R

+=

For direct head-on collisions:• As mass of target nuclei

increases:•Energy of recoil nucleus . •Energy of the scattered neutron .

• The fractional energy transfer is independent of incident neutron energy.

• Nuclei with lower mass are more effective on a “per collision” basis for slowing down neutrons!


Energy Distribution of Recoil Nuclei (from Elastic Neutron Scatter)

• In principle all scattering angles are allowed, expect a continuum between the two extremes.

• For most target nuclei, forward and backward scattering are somewhat favored.• See ch15 on G. Knoll. Radiation Detection and

Measurement


Inelastic Scatter of Fast Neutrons (n,n’)

1. Neutron collides with nucleus 2. Some of the kinetic energy of

the neutron excites the nucleus

3. Excitation energy is emitted as gamma photon, γ

can

have substantial energy.4. Neutron (not necessarily the

incoming neutron) is emitted.

• Compound Nucleus Model – neutron is captured by target nucleus and a neutron (may not be same neutron) is reemitted along with gamma photon.

Inelastic Scatter of Fast Neutrons

• Total energy of outgoing neutron and nucleus is much less than the energy of the incoming neutron.• Part of original kinetic energy is used to excite

compound nucleus.• Can not write simple expression for energy loss

because it depends on the energy levels of the target nucleus.

• If all excited states of compound nucleus too high, inelastic scatter is impossible.


Inelastic Scatter of Fast Neutrons

• Inelastic Scatter = Threshold Phenomenon• Infinite threshold for H (inelastic can not occur)• 6MeV Threshold for O• 1MeV Threshold for Ur• Note: Inelastic scatter with Hydrogen is

impossible because Hydrogen does not have excited states.

• Cross section increases with increasing energy.


General Neutron Interactions Nonelastic Processes

Nonelastic Processes• Similar to inelastic scatter in that the process follows a

compound nucleus model and that there is a recoil neutron. • but instead of emitting γ-rays, additional secondary particles

can be emitted (in addition to scattered neutron). • Nucleus has different number of p+ and no after interaction.• Different from absorption because neutron is not absorbed, a

scattered neutron is emitted (may not be the same one that entered rxn).

• Sometimes called nonelastic scatter


Thermal Neutron Interactions Absorption (sometimes called neutron capture)• As neutrons reach thermal or near thermal

energies, their likelihood of capture by an absorber nucleus increases.• In this energy range, the absorption cross-section of

many nuclei, has been found to be inversely proportional to the square root of the velocity of the neutron.

νσ 11

∝∝E

one-over-v law for slow neutron absorption

1/υ region

Lilly, fig 1.14


Thermal Neutron Interactions Absorption

• Thermal neutron cross sections (tabular data) are usually given for neutrons whose most probable energy is 0.025eV.

• If the cross section at E0 is σ0 , then the cross section for any other neutron (within the validity of the 1/v law is given by:

EE00

0

==νν

σσ


Thermal neutron cross sections

Isotope Abunda nce

IsotopeProduced

Half-life Cross section[barn atom-1]

23Na 100% 24Na 15 h 0.9331P 100% 32P 14.3 d 0.1841K 6.9% 42K 12.4 h 1.46

58Fe 0.33% 59Fe 45.1 d 1.1559Co 100% 60Co 5.26 y 37197Au 100% 198Au 2.69 d 99

10B 19.8% 7Li Stable 3837B (all isotopes) 759

113Cd 12.3% 114Cd Stable 20000Cd (all isotopes) 2450


Thermal Neutron Interactions Activation (follows absorption)

• Nuclei are often in excited state following neutron absorption.

• Activated nuclei decay by normal processes.

Example • 14N(n,p)14C• 10B(n,a)7Li• 113Cd(n,g)114C


General Neutron Interactions Activation

• Why is this important to us?• Radiation Hazard after

neutron beam turned off.

• How can we use this to our advantage?• Tool for measuring

neutron flux.

• Detection class: We will discuss neutron detection via activation foils.

Thermal Neutron Interactions Activation 197Au Activation Foils

• 197Au has a large thermal neutron absorption cross section (98.8 barns at 2200m/s).

• 198Au atoms are formed following neutron capture. Then 198Au decays in a β−γ

cascade

198Au

198Hg

T1/2

=12ps

γ = 411.8 KeV

β

Measure This!

T1/2

2.7d

Neutron Interactions in Tissue

“Most Common”


Neutron Interactions with Tissue• Neutrons are indirectly ionizing and but give rise to

densely ionizing (high LET) particles: recoil protons, α-particles, and heavier nuclear fragments.

• The most common elements in the human body are Hydrogen, Carbon, Nitrogen, and Oxygen.• Interactions with these elements contribute to dose in

tissue.



• Fast neutrons lose energy through scatter interactions with atoms in their environment.• At higher energies inelastic scatter dominates, while at

lower energies elastic scatter dominates.• Fast neutrons also interact via nonelastic processes

involving C and O.

• After being slowed to thermal or near thermal energies, absorption processes can occur.


Fast Neutron Interactions with Oxygen and Carbon

• Non-elastic processes results in recoil α- particles (high Let particles).

A neutron interacts with a Carbon atom (6 protons and 6 neutrons), resulting in three α-particles. (Hall, Fig 1.10)

A neutron interacts with an Oxygen atom (8 protons and 8 neutrons) , resulting in four α-particles. (Hall, Fig 1.10)


Intermediate Neutron Interactions in Tissue Interact primarily via elastic scatter with Hydrogen

• For intermediate energy neutrons, the interaction between neutrons and hydrogen nuclei is the dominant process of energy transfer in soft tissues.

1.Hydrogen is the most abundant atom in tissue.

2.A proton and a neutron have similar mass, 938 MeV/cm2

versus 940 MeV/cm2.3.Hydrogen has a large collision

cross-section for neutrons.

3 Reasons


Thermal Neutron Interactions in Tissue

• The major component of dose from thermal neutrons is a consequence of the 14N(n,p)14C + 0.62 MeV• 0.04 MeV to recoil nucleus (local absorption)• 0.58 MeV to proton (range of ~10-6 m – local)• Dominant energy transfer mechanism in thermal and

epithermal region in body• Kerma = dose

• Another thermal neutron interaction of some consequence is the 1H(n,γ)2H + 2.2 MeV• 2.2 MeV to gamma (nonlocal absorption)• Small amount of energy to deuterium recoil (local absorption)• Kerma ≠

dose (non-local absorption)


References• J. Lilly. Nuclear Physics Principles and

Applications. (2001)• G. Knoll. Radiation Detection and Measurement 2nd

ed. (1989)• P. Rinard. Ch-12 Neutron Interactions with Matter.

http://www.integral.soton.ac.uk/~ajb/00326407.pdf.• Eric J. Hall. Radiobiology for the Radiologist 5th Ed.

(2000)• NCRP Report 38. Protection against Neutron

Radiation. (1971)

http://www.integral.soton.ac.uk/~ajb/00326407.pdf

neutron interactions part i - uthgsbsmedphys.org neutron lecture 01 200… · neutron interactions...

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