  We examine whether protons and deuterons in the crystal of
KH$_{0.76}$D$_{0.24}$CO$_3$ at 300 K are particles or matter waves. The neutron
scattering function measured over a broad range of reciprocal space reveals the
enhanced diffraction pattern anticipated for antisymmetrized macroscopic states
for protons (fermions). These features exclude a statistical distribution of
protons and deuterons. Raman spectra are consistent with a mixture of KHCO$_3$
and KDCO$_3$ sublattices whose isomorphous structures are independent of the
isotope content. We propose a theoretical framework for decoherence-free proton
and deuteron states.
