Past exam of the particle physics course of the University of Oxford / 2017 / 3 / e / Solution

Place a far detector near the first atmospheric disappearance maximum, approximately $1.2\mathrm{km}$ for the source's monochromatic energy and splitting, and a nearly identical near detector a few hundred metres from the reactor complex. Their flux-corrected comparison largely cancels reactor power, emitted-spectrum and absolute-efficiency uncertainties. For a broad reactor spectrum one fits energy-dependent disappearance instead of treating that single baseline as a universal exact optimum.

Detect ${\bar{\nu }}_{e}p\to e^{+}n$ in a hydrogen-rich target, for example liquid scintillator with neutron-capture enhancement. The prompt Positron signal estimates neutrino energy; the delayed neutron-capture signal supplies a time-and-position coincidence that strongly reduces random backgrounds. Use sufficient target mass and exposure, low radioactivity, overburden and a muon veto to reduce cosmogenic backgrounds, calibrated relative energy response and efficiency, and monitored reactor powers and baselines. Account for multiple reactor cores, spent-fuel backgrounds and accidental coincidences. At kilometre baselines the slow solar phase is small, so the disappearance depth directly probes ${\sin }^2(2{\theta }_{13})$ with little sensitivity to the CP phase or mass ordering.