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Wigner-Wilkins Neutron/Nucleus Scattering Kernel Quantum Mechanically Derived

J. A. Grzesik

Nuclear Science and Engineering / Volume 197 / Number 6 / June 2023 / Pages 1255-1263

Technical Note / dx.doi.org/10.1080/00295639.2022.2138064

Received:August 15, 2022
Accepted:October 17, 2022
Published:May 4, 2023

We undertake to derive herein the Wigner-Wilkins (W-W) neutron/nucleus scattering kernel, a foundation stone in neutron thermalization theory, on the basis of a self-contained calculation in quantum mechanics. Indeed, a quantum-mechanical derivation of the W-W kernel is available in the literature, but it is, in our opinion, robbed of conviction by being couched in terms of an excessive generality. Here, by contrast, we proceed along a self-contained route relying on the Fermi pseudopotential and a first-order term in a time-dependent Born approximation series. Our calculations are fully explicit at every step, and, in particular, we tackle in its every detail a final integration whose result is merely stated in the available literature. Furthermore, and perhaps the most important point of all, we demonstrate that the quantum-mechanical W-W kernel outcome is identical down to the last iota with its classical antecedent, classical not only by virtue of historical precedence but also by being based on classical Newtonian mechanics.