Yields of nature’s rarest isotopes La^{138} and Ta^{180} are calculated by neutrino processes in the Ne-shell of density $\rho ≈ 10^4 g/cc$ in a type II supernova (SN II) progenitor of mass 20 $M_\odot$. Two extended sets of neutrino temperature $- T_{\nue}$ = 3, 4, 5, 6 MeV and $T_{\nu(\mu/\tau)}$= 4, 6, 8, 10, 12 MeV respectively for charged and neutral current processes are taken. Solar mass fractions of the seeds La¹³⁹, Ta¹⁸¹, Ba¹³⁸ and Hf¹⁸⁰ are taken for calculation. They are assumed to be produced in some s-processing events of earlier generation massive ‘seed stars’ with average interior density range $\langleρ\rangle \approx 10^3−10^6 g/cc$. The abundances of these two elements are calculated relative to O¹⁶ and are found to be sensitive to the neutrino temperature. For neutral current processes with the neutron emission branching ratio, $b_n = 3.81 \times 10^{-4}$ and $b_n = 9.61 \times 10^{−1}$, the relative abundances of La¹³⁸ lie in the ranges $4.48 \times 10^{−14}−2.94 \times 10^{−13}$ and $1.13 \times 10^{−10} − 7.43 \times 10^{−10}$ respectively. Similarly, the relative abundances of Ta¹⁸⁰ lie in the ranges $1.80 \times 10^{−15} − 1.17 \times 10^{−14}$ and 4.53 \times 10^{−12}−2.96 × 10^{−11} respectively for the lower and higher values of the neutron emission branching ratio. For charged current processes, the relative abundances of La¹³⁸ and Ta¹⁸⁰ are found to be in the ranges $1.38 \times 10^{−9} − 7.62 \times 10^{−9}$ and $2.09 \times 10^{-11} − 1.10 \times 10^{−10}$ respectively. Parametrized by density of the ‘seed stars’, the yields are found to be consistent with recent supernova simulation results throughout the range of neutrino temperatures. La¹³⁸ and Ta¹⁸⁰ are found to be efficiently produced in charged current interaction.