Monoenergetic muon neutrinos at 236 MeV are readily produced in intense medium-energy proton facilities $(\gtrsim 2–3\mathrm{GeV})$ when a positive kaon decays at rest (KDAR; $K^{+}\to {\mu }^{+}{\nu }_{\mu }$). These neutrinos provide a unique opportunity to both study the neutrino interaction and probe the nucleus with a monoenergetic weak-interaction-only tool. We present cross-section calculations for quasielastic scattering of these 236-MeV neutrinos off ${}^{12}\mathrm{C}$ and ${}^{40}\mathrm{Ar}$, paying special attention to low-energy aspects of the scattering process. Our model takes the description of the nucleus in a mean-field approach as the starting point, where we solve Hartree-Fock equations using a Skyrme type nucleon-nucleon interaction. Thereby, we introduce long-range nuclear correlations by means of a continuum random-phase approximation (CRPA) framework where we solve the CRPA equations using a Green's function method. The model successfully describes ($e,e^{\prime }$) data on ${}^{12}\mathrm{C}$ and ${}^{40}\mathrm{Ca}$ in the kinematic region that overlaps with the KDAR ${\nu }_{\mu }$ phase space. In addition to these results, we present future prospects for precision KDAR cross-section measurements and applications of our calculations in current and future experiments that will utilize these neutrinos.

• Received 19 October 2020
• Revised 10 February 2021
• Accepted 10 May 2021

DOI:https://doi.org/10.1103/PhysRevC.103.064603