Neutron conversion and cascaded cooling in paramagnetic systems for a high-flux source of very cold neutrons

Abstract

A new neutron-cooling mechanism is proposed with potential benefits for novel intense sources of very cold neutrons with wavelengths $g2$ nm, and for enhancing the production of ultracold neutrons. It employs inelastic magnetic scattering in weakly absorbing, cold paramagnetic systems. Kinetic energy is removed from the neutron stepwise in constant decrements determined by the Zeeman energy of paramagnetic atoms or ions in an external magnetic field, or by zero-field level splittings in magnetic molecules. The stationary neutron transport equation is analyzed for an infinite, homogeneous medium with Maxwellian neutron sources, using inelastic scattering cross sections derived in an appendix. Nonmagnetic inelastic scattering processes are neglected. The solution therefore still underestimates very cold neutron densities that should be achievable in a real medium. Molecular oxygen with its triplet ground state appears particularly promising, notably as a host in fully deuterated ${\mathrm{O}}_{2}$-clathrate hydrate. Other possibilities are dry ${\mathrm{O}}_{2}\text{\ensuremath{-}}^{4}\mathrm{He}$ van der Waals clusters and ${\mathrm{O}}_{2}$ intercalated in fcc-${\mathrm{C}}_{60}$. For conversion of cold to ultracold neutrons, where an incident neutron imparts only a single energy quantum to the medium, the paramagnetic scattering in the clathrate system is found to be stronger, by more than an order of magnitude, than the single-phonon emission in superfluid helium, when evaluated for an incident neutron spectrum with the optimum temperature for the respective medium. Moreover, the multistep paramagnetic cooling cascade leads to further strong enhancements of very cold neutron densities, e.g., by a factor 14 (57) for an initial neutron temperature of $30\phantom{\rule{4pt}{0ex}}\mathrm{K} (100\phantom{\rule{4pt}{0ex}}\mathrm{K})$, for the moderator held at about $1.3\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Due to a favorable Bragg cutoff of the ${\mathrm{O}}_{2}$ clathrate, the cascade-cooling can take effect in a moderator with linear extensions smaller than a meter.