Thermal, Epithermal and Fast Neutron Spectra
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General Properties of Key Fissile and Breeder NucleiEdit
Key nuclear data for the nuclides ^{232}Th, ^{233}U, ^{235}U, ^{238}U, ^{239}Pu and ^{241}Pu is provided in the table below. To complement the table, a brief description of practice for defining and quantifying thermal and epithermal neutron fluxes is first given.
In the literature, the ‘cadmium cutoff’ energy defines the boundary between terming a neutron to be in the thermal or epithermal energy regime. The definition arises from ^{113}Cd, which has a particularly large neutron absorption coefficient below neutron energies of 0.55 eV, above this energy the probability of neutron absorption rapidly reduces, see the Figure to the right. The probability of capturing thermal neutrons is sometimes quoted at the velocity 2200 ms^{1}. This corresponds to the mode neutron velocity for a Maxwellian energy distribution at 20 °C ( eV).
The (n,γ) reaction rate can be described as, for thermal and epithermal neutrons combined. Where the rate of neutron absorption is, (s^{1}); and are the conventional thermal and epithermal neutron fluxes (cm^{2}), respectively; is the neutron capture crosssection at 2200 ms^{1} (barns); is the infinite dilution resonance integral (cm^{2}); and is the epithermal flux distribution parameter [Verhijke 2000].
Whereas the thermal energy spectrum can be described simply by the neutron flux and the corresponding crosssections for absorption, describing the absorption of epithermal neutrons is more complex as a result of the presence of resonances. The conventional epithermal neutron flux term, , is specifically defined as the integrated flux of all neutrons whose energies lie in the epithermal range. The equation that determines the infinite dilution resonance equation (which is equivalent to the thermal neutron absorption crosssection) includes a term that makes the magnitude of its crosssection inversely proportional to the energy of a neutron (this corrects for the nonuniform neutron flux distribution for different energies, not accounted for by the term). In real reactors the neutron flux is not only nonuniform, but also not an ideal distribution, the energy dependence correction to is therefore also modified, this time by the epithermal flux distribution term, [Yucel and Karadag 2004, Karadag and Yucel 2004].
The notation in the table belowis such that is the crosssection for thermal or fast neutron absorption, of which fissions and captures; epithermal crosssections use the same notation style, replacing with ; is the mean number of neutrons emitted by a fission event; is the net number of fissionneutrons yielded per neutron absorbed; is the fraction of those yielded neutrons that are emitted only after the β^{}decay of a fission fragment or one of its daughters, they are hence the delayed neutron fraction. In addition to the data presented in the table below a series of figures are given in the section on selected nuclear data (below), these show evaluated nuclear data for a range of neutron energies regarding capture and fission crosssections and fission neutron yields. The data is taken from the National Nuclear Data Center.
Nuclear Data 
^{232}Th 
^{233}U 
^{235}U 
^{238}U 
^{239}Pu 
^{241}Pu 

Crosssection (barns)  
Thermal  
Absorption 
4.62 
364 
405 
1.73 
1045 
1121 
Fission 
0 
332 
346 
0 
695 
842 

0.096 
0.171 
0.504 
0.331  

2.26 
2.08 
1.91 
2.23  
Epithermal  
Infinite dilution epithermal resonance integral () 
0 
764 
275 
0 
301  

85.6 
882 
405 
278 
474 
740 

746 
272 
293 
571  

0.182 
0.489 
0.618 
0.296  

2.10 
1.63 
0.618 
0.296  
Fast (averaged)  
Absorption 
0.317 
2.948 
2.321 
0.345 
2.213 
2.948 
Fission 
0.0086 
2.684 
1.814 
0.037 
1.751 
2.426 

