Neutron distribution

Parity violating electron scattering. Recently it has been proposed to use the (parity violating) weak interaction to probe the neutron distribution. This is probably the least model dependent approach [31]. The weak potential between electron and a nucleus... 

Up to now,we always assumed a U coupled pair distribution to give a good description of both the proton 2p-2h excitation and of the neutron distribution over the valence model space.The quadrupole component of the proton-neutron force will induce 0+- 2+ pair breaking for both protons and neutrons which we call the core polarization effect.Thus,0 ground state and intruder wave functions... 

It is important to recognize these limitations on the performance of neutron interrogation systems using 14MeV neutrons with respect to uniformity of sensitivity and potential application of timing methods, because, as we have seen, these sources have essentially isotropic neutron distributions. 

The experimental equipment serves to measure a relative neutron flux density and can be used for recording and time analysis of neutron distribution when determining SRP subcriticality by pulse and stationary methods. 

I85,i87j g74+ j32]. There is thus renewed interest in the analysis of the so-called Bohr-Weisskopf effect [17,18], calling for an improved theoretical description of the nucleus [32], and a suitable way to relate the electronic and nuclear parts of the calculation. The situation is similar to the studies of parity non-conservation, where the unknown neutron distribution would lead to an uncertainty in the interpretation of experiments for chains of isotopes [33,34], larger than the expected experimental uncertainty. 

In the absence of an experimental neutron density, we use the theoretical neutron distribution function from a calculation that reproduces the experimental charge radius [47]... 

In the determination of the number of fissions in an irradiated sample by the use of flux monitors, account must be taken of the flux depression in the sample due to self-shielding to obtain an effective flux. Also, the capture cross sections of the monitors and the fission cross sections of the sample are neutron energy dependent. It is, therefore, necessary to know the eneigy distribution of the neutrons or the neutron temperature and to determine effective cross sections (Section IV). This can be done by using two monitors such as cobalt and samarium, the one monitor being used to determine the neutron temperature corresponding to the neutron distribution as described by Fritze et al. (35). 

Effective attenuation length beneath inclined or partially shaded surfaces. As the attenuation length A for cosmogenic nuclide production by spallation (Eqn. 20) is determined by the angular cosmic ray neutron distribution, it increases when part of the... 

Liu B, Phillips FM, Fabryka-Martin JT, Fowler MM, Stone WD (1994) Cosmogenic C1 accnmulation in unstable landforms 1. Effects of the thermal neutron distribution. Water Resom Res 30 3115-3125 Mamyrin BA, Tolstikhin IN (1984) Helium Isotopes in Nature. Elsevier Science Pnblishers, Amsterdam Marti K, Craig H (1987) Cosmic-ray-produced neon and helium in the snimnit lavas of Maui. Nature 325 335-337... 

The first-order approximations in the integral transport theory formulations partially account for the effect of the perturbation on the neutron distribution. 

Second, there are the characteristics that depend on the neutron distribution in the system. These characteristics also have, usually, a direct dependence on the material densities. Examples of characteristics of this type, to be referred to as nucleonic characteristics, are breeding ratio, total power, power shape factor, and reactivity worth. The variation of the functional fiV/], denoting a general nucleonic characteristic, caused by a small but otherwise arbitrary variation 5N in the density distribution of the ith material, is... 

The orthogonality condition of Eq. (253) can be interpreted somewhat differently. Since there are no negative neutrons (or anti-neutrons), and no processes to produce them, the source-free self-sustaining (or critical) system will have a neutron distribution that is positive definite. The neutron density in a critical reactor that is subjected to a physical source is ever increasing. In other words, the time-independent Eq. (252) can have no solution when T is a physical source. In order for Eq. (252) to have a steady-state solution,... 

The adjoint source in Eq. (259) represents some detector distribution which, when integrated over the reactor space (after weighting with the neutron distribution), yields a single measure of the reactor behavior. Physically, there is no reason why such a detector distribution should be positive definite. The existence condition [Eq. (260)] for a solution to Eq. (259) in a critical system, however, as in the neutron balance equation, requires the orthogonality of and V and since is (physically) positive definite, must be part positive, part negative. Physically, this orthogonality condition, therefore, expresses the idea that the acceptable virtual adjoint sources are detector distributions which, when reacting to the distribution of neutrons in the fundamental mode, lead to no total or net effect. 

While a detector distribution with varying sign is physically acceptable, we may easily see that the fundamental solution of the critical adjoint equation must be nonoscillating (either positive definite or negative definite) if the fundamental neutron distribution is positive definite. The fundamental adjoint solution describes the relative contribution of neutrons at different places in the system when the ultimate progeny of these neutrons have distributed themselves into the fundamental mode and are all positive of course. Whatever the detector distribution at that time, therefore, the effect of the earlier neutron upon it varies with the location of that neutron according to some scale factor, but may not vary in sign. 

