Probing Neutron Skins with KDAR Neutrinos: From Coherent to Diffractive Elastic Neutrino–Nucleus Scattering

Abstract We investigate coherent elastic neutrino–nucleus scattering (CEνNS) induced by pion-decay-at-rest (πDAR) and kaon-decay-at-rest (KDAR) neutrinos, with emphasis on the transition from strict coherence to the coherent–to–diffractive regime. Organizing CEνNS observables in terms of the dimensionless variable qR, we show that πDAR measurements remain largely confined to the near-coherent region for the nuclei considered here, whereas KDAR neutrinos (Eν = 236 MeV) extend the kinematics into qR ≳ 1, where recoil spectra begin to develop shape sensitivity to the nuclear weak form factor. Using representative light, medium-mass, and heavy nuclei (12C, 40Ca, 48Ca, and 208Pb), we compare Helm and two-parameter Fermi weak-density models and quantify benchmark statistical sensitivities to neutron-skin variations at a JSNS2-like facility. For a total exposure of 10 ton·year and representative KDAR fluences, the one-parameter, stat-only sensitivities improve from about $\Delta R_{np}^{(1\sigma )}\simeq 0.09$ to 0.02 fm for 48Ca and from ≃ 0.07 to 0.02 fm for 208Pb as the fluence increases. We further perform two-parameter benchmark checks in the Helm and 2pF model spaces to quantify how the leading surface-shape nuisance affects the weak-radius inference and its local neutron-skin equivalent. This nuisance produces the largest degradation for 12C, moderate degradation for 40Ca and 48Ca, and only a small effect for 208Pb under the detector assumptions adopted here. These results indicate that KDAR-based CEνNS can provide a complementary electroweak probe of weak-charge distributions and neutron-surface structure beyond the near-coherent limit, while emphasizing the benchmark and model-dependent scope of the present sensitivity estimates.