Abstract
A study of convergence in the orthogonal expansion method for analyzing time-eigenvalue problems in neutron thermalization has been made using several kinds of base functions (orthonormal system). The results confirmed the superiority of the velocity polynomials over the energy polynomials, but demanstrated further that still other base functions can provide convergence even faster than with the velocity polynomials. In particular, a newly developed base in the form of an exponential series in energy offers a convenient tool. Time-eigenvalue problems are analyzed for the cases of proton gas, heavy gas and heavy Einstein solids, where particularly characteristic spectra are studied in some detail using the new base functions.
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