Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering

We consider here the numerical determination of the discrete spectrum of the neutron transport operator in a homogeneous subcritical infinite medium in the case of highly anisotropic scattering. Under mild assumptions on the scattering coefficients, one knows that the discrete spectrum is a finite set whose elements are real with absolute values larger than 1. Under these assumptions, we describe a method to compute all eigenvalues for an arbitrary order of anisotropic scattering. The method has been implemented in a C++ library using IEEE double precision arithmetic, allowing for fast calculations. Numerical results are compared to values in literature and to high‐precision calculations using Maple.

Keywords:

• Neutron transport operator
• Discrete spectrum
• Anisotropic scattering

Acknowledgments

The authors wish to thank the referees for their valuable comments and suggestions for improving the paper. The last author acknowledges continuous financial support from the Belgian Fonds National de la Recherche Scientifique (FNRS).