Effective Resonance Integral Research Articles

Dependence of Effective Resonance Integrals on Moderator Slowing Down Properties

Effective resonance integrals calculated by means of the usual approximations do not have the dependence on moderator slowing down properties which is shown by “exact” calculations. In this paper a modified effective resonance integral is defined in such a way as to fit the exponential form of the resonance escape probability. Application of a generalised “intermediate-resonance” approximation to this modified effective resonance integral shows a dependence on the slowing down properties of the moderating nuclei in good agreement with “exact” calculations.

The Effective Resonance Integral of Thorium Oxide Rods

The effective resonance integral of thorium oxide rods has been determined as a function of their surface-to-mass ratio. The range of S/M values covered is 0.15 - 0.65 cm2/g. An experimental techni...

Dependence of Effective Resonance Integrals on Moderator Slowing Down Properties

Effective resonance integrals calculated by means of the usual approximations do not have the dependence on moderator slowing down properties which is shown by “exact” calculations. In this paper a modified effective resonance integral is defined in such a way as to fit the exponential form of the resonance escape probability. Application of a generalised “intermediate-resonance” approximation to this modified effective resonance integral shows a dependence on the slowing down properties of the moderating nuclei in good agreement with “exact” calculations.

The temperature dependence of effective resonance integrals

Algebraic approximations to the function J( ϵ, β) are derived to investigate temperature behaviour of the effective resonance integrals of resonances of different energy. Temperature dependences between − 1 2 for high-energy resonances and T +1 for low-energy resonances are shown to exist. The effect on the overall temperature behaviour of effective resonance integrals is discussed.

Effect of Temperature Variation on “Intermediate-Resonance” Formulas

>Calculations were made on the effects of working temperatures on the intermediate-resonance'' interpolation formulas of Goldstein and Cohen (ibid., 13: 132) for effective resonance integrals in homogeneous systems. The results, computed by a numerical FORTRAN procedure, are tabulated for several resonances of U/sup 238/ in a homogeneous 1: 1 dilution in H/sub 2/ and for the 192-ev resonance of U/sup 238/ in 1:1 to 1:100 dilutions in H/sub 2/ at 0 to 900 deg K. It is concluded that the temperature variation has only a small effect on the integral. (D.L.C.)

3組拡散近似臨界方程式の一改良

The critical equation in the 3-group diffusion approximation was improved by taking into account all the epithermal reactions. For the effective cross section, Westcott's formulation is followed, wherein the s-factor was modified so as to give the epithermal effect accurately. In connection with evaluating the modified s-factor, simple formulas for the effective resonance integrals of U²³⁵ and U²³⁸ were derived for a very dilute homogeneous system and for a natural uranium rod. The present method was applied to the criticality calculation for JRR-3 (Japan Research Reactor No. 3), a natural uranium-heavy water moderated heterogeneous reactor, which went critical on Sept. 13, 1962. The prediction as to the criticality was verified fairly well. (auth)

Some Experimental Results Pertinent to Equivalence Relations for Effective Resonance Integrals

An experimental test of several equivalence relations for effective resonance integrals is obtained from measurements of U238 resonance escape probability for lattices of the TRX critical facility,...

Effective Resonance Integral Dependence on the Moderator Slowing Down Properties

It is shown by exact calculation of the resonance absorption in an infinite homogeneous mixture for resolved resunances of U/sup 238/ how far the moderator slowing down properties and the interference scattering actually influence the effective resonance integral and its temperature coeificient. Results are compared with the narrow resonance and narrow resonance infinite mass absorber approximations. (W.D.M.)

The measurement of the effective resonance integrals of uranium and thorium using the pile oscillator operating inside a cadmium tube

The feasibility of determining resonance absorption integrals by performing pile oscillator measurements inside a cadmium tube has been studied. It was concluded that reliable results could be obtained with this technique for strong resonance absorbers, but that large corrections were necessary for weakly absorbing materials, particularly those of low atomic weight. The technique has been used to determine the effective resonance integrals of uranium and thorium metal and oxide rods of various sizes.

Resonance absorption in 239Pu and its effect on the temperature coefficient of irradiated uranium rods

The effective resonance integral for both fission and radiative capture is first calculated for differentsized rods of pure 239Pu at various temperatures in a graphite-moderated lattice. Then the contribution from 239Pu to the effective resonance integral of irradiated uranium rods in a graphite moderator is evaluated for the same rod sizes and temperatures, concentrations of 0·15 per cent and 0·2 per cent 239PU being considered in turn. The fuel temperature coefficient is estimated at both concentrations and compared to the temperature coefficient of the same rods at zero irradiation. The fractional change in fuel temperature coefficient due to 239Pu build-up is found to be small, in the absence of any allowance for neutron spectrum distortion in the region of the lowest 239Pu resonance, due to neutron thermalization.

Calculation of the Effective Resonance Integral of U238

Methods for determining an effective resonance integral from available resonance parameter data are examined and applied to lumped systems where the absorber is U238. Agreement with experiment is s...

