Neutron importance

E. Greenspan, Theory and Measurement of Neutron Importance in Nuclear Reactors, CURL-15 Cornell Univ. Reactor Lab. (1966) see also E. Greenspan and K. B. Cady, Trans. Amer. Nucl. Soc. 9, 243 (1966). 

The adjoint function and neutron importance. Equation (64) leads to an interesting interpretation of the adjoint function mo which may be used to gain an intuitive understanding of the results of perturbation theory. A neutron may be regarded as having an importance to the chain reaction that is proportional to the amplitude of the persistent mode that it eventually goes into. The adjoint function mo(a ) may then be called the importance of a neutron at a . It is also known as the iterated fission probability. A natural normalization is such that the importance is unity for one neutron distributed in the persistent mode. Equivalently, the average importance is unity for neutrons in the persistent mode. In this normalization... 

Thus, N may be regarded as the total neutron importance in the reactor as in Equation (68), the Ct as the latent importance of the delayed neutron emitters as in Equation (69), and... 

The effect of a thermal-neutron absorber on the reactivity of a nuclear reactor is found experimentally as a function of the absorber position in the reactor. The relative thermal flux at each location of the absorber is determined by counting a wire, made of dysprosium dispersed in aluminum, which is irradiated in the reactor. The experimentally determined absorber importance function is compared with the importance function based on one-group perturbation theory, and a neutron importance in the reactor as a function of position is determined by comparison with the results of a two-group perturbation theory. 

The reactivity effect of the sample is therefore found to be proportional to the product of the neutron flux and the neutron importance at the location of the sample. The product is known as the importance function for an absorber placed in the reactor. 

In reactor perturbation theory, the neutron importance 0+ is the adjoint flux obtained by interchanging rows and columns in the neutron-flux matrix operator and solving. The resulting solution is orthogonal to the flux. 

In one-group perturbation theory the neutron flux is self-adjoint, that is, the neutron importance has the same variation with position in the reactor as does the flux. For this case, the importance function becomes the square of the flux or, for an absorber placed in the reactor. 

Two-group perturbation theory predicts a neutron importance having a somewhat different variation with position than does the neutron flux. 

The normalized thermal-flux-squared curve is obtained by squaring values obtained from the smooth curve drawn through the flux data points. The neutron importance is obtained by dividing the importance function values found from the importance function curve by the thermal-flux values... 

Results will consist of the normalized plots of thermal flux, thermal-flux squared, importance function, and neutron importance as a function of position in the reactor. 

Am undergo fission with thermal neutrons of these isotopes and Pu are the most important as they are most readily obtainable. Other heavy nuclei require fast neutrons to induce fission such neutrons are much more difficult to control into a self-sustaining chain-reaction. 

The use of IP can enable the NR and neutron imaging in general with rather low intensity neutron beams which is Of importance both for neutron beam research as well as for extending NR for the in-the field use in the industry. With the existing reactor based neutron facilities the use of IP can drastically reduce the inspection time ... 

Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. 

The structure of a fluid is characterized by the spatial and orientational correlations between atoms and molecules detemiiued through x-ray and neutron diffraction experiments. Examples are the atomic pair correlation fiinctions (g, g. . ) in liquid water. An important feature of these correlation functions is that... 

Because the neutron has a magnetic moment, it has a similar interaction with the clouds of impaired d or f electrons in magnetic ions and this interaction is important in studies of magnetic materials. The magnetic analogue of the atomic scattering factor is also tabulated in the International Tables [3]. Neutrons also have direct interactions with atomic nuclei, whose mass is concentrated in a volume whose radius is of the order of... 

Many scientifically and teclmologically important substances caimot be prepared as single-crystals large enough to be studied by single crystal diffraction of x-rays and, especially, neutrons. If a sample composed of... 

The development of neutron diffraction by C G Shull and coworkers [30] led to the detennination of the existence, previously only a hypothesis, of antiferromagnetism and ferrimagnetism. More recently neutron diffraction, because of its sensitivity to light elements in the presence of heavy ones, played a cmcial role in demonstrating the importance of oxygen content m high-temperature superconductors. 

Two of the most important functions in the application of neutron scattering are the use of deuterium labelling for the study of molecular confomiation in the bulk state and the use of deuterium solvent in polymer solutions. In the following, we will consider several different applications of die general fomuda to deuteration. 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

For bulk structural detemiination (see chapter B 1.9). the main teclmique used has been x-ray diffraction (XRD). Several other teclmiques are also available for more specialized applications, including electron diffraction (ED) for thin film structures and gas-phase molecules neutron diffraction (ND) and nuclear magnetic resonance (NMR) for magnetic studies (see chapter B1.12 and chapter B1.13) x-ray absorption fine structure (XAFS) for local structures in small or unstable samples and other spectroscopies to examine local structures in molecules. Electron microscopy also plays an important role, primarily tlirough unaging (see chapter B1.17). 

Uranium-235 is of even greater importance because it is the key to utilizing uranium. 23su while occuring in natural uranium to the extent of only 0.71%, is so fissionable with slow neutrons that a self-sustaining fission chain reaction can be made in a reactor constructed from natural uranium and a suitable moderator, such as heavy water or graphite, alone. 

Its importance depends on the nuclear property of being readily fissionable with neutrons and its availability in quantity. The world s nuclear-power reactors are now producing about 20,000 kg of plutonium/yr. By 1982 it was estimated that about 300,000 kg had accumulated. The various nuclear applications of plutonium are well known. 238Pu has been used in the Apollo lunar missions to power seismic and other equipment on the lunar surface. As with neptunium and uranium, plutonium metal can be prepared by reduction of the trifluoride with alkaline-earth metals. 

Atoms with the same number of protons but a different number of neutrons are called isotopes. To identify an isotope we use the symbol E, where E is the element s atomic symbol, Z is the element s atomic number (which is the number of protons), and A is the element s atomic mass number (which is the sum of the number of protons and neutrons). Although isotopes of a given element have the same chemical properties, their nuclear properties are different. The most important difference between isotopes is their stability. The nuclear configuration of a stable isotope remains constant with time. Unstable isotopes, however, spontaneously disintegrate, emitting radioactive particles as they transform into a more stable form. 

One of the important advantages of NAA is its applicability to almost all elements in the periodic table. Another advantage of neutron activation is that it is nondestructive. Consequently, NAA is an important technique for analyzing archaeological and forensic samples, as well as works of art. 

A neutron is characterized by having no electrical charge but has one unit of atomic mass, the same as that of a proton (Figure 46.2). Neutrons, like protons, reside in the atomic nucleus and contribute to the mass of the atom. The chemistry of an atom, like its size, is determined by the electrons in the atom. The mass of the atom is characterized mainly by the total number of neutrons and protons in the nucleus (atomic binding energies are ignored in this discussion). For mass spectrometric purposes of measurement, it is the mass that is important in establishing m/z values. 

Chain reactions do not go on forever. The fog may clear and the improved visibility ends the succession of accidents. Neutron-scavenging control rods may be inserted to shut down a nuclear reactor. The chemical reactions which terminate polymer chain reactions are also an important part of the polymerization mechanism. Killing off the reactive intermediate that keeps the chain going is the essence of these termination reactions. Some unusual polymers can be formed without this termination these are called living polymers. 

Plutonium as the important isotope Pu is prepared in ton quantities in nuclear reactors. It is produced by the following reactions, wherein the excess neutrons produced by the fission of are captured by to yield Pu. 

---