Neutron s

Classification of ne utrons by energy

Therm a l: E < 1 eV (0.025 eV) Epithermal: 1 eV < E < 10 keV Fast: > 10 keV

Neutron sources Neutron energies

Reactors neutrons i n the few keV to several MeV

Fusion reactions 14 MeV

Large accelerators Hundreds of MeV

Energy Deposition by Neutrons

 Neutrons are generated over a wide range of energies by a variety of different processes.

 Like photons, neutrons are uncharged and do not interact with orbital electrons.

 Neutrons can travel considerabl e distances through matter without interacting.

 Neutrons will interact with ato m ic nuclei through se veral mechanism s .

o Elastic scatter

o Inelastic scatter

o Nonelastic scatter

o Neutron capture

o Spallation

 The type of interaction depends on the neutron energy

Cross Sections

 Because mass attenuation coefficients, µ/ ρ (cm 2 /g) have dimensions of cm 2 in the numerator, they have come to be called “ cross sections ”.

 Cross sections do not repres ent a physical area, but a probabili t y of an interaction.

 Cross sections usuall y expre ssed in the unit, barn: (10 -24 cm 2 )

 The ato m ic cross sections can be derived from the mass attenuation coefficient.

Photons

Cross sections are att e nuation coeffici ents, expressed at the atom l e vel (Probability of interaction per atom )

N A = atom density (#atom s/cm 3 )

N A 



A N 0

 A = atomic cross section (cm 2 /atom )

0

= 6.02 x 10 23 ato m s/ mol e

  N A  A

 = g/cm 3

A = g/ mole

   N 

A 0 A

 N 0  A     A 

  A

 A      N 

   0 

Neutron Cross Sections

Analogous to photons

 Neutrons interact by different mech anism s depending on the neutron energy and the material of t h e absorber

o Scattering

 elastic

 inelastic

o Capture

 Each ener gy loss mechanis m h a s a cross section

 Neutron cross sections expre ssed in barns (1 barn = 10 -24 cm 2 ).

 These cross sections depend on th e neutron energy and the absorber

Moderation : slowing down of fast neutrons

Fast neutrons lose energy in a series of scatter even ts, mostly elastic s cat ter. Lower energy neutrons:

 scattering continues

 probabil i t y of capture increases (captu re cross sections increase at lower energies)

Thermal Neutron Cross Sections

Nuclide	Cross sect ion (barns)
10 B	3 8 3 7
11 B	0.005
12 C	0 . 0 0 3 5
1 H	0 . 3 3
14 N	1 . 7 0
35 C l	4 3 . 6
23 N a	0 . 5 3 4
157 G d	2 5 4 , 0 0 0
153 G d	0 . 0 2

Cross Sections

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Total cross sections for neutrons with hydrogen and carbon as a function of energy

 For hydrogen the co ntributors to the total cross sect ion are el astic scatter (predom inant) and neutron capture (  = 0.33 barns at thermal neutron energy).

 For carbon, the cross section is co mplex due to the different nuclear states possi ble that may enhance or suppress elastic or inelas tic scatter at particular neutron energies.

Neutron Interactions

Elastic scatter : The m o st im portant process for slow ing down of neutrons.

 Total kinetic energy is conserved

 E lost by the neutron is transferred to the recoiling particle.

 Maxim u m energy transfer occurs with a h ead-on collision.

 Elastic scatter cross sections depend on energy and material.

Q  4 mME n

max ( M  m ) 2

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Inelastic scatter

 The neutron is absorbed and then re-em itted

 The nucleus absorbs some en ergy internally and is left in an excited state. e.g., 14 N(n,n  ) 14 N E  = ~ 10 MeV

 De-excitation em its a gamma ray.

 In tissue, inelastic scatter reactions can occur in carbon, nitrogen and oxygen.

Nonelastic scatter

 Differs from inelastic scattering in that a secondary particle that is not a neutron is em itted after the cap ture of the initial neutron.

e.g. , 12 C(n,  ) 9 Be E  = 1.75 MeV

 Energy is transferred to the tissue by th e alpha particle and the d e -excitatio n gamma ray.

Neutron capture

 Sam e as nonelastic scatter, but by defi niti on, neutron capture occurs onl y at low neutron energies (therm al en ergy range is < 0.025 eV).

 Capture leads to the disa ppearance of the neutron.

 Neutron capture accounts for a significan t fraction of the energy transferred to tissue by neutrons in the low energy ranges.

e . g . , 14 N(n,p) 14 C Q = 0.6 26 MeV E p = 0.58 MeV

1 H(n,  ) 2 H Q = 2.2 MeV E  = 2.2 MeV

 The hydrogen capture reaction is the m a jo r contributor to dose in tissue from thermal neutrons. Because th e gamma is fairly energetic, the dose to tissue will depend on the volum e of tissue irradiated.

 Boron Neutron Capture

10 1

5 0

 4 He 

7 Li

 0 . 48 MeV 

Q = 2.31 MeV

E α = 1.47 MeV E Li = 0.84 MeV

Spallation

 In this process, after the neutron is captured, the nucleus fragments into several parts. Only im portant at ne utron energies in excess on 100 MeV. (cross sections are higher at 400-500 MeV).

 The dose t o tissue comes fro m t h e seve ral neutrons a nd de-excitation gamma rays which are em itted.

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