Isomer residual ratio of odd-odd isotope ¹⁸⁰Ta in supernova nucleosynthsis

The nucleosynthesis of ¹⁸⁰Ta has remained an unsolved problem and as its origin many nucleosynthesis mechanisms have been proposed. This isotope has the unique feature that the naturally occurring abundance of ¹⁸⁰Ta is actually a meta-stable isomer (half-life of ≥ 10 ¹⁵ yr), while the ground state is a 1⁺ unstable state which β -decays with a half-life of only 8.15 hr. We have made a new time-dependent calculation of ¹⁸⁰Ta meta-stable isomer residual ratio after supernova neutrino-induced reactions. This residual isomer ratio is crucial for understanding the production and survival of this naturally occurring rare isotope. We have constructed a new model under temperature evolution after type II supernova explosion. We include the explicit linking between the isomer and all known excited states and found that the residual ratio is insensitive to astrophysical parameters such as neutrino energy spectrum, explosion energy, decay time constant. We find that the explicit time evolution of the synthesis of ¹⁸⁰Ta avoids the overproduction relative to ¹³⁸La for a neutrino process neutrino temperature of 4 MeV.