Beta decay of $^{24}$Si and mirror asymmetry of Gamow-Teller transition strength

We performed the $\beta$ decay spectroscopy on $^{24}$Si in order to study the behavior of a weakly-bound $s$-wave proton. The behavior of a weakly-bound proton in a proton-rich nucleus is one of the interesting topics to explore exotic nuclear structures such as proton halo. Thomas-Ehrman shift of the proton $s_{1/2}$ orbital induces a configuration change in the wave function. The change can be investigated in terms of the mirror asymmetry for Gamow-Teller transition strengths $B$(GT) for a proton-rich nucleus of $^{24}$Si. The experiment was carried out at the RIPS facility. In this presentation, we will report the experimental results. Discussion on the comparison with theoretical calculations which takes into account the Coulomb force and the Thomas-Ehrman shift is also given.