Basic Definitions for Nuclear Structure

Introduction

In the Rutherford–Bohr atomic model, most of the atomic mass is concentrated in the atomic nucleus, which consists of protons and neutrons. The protons carry a positive charge, while neutrons are neutral. The nucleus is surrounded by electrons that carry a negative charge.

In nuclear physics, a nucleus is commonly denoted as $X{A}_Z$, where $A$ is the atomic mass number and $Z$ is the atomic number. For example, the 60Co nucleus is denoted as ${\mathrm{60}}_{\mathrm{27}}$ and the 226Ra nucleus is written as ${\mathrm{226}}_{\mathrm{88}}$.

Understanding these nuclear terms and classifications is essential in the field of nuclear physics. The following definitions and conventions are commonly used:

Isotopes, Isobars, and Isotones

Isotopes, isobars, and isotones are terms used to classify nuclear species:

• Isotopes: Atoms of the same element with the same number of protons ($Z$) but different numbers of neutrons ($\mathrm{A\; -\; Z}$). For example, ${\mathrm{59}}_{\mathrm{27}}$ and ${\mathrm{60}}_{\mathrm{27}}$ are isotopes of cobalt.
• Isobars: Atoms with the same atomic mass number ($A$) but different numbers of protons. For example, ${\mathrm{60}}_{\mathrm{27}}$ (cobalt) and ${\mathrm{60}}_{\mathrm{28}}$ (nickel) are isobars with the same mass number $A=\; 60$.
• Isotones: Nuclei with the same number of neutrons ($\mathrm{A\; -\; Z}$) but different numbers of protons. For example, ${\mathrm{67}}_{\mathrm{31}}$ (gallium), ${\mathrm{67}}_{\mathrm{32}}$ (germanium), and ${\mathrm{67}}_{\mathrm{33}}$ (arsenic) are isotones with the same number of neutrons ($\mathrm{A\; -\; Z\; =\; 36}$).

Definitions for Nuclei and Isomeric States

A nuclide is an atomic species characterized by its nuclear composition, including the atomic number $Z$, atomic mass number $A$, and the arrangement of nucleons within the nucleus.

The term isomeric state refers to a nucleus that exists in an excited state for some time, known as a metastable state. Isomeric nuclei have the same atomic number $Z$ and the same atomic mass number $A$, but differ in the energy of the nucleus. For example, ${\mathrm{99}}_{\mathrm{43}}$mTc is an isomeric state of ${\mathrm{99}}_{\mathrm{43}}$Tc.

Summary:

• Isotopes: Same number of protons $Z$, different number of neutrons $\mathrm{A\; -\; Z}$.
• Isobars: Same atomic mass number $A$, different atomic number $Z$.
• Isotones: Same number of neutrons $\mathrm{A\; -\; Z}$, different atomic number $Z$.