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Cosmological origins of the two heaviest odd-odd nuclei, $^{138}$La and$^{180}$Ta, are believed to be closely related to the neutrino-process. Weinvestigate in detail neutrino-induced reactions on the nuclei. Charged current(CC) reactions, $^{138}$Ba$ (\nu_e, e^{-}) ^{138}$La and $^{180}$Hf$ (\nu_e,e^{-}) ^{180}$Ta, are calculated by the standard Quasi-particle Random PhaseApproximation (QRPA) with neutron-proton pairing as well as neutron-neutron,proton-proton pairing correlations. For neutral current (NC) reactions,$^{139}$La$ (\nu \nu^{'}) ^{139}${La}$^*$ and $^{181}$Ta$ (\nu, \nu^{'})^{181}$Ta$^*$, we generate ground and excited states of odd-even target nuclei,$^{139}$La and $^{181}$Ta, by operating one quasi-particle to even-even nuclei,$^{138}$Ba and $^{180}$Hf, which are assumed as the BCS ground state. Numericalresults for CC reactions are shown to be consistent with recent semi-empiricaldata deduced from the Gamow-Teller strength distributions measured in the($^{3}$He, t) reaction. Results for NC reactions are estimated to be smaller bya factor about 4 $\sim$ 5 rather than those by CC reactions. Finally, crosssections weighted by the incident neutrino flux in the core collapsingsupernova are presented for further applications to the network calculationsfor relevant nuclear abundances.

Neutrino reactions on $^{138}$La and $^{180}$Ta via charged and neutral currents by the Quasi-particle Random Phase Approximation (QRPA)