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

TL;DR

This study reanalyzes nucleon-transfer sum rules in well-deformed nuclei, combining historical data with new measurements, and finds that the sum rules are generally consistent but sensitive to reaction mechanisms and nuclear shape assumptions.

Contribution

It provides a comprehensive reanalysis of transfer sum rules in deformed nuclei, incorporating new experimental data and examining the impact of reaction mechanisms on sum rule normalization.

Findings

Sum rules are remarkably consistent across studied nuclei.

Normalization sensitivity to reaction mechanism assumptions.

Differences observed between deformed and spherical nuclei sums.

Abstract

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 $92\leq N\leq108$, 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.