Modern models of s-process nucleosynthesis in stars require stellar reaction rates with high precision. Most of the neutron capture cross sections in the s-process have been measured and for an increasing number of reactions the required precision is achieved. This does not necessarily mean, however, that the stellar rates are constrained equally well because only capture on the ground state of a target is measured in the laboratory. Captures on excited states can considerably contribute to stellar rates already at typical s-process temperatures. We show that the ground state contribution X to a stellar rate is the relevant measure to identify reactions which are or could be well constrained by experiments and apply it to (n,gamma) reactions in the s-process. It is further shown that the maximally possible reduction in uncertainty of a rate through determination of the g.s. cross section is directly given by X. An error analysis of X is presented and it is found that X is a robust measure with overall small uncertainties. Several specific examples (neutron capture on 79Se, 95Zr, 121Sn, 187Os, and 193Pt) are discussed in detail. The ground state contributions for a set of 411 neutron capture reactions around the s-process path are presented in a table. This allows to identify reactions which may be better constrained by experiments and such which cannot be constrained by only measuring ground state cross sections (and thus require supplementary studies). General trends and implications are discussed.
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