Isotropic neutron sources

Consider, therefore, planar distributions of isotropic neutron sources in an infinite homogeneous slab. The medium is of infinite extent in both y and z directions and of width 2a in the x direction (d is the extrapolated... 

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 most practical neutron source for NAA is a nuclear reactor, which produces neutrons via the nuclear fission process (see Chap. 57 in Vol. 6). Many research reactors are equipped with irradiation facilities that provide a stable, well-tailored, isotropic neutron field with sufficiently high flux. Low-energy (thermal) neutrons comprise the most important part of the reactor spectrum hence the degree of moderation is an important parameter. The irradiation channels are usually created in moderator layers, such as a thermal column or a Be reflector blanket. 

In the limit as r —> 0, we obtain from (5.83) the relation AwDB = 90. The neutron flux due to an isotropic point source is, therefore,... 

Plane-source Distribution. The plane source of neutrons may be regarded as a uniform distribution of point sources over an infinite plane. Consider then the case in which isotropic point sources are distributed uniformly over a plane at x = 0, such that qo neutrons are released per unit time per unit area from all points of this plane. The flux at any... 

Consider, therefore, an isotropic point source of fast neutrons in an infinite medium. If denotes the macroscopic scattering cross section of the fast source neutrons, and the source releases go neutrons per unit time, then the density of first-scattering collisions at radial distance r from the source is given by... 

Let us examine now the analogous problem of the distribution of one-velocity neutrons in the space-time system. Consider, then, an isotropic plane source of neutrons in an infinite medium. The initial condition is that a burst of neutrons per unit area is released from the source (placed for convenience at the origin) at time, say, t = 0. These neutrons have speed i>, and they retain this speed for all subsequent time ... 

Because the neutron direction is known, the FNAP approach does not require the use of coUimators to focus the incident beam and there is no need to pulse the source. However, as the neutrons are emitted in an essentially isotropic distribution, many neutrons still fail to impact the target bag and neutron shielding is needed in aU directions surrounding the source and bag regions. In addition, the scattering of the neutrons in the shielded material along with the resulting inelastic and capture... 

Finally, we can compute the flux from a source of neutrons Sn assuming the source is isotropic. (This is true of sealed tube sources. Note that even if API is used, the source is still isotropic although we may generate a trigger only for the forward-going neutrons.) The flux, at a distance rs, is just the total source strength divided by the area of a sphere of radius rs, so we get... 

In source development, there is a need for more compact and reliable accelerator-based neutron systems. The advantage of accelerator-based technology (as distinguished from DD or DT systems) lies in the ability to both vary the energy of the neutrons and, with kinematic focusing, limit the angles of neutron production, i.e. produce neutrons in the forward direction rather than isotropically. However, sealed tube generators, both... 

The source neutrons can be isotropically distributed in direction, in a fixed direction, or within given ranges of the direction cosines. 

Scattering experiments using either neutron or X-ray sources can serve information on the atomic displacement parameters of atoms at specific crystallographic sites. The framework forming atoms can be considered as Debye sohd, wherein the isotropic ADPs (Ujso) are related to Gq via. 

We suppose that there are no extraneous sources, and that fission neutrons are produced isotropically. Then the number of fission neutrons produced in unit interval around (x,E,Sl,t) is... 

Equation (1) is the general kerjiel form of the reactor equation for the angular flux under the restriction of no extraneous sources, constant ratio of fissionable species, and isotropic emission of fission neutrons. 

Measurements of fast neutron dose in water have also been made with an isotropic, monoenergetic (14.1 Mev) source [7]. For penetrations up to six mean free paths the experimental results are about 15% higher than the results of a moment calculation. The discrepancy is presumably due to the uncertainty as to the scattering cross sections for oxygen which must be fed into the calculation. 

By analyzing a particularly simple special case, namely, that of neutrons created by a plane isotropic source and diffusing in an infinite homogeneous medium, Marshak [5] has concluded that the approximations made in the derivation of the age equation from the Boltzmann equation are valid provided that ... 

Here the quantities g and S are not functions of Q (the isotropic assumption) an equation like (1) is present for each neutron velocity group (the multigroup approach), so that v, g, N, and S receive subscripts g, g = I, 2, , G. The equations are coupled through the source S, here defined as a linear combination of the average fluxes Ng, plus an independent source Qg ... 

The multiplication factors were calculated using the 16-group cross sections of Hansen and Roach for uranium and carbon and the KENO code which is a multigroup Monte Carlo method with isotropic scattering and with neutron slowing down treated by a transfer matrix. Twenty-one thousand neutron histories (105 batches of 200 source neutrons each) were calculated requiring a time of 20 min on the IBM 360-75 for each proUem. The source neutrons were put in the uranium uniformly and the first five batches were discarded. 

Boundary condition (1) is essentially as before. Boundary condition (2 ) may be illustrated by deriving the appropriate relations for the interface condition in a system in which the flux is a function of only one space coordinate. Consider, therefore, two semi-infinite media with different diffusion properties and with a common boundary at x = 0. Denote the medium to the left by the index m = 1 and that to the right by m = 2. Further to generalize the problem, assume that at the interface there is a plane of isotropic sources with strength go neutrons per unit area per unit time. Assume also that the presence of this source does not alter the diffusion properties of the media. If denotes the partial... 

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