All CPT self-conjugate particles, in particular the Majorana fermion, are forbidden from having any multipole moments other than toroidal moments. At tree level (i.e. without allowing loops in Feynman diagrams) an anapole-only particle interacts only with external currents, not with free-space electromagnetic fields, and the interaction cross-section diminishes as the particle velocity slows. For this reason, heavy Majorana fermions have been suggested as plausible candidates for cold dark matter.