Nuclear Reactions and Decay

Alpha Decay

• Inside the barrier, the probability of alpha decay decreases exponentially, explaining why low-energy alpha-particle emitters have long half-lives.

Beta Decay

• Beta decay includes β- decay, β+ decay, and EC (Electron Capture) decay.
• Electrons or positrons cannot exist inside the nucleus, so they are created at the moment of nucleus disintegration.
• During EC, the electron is captured by the nucleus, disappearing and converting its mass into energy.

Conditions for Spontaneous Decay

• Using the principle of conservation of energy, we can determine whether an unstable beta nucleus will decay through β- emission, β+ emission, or electron capture.
• The three processes can be represented as:
  • β- emission: a proton becomes a neutron, and an electron is emitted.
  • β+ emission: a neutron becomes a proton, and a positron is emitted.
  • Electron Capture (EC): a proton in the nucleus captures an electron, becoming a neutron.

Energy Available for Disintegration

• Conserving energy, we can show that the energy available for beta emission is related to the masses of the parent (X) and daughter (Y) nuclei and the electron (e).

Gamma Decay

• When a nucleus disintegrates, it is usually left in an excited state, which can lead to gamma-ray emission, internal conversion, or the creation of internal pairs.
• These processes are caused by electromagnetic interactions.
• Internal conversion is more frequent in heavy excited nuclei, while the creation of internal pairs is more frequent in light nuclei and requires energy > 1.02 MeV.

Gamma-Ray Emission

• Gamma-ray spectra of excited nuclei consist of discrete energies, indicating discrete energy levels in the nucleus.
• Nuclei can decay through alpha or beta emission, leaving them in discrete excited energy states.

Radioactive Decay

• There are approximately 65 radioactive nuclei found in nature.
• Radioactive nuclei produced in the laboratory exhibit artificial radioactivity, with over 1000 isotopes produced.
• Both naturally occurring and artificially produced radioactive isotopes often decay through successive disintegration.
• The parent-daughter-granddaughter decay chain continues until the nucleus reaches stability.

Radioactive Isotopes

• Radioisotopes are common among elements with atomic numbers between Z=81 and Z=92 due to Coulomb repulsion between protons.
• To decrease the Coulomb repulsive force, unstable nuclei decay by emitting α-rays, losing two protons and two neutrons.
• This leads to an excess of neutrons, causing the nucleus to decay further by emitting β-rays, converting a neutron to a proton.