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

Nucleon-transfer sum rules have been assessed via a consistent reanalysis of cross-section data from neutron-adding ($d$,$p$) and -removing ($d$,$t$) reactions on well-deformed isotopes of Gd, Dy, Er, Yb, and W, with $92leq Nleq108$, studied at the Niels Bohr Institute in the 1960s and 1970s. These are 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 single overall normalization is used in the analysis, which appears to be sensitive to assumptions about the reaction mechanism, and in the case of sums using the ($d$,$t$) reaction, differs from values determined from reactions on spherical systems.