Quantum formulation of a magneto-catalytic reaction

A general quantum formulation of an ortho-para hydrogen conversion reaction on dilute paramagnetic catalysts by means of tensorial algebra is developed. An efficiency operator describing the tensorial structure of the conversion rate is built, and important selection rules pertaining to the tensorial ranks are derived. Taking into account the time and spatial symmetries of the system, an expansion of the density operator over some multipole operators is performed. A magnetic field allows one to separate and thus to measure the relative influence of the magnetic dipoles and electric quadrupoles. It is concluded that the important field acceleration, observed by Selwood, corresponds to "dipole" highly polarized states. These states may be described by an alignment of the H₂ nuclear spins along the electronic spins of chromium catalysts, or along the H₂ rotational angular momentum when rare-earth catalysts are used.