Quantum Induced Broadening- A Challenge For Cosmic Neutrino Background
  Discovery
  A recent preprint by Cheipesh {\it et al.} pointed out that the zero-point
motion of Tritium atoms bound to Graphene may blur the measured energies of
$\beta$ electrons. Smearing due to zero point motion is well known. Such an
effect features in studies of the $\beta$ spectrum expected in experiments like
KATRIN using diatomic Tritium. The recent preprint may, however, challenge new
planned experiments seeking to discover the Cosmic Neutrino Background (CNB)
neutrinos (and/or other neutrinos of masses smaller than $0.1$ eV) which plan
to use Tritium adsorbed onto Graphene or other materials. Our paper clarifies
these issues and examines the more general problem of smearing induced by
quantum uncertainty. We find that the effect of Cheipesh {\it et al.} is
reduced considerably. The importance of the chemical evolution of the $^{3}$H
atom hosting the Tritium nucleus into a tightly bound neutral $^{3}$He atom is
emphasized. We estimate the excess blurring caused by the dense spectrum near
the lowest state of the Graphene or other hosts of the Tritium atom, generated
by the electronic response to the "sudden" escape of the $\beta$ electron. Our
analysis suggests yet larger effects and difficulties facing many experiments
searching for small mass neutrinos. We speculate on a possible experimental
setup which could minimize quantum broadening.
