La138-Ce138-Ce136nuclear cosmochronometer of the supernova neutrino process

Abstract

The $^{138}\mathrm{La}$ (${T}_{1/2}=102$ Gyr)-$^{138}\mathrm{Ce}$-$^{136}\mathrm{Ce}$ system is proposed to be used as a nuclear cosmochronometer for measuring the time elapsed from a supernova neutrino process. This chronometer is applied to examine a sample affected by a single nucleosynthesis episode as presolar grains in primitive meteorites. A feature of this chronometer is to evaluate the initial abundance ratio of $^{136}\mathrm{Ce}$/$^{138}\mathrm{Ce}$ using an empirical scaling law, which was found in the solar abundances. We calculate the age of the sample as a function of isotopic ratios $^{136}\mathrm{Ce}$/$^{138}\mathrm{Ce}$ and $^{138}\mathrm{La}$/$^{138}\mathrm{Ce}$ and evaluate the age uncertainty due to theoretical and observational errors. It is concluded that this chronometer can work well for a sample with the abundance ratio of $^{138}\mathrm{La}$/$^{138}\mathrm{Ce}$ \ensuremath{\ge} 20 when the ratios of $^{136}\mathrm{Ce}$/$^{138}\mathrm{Ce}$ and $^{138}\mathrm{La}$/$^{138}\mathrm{Ce}$ are measured within the uncertainty of 20%. The availability of such samples becomes clear in recent studies of the presolar grains. We also discuss the effect of the nuclear structure to the \ensuremath{\nu} process origin of $^{138}\mathrm{La}$.