There are not enough experimental data for spherical even-even nuclei to fix the time-odd isovector coupling constants; the ability to do calculations in deformed nuclei should help there. We could, however, choose values that reproduce the data we do analyze, without spoiling our description of high-spin superdeformation. Doing a lot better may require improving our time-even energy functionals. GT resonance energies and strengths depend significantly on spin-orbit splitting as well as the residual spin-isospin interaction. Until we are better able to reproduce single-particle energies, therefore, a fit of the time-odd interaction will be tentative.
We have not considered isoscalar time-odd interactions. The couplings there will be harder to fix because there are fewer data on the response, which is not as collective as in the charge-exchange channel. In addition, the isovector time-odd terms will play a role in calculations of isoscalar observables. Though a lot clearly remains to be done, our work can already be put to good use. We will, for example, employ the new values for the isovector time-odd coupling constants in future calculations of beta decay and in the observables that tell us about the extent of real time-reversal violation in nuclei. This work was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-FG02-97ER41019 (University of North Carolina), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research), by the Polish Committee for Scientific Research (KBN) under Contract No. 5 P03B 014 21, and by the Wallonie/Brussels-Poland integrated actions program. We thank the Institute for Nuclear Theory at the University of Washington for its hospitality during the completion of this work.