Radial dependence of the doppler effect in bars of uranium and thorium

If a lump containing uranium or thorium is heated in a reactor spectrum, the rate of neutron capture changes. This is called the ‘Doppler effect’. An experimental investigation shows that uniform heating of a sample of thorium or uranium causes a constant fractional increase in activation per atom throughout the main volume of the sample, upon which is superposed a peak close to, but inside, the surface of the samples. The peak rises above the volume effect by factors of 8 and 3 for uranium and thorium respectively and extends to a depth of 0·2 mm and 1·5 mm in the two cases. It is shown theoretically that this peak in the Doppler effect is due to activation in the resonances below 100 eV from impinging neutrons which have not suffered a potential scattering event. However, the theory predicts that at large penetrations the Doppler effect in the uncollided flux results in a decrease in activation with increasing temperature i.e. the opposite sign from the peak. Thus when averaged through a thick rod the net contribution of the resonances below 100 eV to the Doppler effect is small. It is predicted that the Doppler effect will be a maximum for uranium lumps 0·2 mm in size, the resonances below 100 eV being responsible for the maximum. An attempt is made to take account of the resonance scattering of the impinging flux. The volume Doppler effect arises mainly from the presence of potential scattering and the unresolved resonances make the larger contribution. Predictions made by L. DRESNER for the temperature dependence of the volume term of the effective resonance integral are consistent with the experimental results at the centre of the sample. For 1 in. bars of uranium and thorium, the experimental values of the Doppler coefficient ( 1 I +) ( d I +/dT ) are found to be (0·90 ± 0·17) × 10 −4 per °C and (2·7 ± 0·1) × 10 −4 per °C, where I + is the average effective resonance integral including the 1 v- contribution above the cadmium cut-off.

The effective resonance absorption integral of 238U in heavy-atom mixtures

The resonance absorption of neutrons by 238U in admixtures containing elements of medium or high atomic weight is considered. The contributions of the eighteen resolved resonances are calculated for three different dilutions corresponding to potential scattering cross-sections per 238U atom of 10 barns (pure 238U metal), 100 barns and 1000 barns. A good approximation is obtained to the exact Hurwitz solution for a non-hydrogeneous moderator, from which the effective resonance integrals are calculated. The effect of Doppler broadening at T = 300°K is included. The region of unresolved resonances is taken from 420 eV to 1 MeV and the resonance integrals are evaluated for this region, taking into account levels associated with l > 0 neutrons. Important differences are found from the predictions of a simple ‘narrow resonance’ approximation.

Resonance Escape Probability in Water Lattice

In light water-moderated reactors the effects of adjacent fuel on resonance escape probability must be considered. These effects are a decrease of surface absorption and modification of the slowing down density by absorption. Modifications of the standard formula for calculating p are described and the results of detailed calculations on enriched uranium-dioxide fuel rods in water lattices are given. The effective resonance integral is calculated by the method of Wigner et al.

The Effective Resonance Integral of Thorium and Thorium Oxide

The effective resonance integral has been measured for thorium metal rods and plates and for ThO/sub 2/ rods of two different densities. Measurements were carried out in a cadmium tube in the center of a swimming-pool type research reactor using conventional danger coefficient'' techniques. Absolute calibration was obtained by the use of boron samples. (auth)

Measurements of the Effective Resonance Integral in Uranium Metal and Oxide in Different Geometries

A series of measurements of the effective resonance integral in uranium metal and oxide, UO2, has been made. Measurements were performed on simple rods, on a few tubes, empty or filled with a moderator, and on clusters of rods. Formulas for the effective resonance integral as a function of S/M and (S/M)½ are given for metal and UO2. In addition the variation of the resonance absorption of neutrons as a function of depth in metal rods has been studied. The results are given in the form of curves.

Resonance Absorption of Neutrons by Thorium Cylinders

The integrated effective resonance neutron absorption cross section of thorium-232 cylinders has been experimentally investigated by danger coefficient measurements in the Hanford Test Pile. The results were interpreted to yield the effective resonance integral as a function of the surface-to-mass ratio of the thorium cylinders. The experiments were extended to determine the Doppler coefficients resulting from heating the thorium in a constant neutron energy spectrum in the reactor. After correction for 1/v neutron absorption, the effective resonance integral can be approximated as a function of the surface-to-mass ratio by ∫ (σa0)effdE′E′=6.11[1+5.0SM(1−0.87SM)]. The value assigned to the Doppler coefficient of the volume absorption of the effective resonance integral is 1A∂A∂T=(2.3±0.2)10−4/∘C. The results are compared to similar measurements on uranium.

Resonance Absorption of Neutrons by Uranium Cylinders

The integrated effective resonance neutron absorption cross section of uranium-238 cylinders has been experimentally investigated in the Hanford Test Pile. The results of reactivity measurements were interpreted to yield the effective resonance integral as a function of the surface-to-mass ratio of the uranium cylinders. The experiments were extended to determine the Doppler coefficients resulting from heating the uranium in a constant neutron spectrum in the reactor. The effective resonance integral, ∫ (σa0)effdE′/E′, can be approximated as a function of the surface-to-mass ratio by ∫ (σa0)effdE′E′=6.0{1+15.6SM[1−2.18SM+2.19(SM)2]}. The Doppler coefficient of resonance escape probability for the reactor is 1p∂p∂T=(−2.14±0.16)10−5/∘C,and the value assigned to the coefficient of the volume absorption of the resonance integral is 1A∂A∂T=(1.56±0.12)10−4/∘C.

Effect of Geometry on Resonance Neutron Absorption in Uranium

A simple theoretical expression has been derived for the geometric dependence of the effective resonance integral of uranium which is independent of the details of resonance structure. Comparison w...