Local mass relations and the NpNn scheme

Atomic nuclei are very complex systems that display a rich and fascinating variety of phenomena. To describe these features, one has to resort to theoretical models, e.g., the shell model and collective models, to study their structure, including the properties of ground states and excited states. On the other hand, the evolution of nuclear structure with changing numbers of nucleons has also offered important insight into nuclear structure, phase transitions, predictions of properties of newly discovered nuclei, signatures of structure, and underlying shell structure. For example, the NpNn scheme (the product of valence proton number and valence neutron number), suggested by Casten and studied extensively by Casten and Zamfir, provides a simple, yet powerful, guide to understanding and predicting the systematic behavior of nuclear properties [1,2].