On the Utilization of Thermal Neutrons

Calculations as will be described below have been made, independently, at various places by C. Eckart in Chicago Fermi, Szilard, and Weil in New York and G. Plass and Wign r in Princeton. The approximations made were, in all cases, those enumerated above and the results are therefore essentially identical. The present Report is being written to make a reference to these calculations easier and also to present a discussion of and corrections for the above approximations. (Cf. Appendices I, II, III for the above approximations.) 

The above approximations make the calculation very simple. At least in the case of a face centered or a body centered lattice, it is a very good approximation to replace the cell by a sphere of equal volume and to assume that the neutron density has zero radial derivative on the surface of the sphere. This is a less good approximation for a simple cubic lattice and the corresponding correction will be given below. This correction constitutes, from the point of view of thermal utilization, the only difference between the simple cubic and face and body centered lattice. For a finite lattice, corrections must be introduced which decrease the thermal utilization. These will be also discussed below. 

If we disregard all these corrections, the neutron density in the inside of the U or oxide will be given by 

The constants with index 0 will all refer to the inner part of the cell i.e., the U or the oxide. The constants of the damper will have to carry an index 1. The kq is the macroscopic absorption coefficient of the inside, given by 

The radius of the U or oxide sphere will be denoted by tq, the radius of the sphere representing the cell by ro + r so that r is the thickness of the layer of damper which surrounds every U or oxide lump. The density of the neutrons in the damper will be 

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Here, r = ln(JB/ thermai) has a somewhat different definition from the usual one it is zero for neutrons, the energy E of which is thermal, (t t) is the transport cross section which may depend on the energy but does not depend on the position thermal neutrons the average logarithmic energy loss (independent of position) <7, the absorption cross section for thermal neutrons which depends on the position. q(r) is the density of fast neutrons per unit r (it is not Fermi s slowing down density Q), multiplied with the velocity, n the density of thermal neutrons times their velocity, /(r) dr is the number of fission neutrons per slow neutron captured in U, for which r is between r and r + dr. Finally pi is the chance of escaping resonance absorption and p2 the thermal utilization. The multiplication constant here... 

Spherical Harmonics Method. Wigner recognized that the diffusion theory approximation in all of these calculations was deficient. However, he was reluctant to invoke more complicated transport theory because the neutrons were not monoenergetic, and any transport correction to the diffusion theory would be obscured by the error caused by the assumption that the thermal neutrons were monoenergetic. He and Breit had used the spherical harmonics method in their original calculations of the size of a bomb, and he supervised the later work at Chicago on the application of the spherical harmonics expansion to calculate the thermal utilization. 

Note that a direct first-order approximation that based the reduction in the thermal utilization on the estimate of the neutrons wastefully absorbed in the cladding, proportional to SLfvN, would not allow for the fact that only a fraction of such neutrons were originally destined to be absorbed in the fuel anyway. Since can be as low as 0.6 or 0.7 at the interface, the correction introduced by the stationary calculation is appreciable. 

Table HI lists the neutron absoiption cross sections for many of the metals described above, as well as their cross section relative to the typical reactor material, zirconium. Materials with a very large cross section relative to zirconium would result in a reduction in the thermal utilization factor f and hence a reduction in Nff. Consequently, Ta, W, V, Mo and Ni based alloys would be impractical choices for a reactor core. From this literature survey, it appears that Fecralloy would provide the greatest promise as a containment material for liquid lead. In addition Tantiron may be an alternate choice. More extensive studies on the applicability of inhibitors such as Ti should be undertaken to determine their affect on the corrosion resistance of these materials. 

The size and composition of the reactor are chosen to be such that the system would be supercritical in the absence of the control rods. The fuel is loaded with the control rods inserted and, on the completion of loading, the control rods are slowly raised, increasing the thermal utilization until criticality is attained. If the control rods are then withdrawn by a further small amount, increasing to a value slightly above unity, the system will be supercritical and the neutron density in the reactor, and hence the fission rate, will increase continuously. Once the desired power level has been attained, the rods are readjusted to restore the system to the critical condition, and the power will remain steady at the chosen level. As has been mentioned earlier, the only reason why the rate of power increase can be held to a practicable value is the existence of delayed neutrons the dynamics of reactor control will be discussed in detail in Chapter 3. 

Nuclear reactors can be designed on the basis of their fuel cycle such that they breed more fissile nuclides than what they use. Breeder reactors can utilize uranium, thorium, and plutonium resources more efficiently. There are two types of breeder reactors (1) fast neutron spectmm breeder and (2) thermal neutron spectmm breeder reactors, which are designed based on (99.2% natural abundance) and Th (100% natural abundance), respectively. Fertile nuclides and Th capture neutrons and trans-form, respectively, to fissile nuclides Pu and U. Through this process, which is known as breeding, the reactor produces more fissile nuclides than what it consumes. Fast-breeder reactors (FBRs) can also be used in order to transmute the long-lived... 

The Th—cycle is of interest due to that the abundance of thorium in the Earth s cmst is between three to five times that of uranium (OECD/NEA and IAEA, 2014). In addition, there are large thorium deposits in some countries such as India, Brazil, Australia, and the USA (WNA, 2015a). The Pu cycle is the most effective with fast neutrons. For Pu, the number of emitted neutrons in a fission reaction per absorbed neutrons is greater when fission is induced by fast neutrons rather than thermal neutrons. The additionally emitted neutrons can be utilized for transforming more nuclides to Pu. Hence, the FBRs are based on Pu in which... 

The radiation - induced changes noted are in weight loss, gas evolution, mechanical sensitivity, thermal sensitivity and stability, and ex pi performance. The effects will be described with the type of nuclear radiation used. The format describes the radiation effects on expls, propints and pyrots with the sequence of radiations utilized (when applicable) as follows, a - particles, neutrons, fission products, reactor radiation (fast and slo w neutrons plus gammas), gammas (7), underground testing (UGT), X-rays, electrons, and other nuclear radiations... 

For the thermal neutron activations, a lOmg Californium-252 ( Cf) source was utilized in a special assembly constructed from a Neutron Howitzer (Trademark of Reactor Experiments, Inc). The assembly is a 6-cu ft cylindrical Lucite tank filled with distilled water and containing three access ports (Fig 3). The large spherical container on the right is the shielded storage cask for the Cf neutron source when not in use... 

T nterest in the separation of isotopes started as a scientific curiosity. The question arose as to whether it was indeed at all feasible or possible to separate isotopes. After this question was answered in the affirmative (24), it became of interest to separate isotopes on a laboratory scale for use in scientific research. A few examples show the range of utility of separated isotopes. Deuterium has attained widespread use as a biochemical and chemical tracer. It is now abundantly available and is used as freely as any cheap chemical reagent. He has opened up an entirely new field of research in low temperature physics and has important applications in the production of temperatures below 1°K. with a thermal neutron cross section of 4,000 barns, has found wide use in nuclear particle detectors—neutron proportional counters. still finds use as a tracer, but in recent years its most frequent use has been in electron spin and nuclear magnetic resonance spectroscopy. occupies a unique position as the only usable tracer for nitrogen. finds application as a... 

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