Uranium resonance absorption

It is possible, by proper physical arrangement of the materials, to reduce substantially uranium resonance absorption. By the use of light elements as described above for slowing materials, a relatively large increment of energy loss is achieved in each collision and therefore fewer collisions are required to slow the neutrons to thermal energies, thus decreasing the probability of a... 

Experiments on the sky. Two experiments have been carried out at the sky, using two laser installations built for the American and French programmes for Uranium isotope separation, respectively AVLIS at the Lawrence Livermore Nat l Lab (California) in 1996 and SILVA at CEA/Pierrelatte (Southern France) in 1999. The average power was high pa 2 x 175 W, with a pulse repetition rate of 12.9 and 4.3 kHz, a pulse width of 40 ns and a spectral width of 1 and 3 GHz. Polarization was linear. The return flux was < 5 10 photons/m /s (Foy et al., 2000). Thus incoherent two-photon resonant absorption works, with a behavior consistent with models. But we do need lower powers at observatories ... 

The paper of 1939 [1 ], On the Chain Decay of the Main Uranium Isotope, studies the effects of elastic and non-elastic neutron moderation and concludes that chain fission reactions by fast neutrons in pure metallic natural uranium are impossible. The 1940 paper, On the Chain Decay of Uranium under the Influence of Slow Neutrons [2 ], is classic in the best sense of this word its value is difficult to overestimate. The theoretical study performed showed clearly that the effect of resonance absorption of neutrons by nuclei of 238U is a governing factor in the calculation of the coefficient of neutron breeding in an unbounded medium it was concluded that a self-sustained chain reaction in a homogeneous natural uranium-light water system is impossible. 

The multiplication factor /ceff can be appreciably increased by heterogeneous arrangement of uranium and moderator, because resonance absorption of the neutrons by is low after the neutrons have been slowed down in the moderator. Then p becomes markedly higher,/ somewhat lower and //becomes higher than in the case of homogeneous arrangement of fissile material and moderator. 

Filters with resonance absorption peaks, which absorb neutrons only in a narrow range of energies are used to determine E. Two filters have been used in the measurements, either a gold filter with Nd = 7.35 x 1019cm-2, which defines a final energy E = 4908 meV, with an approximately Lorentzian shape of half width at half maximum (HWHM) AE] 140 meV, or a uranium filter with Nd = 1.46 x 102° cm-2, E = 6671 and an approximately... 

Effective neutron cross sections in a uranium-fueled PWR are given in Sec. 6. Because of resonance absorption, effective absorption cross sections for U, U, Pu, and Pu are much higher than the cross sections for 2200 m/s neutrons given in Fig. 3.1. 

The results obtained on the first two subjects were used by me to calculate the optimal geometry and multiplication constant for oxide lattices and to obtain estimates for the same quantity in metal lattices. I arrived at the conclusion - around the middle of November - that the multiplication constant in Fermi s Columbia pile could be increased by about 5% by going over to a lattice with a considerably smaller lattice constant. I expected a further increase of another 5% if one could replace the oxide by metal. This last increase was not really based on the measurements of Creutz and Wilson, but on a theory of the resonance absorption which I developed around this time. On the basis of these calculations and because it became evident that a very considerable improvement in the multiplication constant can be achieved by using materials of a higher purity, I became convinced that a chain reaction is possible in a graphite-uranium mixture and estimated the multiplication constant obtainable with an oxide-graphite lattice as 1.02, with a metal-graphite lattice as 1.07. 

E.Creutz, H. Jupnik, and E.P.Wigner, Effect of Temperature on Total Resonance Absorption of Neutrons by Spheres of Uranium Oxide , J. Appl. Phys. 26, 276 (1955). 

The papers 5-9 record results of experiments on absorption of resonance and thermal neutrons in spheres of uranium performed under Wigner s guidance at Princeton in 1941. These papers appeared originally as project reports but all except Paper. 9 were subsequently published in the open literature. These experiments provide the data on resonance absorption that Wigner used in all calculations of multiplying lattices Paper 9 gives a value for the diffusion length of thermal neutrons in uranium. 

Review of the Measurements of the Resonance Absorption of Neutrons by Uranium in Bulk... 

