New experimental techniques for the determination of neutron capture c
ross sections, e.g. the Karlsruhe 4pi Barium Fluoride Detector, have r
educed the respective uncertainties by a factor five compared to previ
ous methods. With these improved data, detailed analyses of branchings
in the s-process path allow to derive constraints on the physical par
ameters during the s-process. As first examples, the neutron capture c
ross sections of the s-only isotopes of tellurium and samarium have be
en determined. We discuss the results in the framework of the classica
l s-process approach and with a stellar model describing the s-process
during helium shell burning in low mass stars. The results for tellur
ium confirm the prediction of the classical approach of a ''local appr
oximation'' within the experimental uncertainty of 1%. The stellar mod
el turned out to overestimate the effect of the branchings at A = 121,
122 by a factor three as a consequence of the temperature profile dur
ing the helium burning episode. The samarium cross sections provide fo
r a considerably improved estimate of the mean neutron density.