The S-process (for slow neutron capture) involves the successive absorption of neutrons and/or emission of electrons to create heavier elements from iron "seed" nuclei. The process occurs only under certain ranges of temperature and neutron flux, which are found in AGB (asymptotic giant branch) stars. As a star passes through the AGB stage, it undergoes thermal pulses which "dredge up" some of the material from the core, including S-process isotopes, to the surface layers, from which material is blown into space by the stellar wind.

AGB stars (eventually including our own sun) end up as white dwarfs. Gravitational sorting would tend to pull the heavier nuclei to the center, but the quantities present may be too small to form a discrete core.
Source(s):
http://en.wikipedia.org/wiki/S-process#The_S-process_in_stars
http://en.wikipedia.org/wiki/Asymptotic_Giant_Branch
http://en.wikipedia.org/wiki/White_dwarf
http://www.as.utexas.edu/astronomy/education/spring01/lambert/classnotes16....

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