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Nucleon-transfer sum rules have been assessed via a consistent reanalysis ofcross-section data from neutron-adding ($d$,$p$) and -removing ($d$,$t$)reactions on well-deformed isotopes of Gd, Dy, Er, Yb, and W, with $92\leqN\leq108$, studied at the Niels Bohr Institute in the 1960s and 1970s. Theseare complemented by new measurements of cross sections using the ($d$,$p$),($d$,$t$), and ($p$,$d$) reactions on a subset of these nuclei. The sum rules,defined in a Nilsson-model framework, are remarkably consistent. A singleoverall normalization is used in the analysis, which appears to be sensitive toassumptions about the reaction mechanism, and in the case of sums using the($d$,$t$) reaction, differs from values determined from reactions on sphericalsystems.

Consistency of nucleon-transfer sum rules in well-deformed nuclei