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Some rare isotopes such as 7Li, 11B, 138La, and 180Ta are considered to be synthesized by neutrino-induced reactions in core-collapse supernovae (neutrino process). The study of the neutrino-process has an important tole for understanding neutrino physics such as neutrino mass hierarchies and explosion mechanism. Here we report the calculated results using the neutrino process in SNe [1].11B is predominantly produced from 12C in outer layers by both charged and neutral current reactions with neutrinos, and 7Li is predominantly produced from 4He in neutrino-process. In contrast, 138La is produced in the inner O/Ne/Mg rich layers. The neutrinos in 4He and 12C rich layers are affected by collective neutrino oscillation in proto-neutron star and MSW effect in outer layers, whereas neutrinos producing 138La in the O/Ne/Mg layers are only affected by the collective neutrino oscillation. Therefore, the abundance ratios of these isotopes give a hint to understand the collective neutrino oscillation. The isotopes ratios of 11B/10B and 7Li/6Lis in presolar grains originating from SNe have been reported. The calculated results shows that the observed ratios cannot be reproduced by standard model, suggesting mixing of intermediate material with SNe ejecta. We further calculated the correlation between 11B/10B (7Li/6Li) and 138La/139La. This shows the clear separation between both neutrino mass hierarchies. We further calculated the correlation between 138La/139La and 50Ti/48Ti, which has been measured in CAI formed in the early solar system formation. The results suggest that ejecta of a SNe contributed to the early solar materials.
[1] X. Yao et al. Astrophys. J. 980, 247 (2025).
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