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Hypersharp Neutrino Lines

Neutrino lines from very long lived nuclei in simple crystals such as metals have hypersharp natural width, motionally narrowed by lattice vibrations in analogy to recoilless emission. A generalized hypersharp line fraction including the recoilless part can be derived in a frequency modulation approach. The nue lines of natural width in 3H to 3He 2-body beta-decay can then be resonantly captured with geometrical cross section. The extreme sharpness DeltaE/E~10-29 of the tritium nue line can probe the Planck length L via its limits on the widths of states, DeltaE/E(L) =L(L/R)beta =10-20(beta ~1) to 10-40 (beta= L/R(fm)). Stringent limits can be set on beta, thus, on models of quantum gravity.