In the self-consistent method, the average nucleonic field is obtained from the nucleonic density. Consequently, in a highly polarized high-spin state, the mean-field potential is expected to acquire appreciable time-odd components [55,56]. However, such terms should be present in all nuclear states with non-zero angular momentum, including ground states of odd-mass and odd-odd nuclei [57]. It is rather clear that without getting a handle on the time-odd fields, it will be impossible to make precise predictions for binding energies of most of the nuclei.

The time-odd terms are very poorly known. An important task is to learn about them through an analysis of high-spin states and spin-isospin excitations. Some of the time-odd fields have been studied in Ref. [58] in the context of Gamow-Teller beta decays in radioactive nuclei by constraining the energy functional to the empirical spin-isospin Landau parameters. The coupling constants of the remaining terms can, in principle, be found by performing systematic studies of rotating nuclei. This strategy has recently been followed in the Skyrme-HF analysis of high-spin terminating states [59,60]. Those fully aligned states have fairly simple single-particle configurations, and they provide an excellent testing ground for the time-odd densities and fields.