The calculation of the heat distribution in the reflector mas based oh the neutron distribution for the very thin slab reactor eithout any thorium (Fig. 4.2.F) since in this case the heat load in the reflector is heaviest. The results are given in Fig. 4.5.A. To simplify the computation of the y- ray absorption, the core and reflector were assumed to be infinite slabs this, leads to an overestimate of the heat load since.the neutron flux was assumed to be uniform over the-whole core and equal to 2, 10. ... 

A2.1.3 Besults and Dincnssion. Experiments were performed with DjO, beryllium, and H O reflectors to find (1) critical mass, (2) neutron distributions, and (3) values of control rods, cavities, etc., in terms of fuel. Various ratios of A1 to HjO were used. These experiments served as a check on the theoretical calculations of critical masses under the same conditions. The values for the critical mass found in both theory and experiment are compared in Table A2.A. 

The situation in spatial neutron distribution is shown in Fig. A2.E, which contains both experimental and theoretical radial distributions. These... 

Vertical neutron distributions were studied also ,typical results.-will be found in Fig. A2.F.. -It will be recalled that no reflector was present at top or bottom of the experimental pile, and the solid lines are cosine curves fitted to. points near the center by a. least-squares method. The slight lateral shift of. the data from center is apparently due to the presence of a portion of a control rod in the top of the pile.- It is clear that the extrapolation distances for thermal and epithermal neutrons are the -same, within the experimental limits. 

Several of the neutron distributions.were Measured as follows ... 

Figures A3.F, G, H These show the neutron distributions along the axes of the. various experimental holes which were planned for the high-fluxreactor. These measurements were made with all seven 6-in. holes (or equivalent) in the reflector. 

NEUTRON DISTRIBUTIONS ALONG AXIS OF 6" HOLE AT EDGE OF REACTOR... 

SIX INCH HOLES IN REFLECTOR LATERAL NEUTRON DISTRIBUTIONS (ALONG AXIS OF EDGE HOLE)... 

The lower solid-line curve in Fig. A3.J represents the total heat production in the reflector calculated from theoretical considerations. This calculation was based oh the neutron distribution for a thinner slab pile (70 by 11 by 60 cm) where the heat load in the reflector is somewhat heavier than in the case of the assembly in which our measurements were made (71 by 17 by 66 cm). The measured spatial thermal-neutron distribution in this assembly is shown as a dotted curve. 

When the manganese samples were exposed covered with Cd, considerable activity was still noticed. Hence, in some cases, a second exposure was made with the samples in the same positions except that all but the monitor sample were covered with cadmium. Thus the non-thermal component could be subtracted. The non-thermal part will be discussed later. Figs. 12 a, b, c, d, e show thermal neutron distributions so obtained in the graphite block in various directions with and without the uranium spheres. Figure 8 shows the agreement... 

B 29 Mn02 U Metal 5.7 8.6 20 cm 2/3 H Narrow Sample Mn neutron distribution across block with sphere (thermal + resonance Mn neutron distribution... 

Since there are no neutrons with energies greater than those corresponding to r < —7.5 in the group of neutrons represented by the first term of (20 a), this term should be taken to be zero when t < —7.5. A similar remark applies to the second term when f < —17. The results are given in Fig. 5. The experiments on the resonance absorption should be carried out where the neutron distribution is most nearly natural in the relevant region (from 5 eV to 15000 eV), i.e. where Qo Is, between t = 1.3 and t = 9.3, most nearly independent of t. 

The neutron distributions in the three regions are determined as solutions of diffusion equations subject to the conditions that the neutron and neutron current densities be continuous across the interfaces and the neutron current vanish at the periphery of the cell. (cf. C-104). The distributions so determined are ... 

As was just mentioned, quantum theory limits the accuracy with which the classical variables of position and velocity can be specified. On the other hand, it introduces a new characteristic for particles their spin. Properly speaking, this should also be one of the variables of the flux O, or, more concretely, two flux functions are actually needed to specify the neutron distribution completely. One of these, 4>r, would describe the flux due to neutrons of right helicity (spin parallel to velocity), the other, Oz, would describe the flux due to neutrons of left helicity (spin antiparallel to velocity). There are transitions in which the helicity of neutrons changes so... 

The higher terms in the expansion of qi represent transients which die away much more rapidly than the fundamental, i = 1, Hence the fact that di (a constant) is a good approximation to the true average disadvantage factor means that the neutron distribution reaches its stationary shape very little below the top of the resonance band. The actual computation of the dj, or equivalently, the computation of A,, is performed by solving the characteristic equation (29). The form of this equation will depend on the particular function Zj, and these functions depend, in turn, on the geometry of the system. 

In order to compare the calculation of the disadvantage factor based on a Gaussian slowing down model (section 5) with its calculation based on an exponential model (section 4) we shall recalculate the neutron distributions of section 4 by expanding them in terms of the characteristic functions of section 5. 

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