36.04 
0.0096 
0.280 
8.414 
0.264 
0.215 
Approx. yield for any neutron energy  
Total neutron yield 
2.16 
2.48 
2.43 
2.54 
2.87 
2.97 
Delayed neutron fraction 
0.026 
0.0031 
0.0069 
0.017 
0.0026 
0.0050 
Fission energy yield (MeV) (excluding neutrino) 
188.5 
191.0 
193.5 
198.0 
198.8 
202.0 
The data in the above tableshows that when exposed to thermal neutrons ^{239}Pu and ^{241}Pu absorb them at approximately 2.5 times the rate that ^{233}U and ^{235}U do. The breeder nuclei, ^{232}Th and ^{238}U, absorb them at a rate 23 orders of magnitude less. ^{239}Pu and ^{241}Pu emit the most neutrons (on average) during fission, however their neutron capture/fission ratio is poor compared to ^{233}U and ^{235}U. Among the presently considered nuclides, ^{233}U emits the most neutrons during fission that will go on to cause another fission reaction. This continues to be the case for an epithermal neutron flux. The capture/fission ratio for all nuclei is less favourable in the epithermal energy regime compared to thermal, however the ratio reduces the least for ^{233}U.
The crosssections for neutron absorption reduces by orders of magnitude for the fissionable isotopes listed above. Small quantities of the breeder nuclei will fission. ^{233}U maintains a near identical ratio for capturesfission, however for ^{235}U, ^{239}Pu and ^{241}Pu the ratio is less good. The trend for other isotopes of these elements and also for minor actinides tends to be that the capturefission ratio improves in the fast spectrum.
The delayed neutron fraction is a significant property when gauging the controllability of a reactor. Increasing the delayed neutron fraction correspondingly reduces the rate of change of reactivity in the core, thus allowing for more time to intervene and return the core reactivity to the desired steady state. ^{235}U has the largest delayed neutron fraction among the presently considered nuclides, the ^{233}U delayed neutron fraction is less than half that of ^{235}U.Per fission, 2.5 MeV less is released for ^{233}U than for ^{235}U.
Between the two breeder nuclides, ^{232}Th has a smaller epithermal resonance crosssection. For nuclei in this energy regime, ^{232}Th is therefore less sensitive than ^{238}U to negative Doppler reactivity feedback.
Verheijke, M.L., 2000, “On the Relationship between the Effective Resonance Energy and the Infinite Dilution Resonance Integral for (n,γ) Reactions”, Journal of Radioanalytical and Nuclear Chemistry, 246, pp. 161163
Yucel, H. and Karadag, M., 2004, “Experimental determination of the αshape factor in the 1/E^{1 + α} epithermalisotopic neutron sourcespectrum by dual monitor method”, Annals of Nuclear Energy 31, pp. 681695
Karadag, M. and Yucel, 2004, H. “Measurement of thermal neutron crosssection and resonance integral for ^{186}W(n,γ)^{187}W reaction by the activation method using a single monitor”, Annals of Nuclear Energy 31, pp. 12851297
Kazimi, M.S., Czerwinski, K. R., Driscoll, M.J., Hejzlar, P. and Meyer, J.E., 1999, “On the use of Thorium in Light Water Reactors” Massachusetts Institute of Technology, USA, MITNFCTR016
NNDC, Updated October 2009, “σigma Evaluated Nuclear Data Files (ENDF) Retrieval and Plotting” Version 3.1, National Nuclear Data Center, USA. http://www.nndc.bnl.gov/sigma/ [Accessed 9th March 2010]
Rubbia, C., Buono, S., Gonzalez, E., Kadi, Y., Rubio, J.A., 1995, “A realistic Plutonium Elimination Scheme with Fast Energy Amplifiers and Thorium‑Plutonium Fuel” European Organisation for Nuclear Research, CERN/AT/95‑53 (ET)
Selected Nuclear DataEdit
The data for all of the following figures has been taken from the National Nuclear Data Center, Evaluated Nuclear Data Files [NNDC 2010].
NNDC, Updated October 2009, “&simga;igma Evaluated Nuclear Data Files (ENDF) Retrieval and Plotting” Version 3.1, National Nuclear Data Center, USA.