Slowing down kernel

It can be seen from Table I that discrepancies of about 2.5% exist between the calculation and the experiments. Possible sourcSs of the discrepancies are the choice of thermal-scattering kernel, slowing-down model and poor high-energy non-elastic cross sections. Calculations of these effects m being performed It is hoped that these calculations plus experimental determination of energy-flux distributions and position dependent reactivity coefficients will serve to Isolate the effects responsible for the miscalculation. 

Finite models. Because of their mathematical simplicity, theoretical models of the types described above are those most frequently analyzed in detail in the reactor literature. However, the self-adjoint nature of the differential operators postulated is not typical of real reactor problems neither is the symmetry of the associated integral kernels. This is because, physically, neutron life-histories are not reversible in heterogeneous reactors, even statistically the optical reciprocity theorem [4, p. 82] is not vaUd when slowing down is considered. 

The calculations used the SPECTRUM code with a polyethylene kernel to obtain thermal cross sections and the GAM slowing down code to generate epithermal group constants. These c ss sections were then used in the S-Xin (Ref. 6) transport theory code to carry out a 4-energy group, 13 double-angle calculation. The microscopic cross sections used are- based on the work of Liikala, except that the Pu-239 cross sections are normalized to those of Sher for 2200 m/sec. 

If a slowing-down model is specified, the neutron age to thermal energy may also be deduced from, the mea- sured d. The two-group diffusion kernel model gives ... 

Fig. 2-6. Comparison of critical concentrations obtained for various slowing-down kernels in D2O. Core radius =39 cm, total age =237 cm for all kernels, diffusion length of pure moderator, Lo = 40,200 cm. Fuel only in core.

The vertices couple density fluctuations of different wavelengths and thereby capture the cage effect in dense fluids [2], It thus enters the theory as a nonlinear feedback mechanism where density fluctuations slow down because of increased friction, and where the friction (precisely the time integral over the memory kernel that dominates the long-time collective friction coefficient) increases because of slow density fluctuations. MCT is a first-principles approach as the vertices are calculated from the microscopic interactions ... 

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