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Monoenergetic muon neutrinos at 236 MeV are readily produced in intensemedium-energy proton facilities ($\gtrsim$2-3~GeV) when a positive kaon decaysat rest (KDAR; $K^+ \rightarrow \mu^+ \nu_\mu$). These neutrinos provide aunique opportunity to both study the neutrino interaction and probe the nucleuswith a monoenergetic weak-interaction-only tool. We present cross sectioncalculations for quasielastic scattering of these 236~MeV neutrinos off$^{12}$C and $^{40}$Ar, paying special attention to low-energy aspects of thescattering process. Our model takes the description of the nucleus in amean-field (MF) approach as the starting point, where we solve Hartree-Fock(HF) equations using a Skyrme type nucleon-nucleon interaction. Thereby, weintroduce long-range nuclear correlations by means of a continuum random phaseapproximation (CRPA) framework where we solve the CRPA equations using aGreen's function method. The model successfully describes ($e,e'$) data on$^{12}$C and $^{40}$Ca in the kinematic region that overlaps with the KDAR$\nu_\mu$ phase space. In addition to these results, we present futureprospects for precision KDAR cross section measurements and applications of ourcalculations in current and future experiments that will utilize theseneutrinos.

Modeling quasielastic interactions of monoenergetic kaon decay-at-rest neutrinos