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This article extends previous studies on the effect of tensor terms in theSkyrme energy density functional by breaking of time-reversal invariance. Wehave systematically probed the impact of tensor terms on properties ofsuperdeformed rotational bands calculated within the crankedHartree-Fock-Bogoliubov approach for different parameterizations covering awide range of values for the isoscalar and isovector tensor coupling constants.We analyze in detail the contribution of the tensor terms to the energies anddynamical moments of inertia and study their impact on quasi-particle spectra.Special attention is devoted to the time-odd tensor terms, the effect ofvariations of their coupling constants and finite-size instabilities.

The tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin