Neutrons have three main categories of energy - thermal, epithermal, and fast. Thermal neutrons have the lowest energy of around 0.025 eV. They interact primarily through elastic and inelastic scattering. Elastic scattering is important for slowing down fast neutrons in nuclear reactors through collisions with light nuclei like hydrogen. Inelastic scattering can excite the target nucleus, which then emits gamma rays. Neutrons are classified based on their energy ranges and most probable velocities depend on temperature according to Maxwell-Boltzmann distribution.

1. Neutron Energies, Velocity & Thermal
Neutrons
Abdul Rizwan (Reg# 2007-Mech-2616)
Waleed Mumtaz (Reg# 2007-Mech-2615)
Adnan Rasheed (Reg# 2007-Mech-2557)
Adnan Khan (Reg# 2007-Mech-2620)
Suhaib Ilyas (Reg# 2007-Mech-2595)

2. Neutron
 Sub atomic particle
 No charge and greater mass
 Free neutrons are unstable
 High penetrating power
 Essential in Fission process

4. Neutron Source
Different sources of neutrons are:
 Radioisotopes which undergo spontaneous fission
 Radioisotopes which decay with alpha particles
 Radioisotopes which decay with high energy photons
co-located with beryllium or deuterium
 Plasma focus and plasma pinch devices
 Light ion accelerators

5. Neutron Energies
 Neutron energy indicates a free kinetic energy,
usually given in electron volts
 En= mnV2/(2*gc) = 5.227*10-13 V2 ( eV)
 Fission neutron energy range is (0.075……..17 ) MeV
 Prompt neutron vs delayed neutron
 Prompt neutrons have average energy of about 2 MeV.

6. Prompt Neutron Energy Spectrum U235

7. Classification of Neutrons
• neutrons are classified according to their energy
• thermal neutrons have an energy of about
~ 0.025 eV
• epithermal neutrons, resonance neutrons, slow
neutrons have energies between 0.01 MeV and 0.1
MeV
• fast neutrons - 0.1 MeV and 20 MeV
• relativistic neutrons

8. Neutron Energy Distribution
Ranges
 Fast neutrons > energy approximately 1 MeV
 Slow neutrons > energy less than or equal 0.4 eV
 Epithermal neutrons > energy 1 eV to 10 keV
 Hot neutrons > energy about 0.2 eV
 Thermal neutrons > energy of about 0.025 eV
 Cold neutrons > energy 5x10−5 eV to 0.025 eV
 Very cold neutrons > energy 3x10−7 eV to 5x10−5 eV
 Ultra cold neutrons > energy less than 3x10−7 eV
 Continuum region >energy 0.01 MeV to 25 MeV
 Resonance region >energy 1 eV to 0.01 MeV
 Low energy region > energy less than 1 eV

9. Thermal Neutrons
 Slow neutron having energy 0.025 eV
 Results from scattering
 Moderator mediums are H , D , BeO, Be
 Neutrons at a given temp posses wide range of
energies and corresponding speeds
 Maxwell-Boltzman distribution:
2π
f (E ) = e − E / kT E 1/2
( πkT )3/2

10. Most Probable Neutron Velocities
• Most probable neutron velocity is given by
• Vm=(2kT/m)0.5=128.39 T0.5
v=most probable velocity of neutron (m/sec)
k=Boltzman's constant (1.3805*10-23 J/ K)
T=absolute temperature in degrees Kelvin ( K)
m =mass of neutron 1.66 x 10-24gram
• The energy corresponding to Vm is given by
Em= kT = 8.617*10-5 T (eV )
At T = 20 0C
Vm = 2200 m/sec
Em =0.025 eV

11. Thermal Neutron Speeds & Energies
Temperature 0C Vm ( m/sec) Em (eV)
20 2200 0.0252
260 2964 0.0459
537.8 3656 0.0699
1000 4580 0.1097

12. Velocity Distribution At Two
Temperatures

13. Interaction of Neutrons
 Neutrons are uncharged and can travel
appreciable distances in matter without
interacting
 Neutrons interact mostly by inelastic scattering
or elastic scattering

14. Inelastic Scattering
• A part of the kinetic energy that is transferred
to the target nucleus upon collision
• The nucleus becomes excited and a gamma
photon/photons are emitted

15. Elastic scattering
• Interaction between fast neutrons and low atomic
number Z
• For slowing down neutrons
• Responsible for neutron – slowing in reactors
• Fast neutrons lose K.E. As A result of scattering
collisions with nuclei which act as moderators

17. Interaction of Neutrons
.......E o , M, V → m.......
(before collision)
.......E, M, V1 → m, ν 1 .......
(after collision)

18. Continued…
• total kinetic energy and momentum are
conserved and we have:
1
2
MV 2 = 1 MV12 + 1 mv 1
2 2
2
and MV = MV1 + mv 1
•Solving for V1 and substituting into:
(M - m)
V1 = V
(M + m)

19. Continued…
1
E 0 = MV for incident neutron
2
2
1
and E = MV12 we get
2
2
M−m
E = E0  
M +m
• The energy transferred to target nucleus is:
  M - m 2 
E 0 - E = E 0 1 -   
 M +m 
 

20. Continued…
1 2 1 2 4mME
Emax = MV -
2 2 MV1 = 2
(M + m )
• when: M = m; E = Emax
•for neutrons in a head on collision with hydrogen all
the kinetic energy can be transferred in one
collision since the mass of neutrons and protons
are almost equal.