Quantum correlations between protons in potassium bicarbonate

It is shown that a contribution to the total scattering of neutrons by a single crystal of KHCO3 held at 15 K arises from a purely quantum-mechanical and diffuse addition to scattering from identical particles which, in this instance, are protons in small dimers in a configuration described by a monoclinic crystal structure. The addition to scattering engages the total single-atom cross-section, and this feature explains why it is not visible in deuterated crystals where the relevant cross-section is down by an order of magnitude. Moreover, two other features of KHCO3 make it a favourable case in which to observe the quantum-mechanical addition to scattering. First, the addition increases with decreasing nuclear spin I and I = 1/2 for protons Secondly, there are two dimer orientations in KHCO3 and their contributions to scattering overlap in reciprocal space and produce high intensity in the form of rods. Our successful model of the observed scattering represents the protons as an ensemble of independent dimers with the appropriate crystal arrangement. Scattering from a dimer is calculated including quantum-mechanical correlations of the nuclei (protons) that in a homonuclear diatomic molecule produce ortho- and parastates.