Reading Wikipedia I get that 56Fe has a fast neutron scattering crosssection of 20 barns vs a thermal neutron crosssection of 10 barns, i.e. lower. Is this really true? If so, are there other materials like that and more exagerated? Also, are there reactors exploiting this fact?
Reading Wikipedia I get that 56Fe has a fast neutron scattering cross section of 20 barns vs a thermal neutron crosssection of 10 barns, i.e. lower. Is this really true?
Fe isn't exactly a moderator, but it does have a relatively high 'fast neutron removal' cross section, and some reactor designs, e.g., some US PWRs, use steel (mostly Fe in SS304) neutron reflector pads (or neutron pads, or panels) to reflect neutrons back to the core and reduce neutron fluence to the reactor pressure vessel.
See Figure 4.2-10 in the following section of an updated UFSAR. https://www.nrc.gov/docs/ML2331/ML23319A066.pdf
Lower Core Support Structure
The major containment and support member of the reactor internals is the lower core support
structure, shown in figure 4.2-10. This support structure assembly consists of the core barrel;
the core baffle; the lower core plate and support columns; the neutron shield pads; and the core
support, which is welded to the core barrel. The major material for this structure is type 304
stainless steel. The lower core support structure is supported at its upper flange from a ledge in
the reactor vessel and, at its lower end, is restrained in its transverse movement by a radial
support system attached to the vessel wall. Within the core barrel are an axial baffle and a
lower core plate, both of which are attached to the core barrel wall and form the enclosure
periphery of the core. The lower core support structure and core barrel provide passageways
and direct the coolant flow. The lower core plate is positioned at the bottom level of the core,
below the baffle plates, and provides support and orientation for the fuel assemblies.
page 4.2-36 of cited UFSAR
The design issues are more complicated that simply looking at the scattering cross sections. One must consider the absorption cross section as well, and for all cross section, one has to consider the entire neutron energy spectrum. For thermal reactors, one would consider the neutron spectrum from 1.0E-3 to 1.0E7 eV. For fast reactors, one may neglect the thermal energy range and address 0.1-1 keV to 10 MeV. Some might consider energies up to 12 to 20 MeV, but the population of fission neutrons above 10 MeV is relatively small. Absorption of neutrons leads to transmutation, and one would have to consider (n,γ) where A increases to A+1, then with β-decay, Z incrases by 1. With fast neutrons, above a certain threshold, nuclei may experience (n,p) and (n,α), whereby upon neutron absorption, the nucleus ejects either a proton or alpha particle. Both p and α then neutralize and form H and 4He, respectively, which are usually found in small cavities, voids or bubbles in the metal crystal structure.
One must also consider the isotopic vector of the elements of intersest. It may be impractical to separate the most desirable isotope from the others. Note the following abundances.
Code:
Z el A Atomic mass Abundance
23 V 51 50.943 957 04(94) 0.997 50(4)
24 Cr 52 51.940 506 23(63) 0.837 89(18)
26 Fe 56 55.934 936 33(49) 0.917 54(36)
74 W 184 183.950 930 92(94) 0.3064(2)
V51 has a very high abundance, Fe-56 less so, and Cr-52 and W-184 much less.
Please see attached figures which compare Fe-56 with W-184, then with Cr-52, and the third adding V-51. Vanadium is of interest since it has relatively low activation, and it fills a gap between Fe-56 and W-184.
Must also consider thermophyscial (density) and thermo-mechanical (e.g., strength), and corrosion resistance.
LWRs use high burnup fuel on the core periphery, since it operates at low power, and reduces the neutron leakage fo the reactor pressure vessel.
Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is
$$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$
##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...
Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark.
Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true.
But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy
\langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67}
The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form
f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
