The nucleosynthesis of nature ’ s rarest isotope ^ { 180 } Ta depends sensitively on the temperature of the astrophysical environment because of depopulation of the long-living isomeric state via intermediate states to the short-living ground state by thermal photons .
Reaction rates for this transition have been measured in the laboratory .
These ground state rates understimate the stellar rates dramatically because under stellar conditions intermediate states are mainly populated by excitations from thermally excited states in ^ { 180 { m } } Ta .
Full thermalization of ^ { 180 } Ta is already achieved for typical s-process temperatures around kT = 25 keV .
Consequently , for the survival of ^ { 180 } Ta in the s-process fast convective mixing is required which has to transport freshly synthesized ^ { 180 } Ta to cooler regions .
In supernova explosions ^ { 180 } Ta is synthesized by photon- or neutrino-induced reactions at temperatures above T _ { 9 } = 1 in thermal equilibrium ; independent of the production mechanism , freeze-out from thermal equilibrium occurs at kT \approx 40 keV , and only 35 \pm 4 % of the synthesized ^ { 180 } Ta survive in the isomeric state .