Therefore, the problems which faced the would-be designers of chain reactors early in 1941 were (1) the choice of the proper moderator to uranium ratio, and (2) the size and shape of the uranium lumps which would most likely lead to a self-sustaining chain reaction, i.e., give the highest multiplication factor. In order to solve these problems, one had to understand the behavior of the fast, of the resonance, and of the thermal neutrons. We were concerned with the second problem which itself consisted of two parts. The first was the measurement of the characteristics of the resonance lines of isolated uranium atoms, the second, the composite effect of this absorption on the neutron spectrum and total resulting absorption. One can liken the first task to the measurement of atomic constants, such as molecular diameter, the second one, to the task of kinetic gas theory which obtains the viscosity and other properties of the gas from the properties of the molecules. The first task was largely accomplished by Anderson and was fully available to us when we did our work. Anderson s and Fermi s work on the absorption of uranium, and on neutron absorption in general, also acquainted us with a number of technics which will be mentioned in the third and fourth of the reports of this series. Finally, Fermi, Anderson, and Zinn carried out, in collaboration with us in Princeton, one measurement of the resonance absorption. This will be discussed in the third article of this series. 

The foregoing facts fairly summarize the information which was available to us when we undertook the investigations to be reported below. Earlier or simultaneous work on resonance absorption includes, first of all, Bethe s calculation of the absorption of uniformly distributed material in a hydrogeneous moderator. Bethe s results were adapted to the particular case of resonance absorption by uniformly distributed (i.e., not lumped) uranium and generalized to other moderators in a classified report by J. A. Wheeler (A-88). We aid not learn about this report until some time in 1943. In addition, both J. Fisk and W. Shockley, and also Eckart, treated the resonance absorption of uranium lumps embedded in a moderator. We still know very little about Fisk s and Shockley s work. Eckart s work... 

Among the theoretical work which is subsequent to ours, we wish to mention the calculations of S. M. Dancoff and M. Ginsburg, contained in report CP-1589. This report gives, on the basis of Anderson s measurements, a quantitative explanation of the results of our third and fourth paper. Our second paper, written before the results of the third and fourth became available, gives only the functional dependence of the resonance absorption on size and shape of the uranium lumps and, as will be seen, only a crude numerical estimate of the absolute magnitude of the resonance absorption of lumps. No calculations have yet been carried out on the basis of the data of reference 12 they are planned, however, when the detailed results become available. 

Effect of Temperature on Total Resonance Absorption of Neutrons by Spheres of Uranium Oxide ... 

The reaction rate of a moderated uranium pile depends on temperature. For example, in a reactor in which the neutron spectrum is approximately Maxwellian, the average velocity will increase with temperature, thus decreasing the absorption cross sections for the low-energy neutrons which vary as 1/v. Resonance levels will be broadened by the Doppler effect, and if lumping of the uranium has been made use of to decrease the total resonance absorption as proposed by Szilard, and later found experimentally to be effective, increased temperature will decrease the advantage thus gained. 

At room temperature both UO2 and UsOg spheres were used. The resonance absorption in the spheres of the higher oxide was greater, as expected, due to the increased scattering of the neutrons by the extra oxygen, thus dropping more neutrons into uranium resonance levels inside the sphere. At the higher temperatures it... 

The absorption of resonance neutrons was dealt with in a report submitted on June 1, 1941. In that report, Appendix A represented results of measurements carried out at Princeton jointly by the Columbia and Princeton groups on The Capture of Resonance Neutrons by a Uranium Sphere Imbedded in Graphite . Appendix A (written by Fermi and Anderson) arrived at a figure of 4800 cm for the volume of a black body equivalent with respect to resonance absorption to a sphere of 8.5 cm radius containing 9170 gm of UaOg. Appendix... 

The absorption coefficient is a macroscopic property characteristic of the material of the sphere. It depends not only upon the absorption cross sections of the constituent atoms and upon their number per cubic centimeter but also upon their scattering cross sections. From the calculated absorption coeflBcient for thermal neutrons and the measurements of resonance absorption already reported for UaOs and in progress for uranium metal and compressed UsOg, it is the intention to deduce the optimum dimensions for the typical cell in the proposed lattice. 

In these and the above equations, the a are cross sections per imit volume, the a in (8) is scattering cross section, the average loss in r per collision. The are used because the material may contain different types of atoms. The (Ta is the thermal absorption cross section r(r) the resonance absorption cross section per unit volume. The = qef is the multiplication constant divided by the resonance escape probability. The product of thermal utilization / and (Ta is the effective cross section of uranium per unit volume, i.e., its cross section per unit volume multiplied by the thermal neutron density in it and divided by the average thermal neutron density. One can write, therefore, (Tu for f(Ta- If one multiplies this with rj the result is the same as crfU where fission cross section for thermal neutrons per unit volume, p the number of fast neutrons per fission. As a result, the third term in (7) can be written also as e is the multiplication by fast effect)... 

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