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

Here, 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 92 ≤ N ≤ 108 , 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.