  A new method is proposed for cooling neutrons by inelastic magnetic
scattering in weakly absorbing, cold paramagnetic systems. Kinetic neutron
energy is removed 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. Analytical solutions of the stationary
neutron transport equation are given using inelastic neutron scattering cross
sections derived in an appendix. They neglect any inelastic process except the
paramagnetic scattering and hence still underestimate very-cold neutron
densities. Molecular oxygen with its triplet ground state appears particularly
promising, notably as a host in fully deuterated oxygen-clathrate hydrate, or
more exotically, in dry oxygen-He4 van der Waals clusters. At a neutron
temperature about 6 K, for which neutron conversion to ultra-cold neutrons by
single-phonon emission in pure superfluid He4 works best, conversion rates due
to paramagnetic scattering in the clathrate are found to be a factor 9 larger.
While in conversion the neutron imparts only a single energy quantum to the
medium, the multi-step 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 K (100 K), for the moderator held at about
1.3 K. Due to a favorable Bragg cutoff of the oxygen-clathrate the
cascade-cooling can take effect in a moderator with linear extensions smaller
than a meter. The paramagnetic cooling mechanism may offer benefits in novel
intense sources of very cold neutrons and for enhancing production of
ultra-cold neutrons.
