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Reply to "Comment on '$$^{138}$$La-$$^{138}$$Ce-$$^{136}$$Ce nuclear cosmochronometer of supernova neutrino process'"

Hayakawa, Takehito; Shizuma, Toshiyuki; Kajino, Toshitaka*; Ogawa, Kengo*; Nakada, Hitoshi*

We have proposed a new nuclear cosmochronometer $$^{138}$$La(T$$_{1/2}$$=102 Gyr)-$$^{138}$$Ce-$$^{136}$$Ce for measuring the time elapsed from a supernova $$nu$$ process episode. $$^{138}$$La is synthesized by the $$nu$$ process. If a 1$$^+$$ excited state exists at energy lower than 72 keV, the 1$$^+$$ state may be a $$beta$$ unstable isomer and $$^{138}$$La synthesized by the $$nu$$ process is destroyed via the isomer. Recently, Byelikov et al. have measured Gamow-Teller strength distributions in $$^{138}$$La. It has been presented that this experiment shows that the existence of a low-energy 1$$^+$$ state in $$^{138}$$La is extremely unlikely. Our calculated result is consistent with their result and we conclude that there is no evidence that suggests the existence of the 1$$^+$$ isomer in $$^{138}$$La.

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