The now extinct { { } ^ { 205 } \kern - 0.8 ptPb } is a pure s-process radionuclide ( t _ { 1 / 2 } = 1.5 10 ^ { 7 } y ) of possible substantial cosmochemical interest .
As a necessary complement to the detailed theoretical study of the nuclear physics and astrophysics aspects of the { { } ^ { 205 } \kern - 0.8 ptPb } - { { } ^ { 205 } \kern - 0.8 ptTl } pair carried out by Yokoi et al .
( 1985 ) , and to the recent calculation of the { { } ^ { 205 } \kern - 0.8 ptPb } production in Wolf-Rayet stars by Arnould et al .
( 1997 ) , this paper addresses for the first time in some detail the question of the survival of this radionuclide in thermally pulsing AGB stars .
This problem is made difficult by the high sensitivity to temperature and density of the rates of the weak interaction processes that are able to produce or destroy { { } ^ { 205 } \kern - 0.8 ptPb } .
In view of this sensitivity , a recourse to detailed stellar models is mandatory .
With the help of some simplifying assumptions concerning in particular the third dredge-up characteristics , some of which ( like its depth ) being considered as free parameters , predictions are made for the { { } ^ { 205 } \kern - 0.8 ptPb } contamination of the stellar surface at the end of a pulse-interpulse cycle following a series of a dozen of pulses in three different intermediate-mass stars ( M = { 3 M _ { \odot } } , Z = 0.02 ; M = { 6 M _ { \odot } } , Z = 0.02 ; M = { 3 M _ { \odot } } , Z = 0.001 ) .
It is concluded that the chances for a significant { { } ^ { 205 } \kern - 0.8 ptPb } surface enrichment are likely to increase with M for a given Z , or to increase with decreasing Z for a given M .
More specifically , following the considered pulses at least , the enrichment appears to be rather unlikely in the { 3 M _ { \odot } } star with Z = 0.02 , while it seems to be much more probable in the other two considered stars .
It is also speculated that the ( { 3 M _ { \odot } } , Z = 0.02 ) star could possibly experience some { { } ^ { 205 } \kern - 0.8 ptPb } enrichment following later pulses than the ones considered in this paper .