Single-Nucleon Energies Changing with Nucleon Number

TL;DR

This paper analyzes experimental data on single-particle energies in nuclei, revealing simple patterns in how these energies depend on the number of neutrons and protons, with minimal reliance on models.

Contribution

It presents a systematic analysis of binding energies for single-particle states, highlighting simple, model-independent patterns in their dependence on nucleon numbers.

Findings

Neutron and proton state energies depend similarly on the number of the other nucleon type.

Dependence of energies on same-type nucleon number is weaker and slightly repulsive.

Patterns are derived with minimal model assumptions.

Abstract

The broad range of accumulated experimental data on the binding energies for single-particle states in nuclei is examined as a function of the constituent number of neutrons and protons and an unexpectedly simple pattern emerges. The dependence of the energies of neutron states on the number of constituent protons, or of proton states on the number of neutrons, are very similar to each other and the sign reflects the well-known strong attraction. For the same kind of nucleons changing as in the state -- energies for neutron states with neutron number changing or proton states with protons -- the dependence is at least a factor of four weaker in magnitude and slightly repulsive, except when the changing nucleons are only within the same orbit as the state. The systematics of the accumulated data are presented with a minimum of use made of model assumptions.