Calculations of liquid helium and neon VUV emission spectra, self-absorption and scattering for a neutrino detector

To evaluate the feasibility of the recently proposed detection scheme of low energy neutrinos released from the Sun and supernovae called CLEAN, Cryogenic Low Energy Astrophysics with Noble Gases, which relies on the transparency of noble-gas cryogenic liquids to VUV radiation produced by neutrinos, we analyze theoretically VUV emission, self-absorption, and scattering of liquid helium and neon, primary candidates for CLEAN. Owing to strong repulsion of noble-gas atoms in the ground states at the equilibrium distance of the relevant excited state, the emission spectrum is substantially shifted from the absorption spectrum, and in principle the absorption is expected very small, allowing building large detectors. Our analysis, however, shows that the self-absorption and Rayleigh scattering are comparable to the size of the proposed detector. Our theoretical emission spectra are found in agreement with experimental observations although some deviation exists due to binary-interaction approximation, and our ab initio Rayleigh scattering lengths are found in agreement with other calculations based on the extrapolation of experimental refraction indices. The absorption process can result in either re-emission, which conserves the number of photons but delays their escape from the liquid, or in non-radiative quenching