Effect of the tensor force on $beta$?-decay is studied in the framework of the proton-neutron random-phase-approximation (RPA) with the Skyrme force. The investigation is performed for even-even semi-magic and magic nuclei, $^{34}$Si, $^{68}$, $^{78}
$Ni and $^{132}$Sn. The tensor correlation induces strong impact on low-lying Gamow-Teller state. In particular, it improves the ?$beta$-decay half-lives. $Q$ and $ft$ values are also investigated and compared with experimental data.
The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model. The Gamow-Teller (GT) strength function of 90Zr and 208Pb are calculated with and without the tensor
terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA.
