Wigner-Wilkins neutron/nucleus scattering kernel quantum-mechanically derived
| Autor: | Grzesik, J. A. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We undertake herein to derive 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, cited below, 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. Comment: v3--missing eq. no. (38) supplied; v2 eq. nos. (38) on, and all refs. thereto, advanced by 1; stray right parenth in 1st line args of eqs (35-40) (new enum) removed; 1st line args in eqs (37-38) (new enum) more perspicuously arranged; v4--ref. 10 framed in sharper focus; two minor textual infelicities repaired |
| Databáze: | arXiv |
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