Nuclear Science and Engineering / Volume 22 / Number 4 / August 1965 / Pages 451-454
Technical Paper / dx.doi.org/10.13182/NSE65-A20631
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Starting from the observation that exponentials of lethargy are just eigenfunctions of the elastic-scattering-energy transfer operator, a Fourier transform with respect to lethargy is applied to the energy-dependent Boltzmann equation. For constant cross sections and isotropic scattering in the center of mass system (but arbitrary anisotropy in the laboratory system) this leads to a ‘one-velocity’ transport equation with a complex number of secondaries. Hence, if the method of Case is now to be applied it has to be extended to cover this situation. For an infinite medium, however, the solution may readily be obtained by a Fourier transform with respect to the space coordinate. Thus, the exact result is a double Fourier inversion integral, which can be calculated numerically. It is shown that well-known solutions can be obtained by an approximate evaluation of this integral.