Editorial Feature

The Heart of Matter: Exploring Nuclear Structure and Decay

The atomic nucleus is the most important part of the atom as it is responsible for its stability, mass, and identity. This article discusses the basic nuclear structure and the physics of radioactive decay.

Nuclear Structure and Decay

Image Credit: Natali _ Mis/Shutterstock.com

The Nuclear Structure

The atomic number refers to the number of protons in the atom’s nucleus and effectively corresponds to the chemical element as it also defines the number of atomic electrons in a neutral atom, while the atomic mass is the sum of the number of neutrons and protons. Both protons and neutrons, which possess almost the same mass, comprise a common set of particles referred to as nucleons.

However, the number of neutrons can vary for a specific atomic number, which leads to isotopes. Although a small number of isotopes remain stable to radioactive decay, a large number of isotopes, which can be produced in astrophysical environments or a laboratory, are radioactive or unstable to a lesser/greater extent.

These unstable isotopes allow physicists to investigate the nuclear structure diversity. The relative stability of various isotopes can be defined by the radioactive decay processes. The binding energy of a specific nuclear system determines nuclear stability.

Initially, the binding energy rapidly increases through the light nuclei before plateauing off and attaining a peak in iron and nickel. Subsequently, the energy reduces slowly towards the heaviest elements such as uranium, which explains the gain in energy by splitting a heavy nucleus into two parts.

Radioactive Decay

Radioactive decay is primarily a stochastic process implying that the decay of individual nuclei occurs randomly, while the decay of an ensemble of nuclei can be considered in statistical terms, such as displaying an exponential decay over time governed by the decay constant (λ).

The mean life/lifetime (τ) of a particular decay process is given as τ= 1/ λ, which corresponds to the time taken for the initial radioactive nuclei sample to decay to 1/e of the initial value.

The mean life can be converted into half-life (t1/2), which implies the time taken for half of the initial radioactive nuclei sample to decay, where t1/2 = 0.693τ. Additionally, the activity of a sample is defined as the number of disintegrations per second.

Alpha Decay

Alpha decay is a crucial decay mode for long-lived isomeric states and ground states in heavy nuclei. The alpha particle emission physics is governed by quantum-mechanical tunneling, which implies that a pre-formed alpha particle in the nucleus does not possess sufficient kinetic energy to escape from the nucleus by overcoming the Coulomb barrier, leading to a decay process that occurs by tunneling through the barrier.

The energetic conditions for quantum tunneling imply that alpha particles emitted from the ground states of nuclei are in the approximate 3–10 MeV range. The alpha-particle emission probability is strongly related to the decay Q value, which refers to the amount of energy released during the decay process.

A strong correlation exists between the alpha decay half-life and Q-value, which is referred to as the Geiger–Nutall relationship. Additionally, the decay Q value is shared between the kinetic energies of the recoiling daughter nucleus and the alpha particle.

Thus, the corresponding kinetic energy of the alpha particle (Tα) by considering the conservation of momentum is Tα = Q/(1 + mα/md), where mα and md are the mass of the alpha particle and daughter nucleus, respectively. The bulk of the decay energy is transferred to the emitted alpha particle’s kinetic energy as alpha decay is a characteristic phenomenon in heavy nuclei for which md >> mα.

Beta Decay

Beta particles represent a more penetrating form of radiation compared to alpha particles. Alpha particles are emitted from the nucleus with discrete energies, while beta particle energies comprise a continuous distribution/the Fermi–Kurie distribution up to some maximum energy governed by the decay Q value.

Beta decay has two modes, including Fermi and Gamow–Teller, which depend on the relative spin direction of the emitted (anti)neutrino and electron(positron). Additionally, the beta decay half-lives vary extensively based on the   Q value of the decay, the degree of forbiddenness, and the mode of the decay.

The three major types of beta decay include β, β+, and electron capture (EC), with β+ and EC competing with each other based on the decay process energetics. Beta decay can only take place when the decay is energetically favorable.

β decay in neutron-rich nuclei involves the transformation of a neutron into a proton within a nucleus, which is accompanied by an antineutrino and an electron emission. The Q value for the decay process represents the energy shared between the emitted antineutrino and electron kinetic energies.

β+ decay is relevant to proton-rich nuclei and involves the transformation of a proton into a neutron within a nucleus accompanied by a positron and a neutrino emission. The positron, which is the antimatter counterpart of the electron and is fundamentally unstable, can annihilate with an electron to release almost twice the electron rest mass energy/1.022 MeV in the form of photons.

The principal annihilation mode is the generation of two photons emitted almost successively, with each photon possessing 511 keV of energy. The positron can either come to rest and form positronium, which consists of a positron and an electron, or annihilate in flight.

EC in proton-rich nuclei is a process where an atomic electron is captured by transforming a proton into a neutron in a nucleus. Although all unbound proton-rich nuclei will possess an EC decay branch, a β+ decay branch will open up for Q values higher than 1.022 MeV and increasingly become dominant as an increasing Q value function.

Gamma Decay

Gamma rays are primarily a form of electromagnetic radiation and correspond to transitions between excited states in nuclei. The typical energy range of gamma rays is of the order 10 keV–few MeV.

Gamma-ray energies overlap with X-ray energies below 100 keV and become physically indistinguishable. Gamma-ray emission can display angular distributions/correlations or can be isotropic based on the scenario.

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References and Further Reading

Jenkins, D. (2020). Radiation Detection for Nuclear Physics: Methods and Industrial Applications. IOP Publishing, 1-34. https://doi.org/10.1088/978-0-7503-1428-2ch1.

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Samudrapom Dam

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Samudrapom Dam

Samudrapom Dam is a freelance scientific and business writer based in Kolkata, India. He has been writing articles related to business and scientific topics for more than one and a half years. He has extensive experience in writing about advanced technologies, information technology, machinery, metals and metal products, clean technologies, finance and banking, automotive, household products, and the aerospace industry. He is passionate about the latest developments in advanced technologies, the ways these developments can be implemented in a real-world situation, and how these developments can positively impact common people.

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