  The time evolution of a neutrino is dependent on its initial properties at
creation including flavor, energy, and wavepacket size. There exists no solid
theoretical prediction for the latter property in the context of nuclear beta
decay, despite the importance of this process for the past, present, and future
of neutrino experimentation. In this paper, we provide a quantitative
prediction for the size of a beta-decay-induced electron antineutrino
wavepacket by treating the parent nucleus decaying to an entangled
antineutrino-recoil system using the formalism of open quantum systems. Of
central importance is the delocalization scale of the parent particle. We
construct a systematic description of the hierarchy of localizing entanglements
that provides an unambiguous statement of the relevant localization scale,
found to be closely related to the diameter of the parent nucleus (e.g.
$\sim$5-6~fm for beta-decaying fission daughters) and as low as the typical
nucleon-nucleon correlation distance ($\sim$1~fm). Inside a nuclear reactor,
for example, this translates to initial electron antineutrino wavepacket widths
in the $\sigma_{\nu,x}\sim10\mathrm{-}400$~pm range for
$E_{\overline{\nu}_e}>1.8$~MeV, with dependencies on decaying nucleus size, the
emitted antineutrino energy, and the kinematics of the recoiling system.
Wavepacket sizes in this envelope do not produce an observable effect on
oscillation probability in foreseeable reactor experiments in the standard
three-neutrino model, including JUNO which is expected to be sensitive to
$\sigma_{\nu,x}\lesssim3$~pm.
