${}^{146}\mathrm{Sm}$, as an extinct $p$-process isotope, plays an irreplaceable role in the timeline construction of the early solar system (ESS) via the geochemical tracing of its $\alpha$ decay to ${}^{142}\mathrm{Nd}$. There have been persistent discrepancies among both measured and theoretical half-lives of ${}^{146}\mathrm{Sm}$, which result in a large uncertainty in the initial ${}^{146}\mathrm{Sm}$ abundance in the ESS and subsequent dating of planetary events after the birth of the Sun. In this study, a newly proposed technique was used to analyze the $\alpha$ decay process within the widely employed $\alpha$-core nuclear potentials, namely, three different Woods-Saxon shapes and the double-folding potential. The half-life is obtained through large-scale random sampling of parameters for each potential, with the robust results subjected to statistical analysis. Additionally, a well-founded extrapolation for $\alpha$ decay energy of ${}^{146}\mathrm{Sm}$, based on the systematic behavior of the neighboring decay chain, is in perfect agreement with the adopted experimental value, further supporting the present evaluation on this crucial half-life. As a result, the half-life of ${}^{146}\mathrm{Sm}$ was determined to be $71.74\pm 7.39$ million years (Ma) with a 95% confidence interval. The initial ${}^{146}\mathrm{Sm}/{}^{144}\mathrm{Sm}$ ratio of $0.0092\pm 0.0014$ at 4568($\pm 10$) Ma, corresponding to the formation of the solar system, is then determined, further leading to a reduced timescale for various planetary silicate mantle differentiation events of the ESS. It is expected that this study paves the way for a theoretically calibrated ${}^{146}\mathrm{Sm}\text{−}{}^{142}\mathrm{Nd}$ chronometer in future studies of nucleosynthesis and in earth and planetary astrophysics.

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• Alpha decay
• Formation & evolution of stars & galaxies
• Lifetimes & widths
• Nuclear astrophysics
• Cluster models