5.2 Beta decay types and neutrino hypothesis

Beta decay is a fascinating process where unstable atomic nuclei transform, emitting electrons or positrons. This section dives into different types of beta decay, including beta-minus, beta-plus, and electron capture, explaining how they change atomic structure.

The neutrino hypothesis, proposed to explain the continuous energy spectrum of beta decay, revolutionized our understanding of particle physics. We'll explore neutrino properties, their experimental discovery, and their role in fundamental interactions.

Beta Decay Types

Beta-Minus and Beta-Plus Decay

• Beta-minus decay occurs when a neutron in an unstable nucleus transforms into a proton
  • Emits an electron and an antineutrino
  • Increases atomic number by 1 while mass number remains constant
  • Represented by the equation: $n \rightarrow p + e^- + \bar{\nu}_e$
• Beta-plus decay involves a proton converting into a neutron
  • Releases a positron and a neutrino
  • Decreases atomic number by 1 while mass number stays the same
  • Equation for beta-plus decay: $p \rightarrow n + e^+ + \nu_e$
• Both processes result from weak nuclear force interactions
• Occur in neutron-rich or proton-rich nuclei to achieve stability

Electron Capture and Energy Spectrum

• Electron capture happens when an inner shell electron combines with a proton
  • Transforms proton into a neutron and emits a neutrino
  • Decreases atomic number by 1, mass number unchanged
  • Represented as: $p + e^- \rightarrow n + \nu_e$
• Continuous energy spectrum characterizes beta decay
  • Energy distributed between emitted particles and recoil nucleus
  • Spectrum ranges from zero to maximum energy (endpoint energy)
  • Contradicts conservation of energy in classical physics
  • Led to neutrino hypothesis to explain missing energy

Neutrino Hypothesis

Neutrino Properties and Discovery

• Neutrino proposed by Wolfgang Pauli in 1930 to explain beta decay spectrum
  • Neutral, nearly massless particle with spin 1/2
  • Interacts very weakly with matter, making detection challenging
• Antineutrino serves as the antiparticle counterpart to neutrino
  • Possesses opposite lepton number but same mass and spin
  • Produced in beta-minus decay
• Experimental confirmation of neutrinos came in 1956 (Cowan-Reines experiment)
  • Used nuclear reactor as neutrino source
  • Detected inverse beta decay reactions

Pauli Exclusion Principle and Fermi Theory

• Pauli exclusion principle states no two identical fermions can occupy the same quantum state
  • Applies to neutrinos, which are fermions
  • Explains why neutrinos and antineutrinos are distinct particles
• Fermi theory of beta decay developed by Enrico Fermi in 1934
  • First quantum field theory description of weak interactions
  • Treated beta decay as point-like four-fermion interaction
  • Accurately predicted shape of beta decay energy spectrum
  • Laid groundwork for modern electroweak theory

Fundamental Interactions

Weak Interaction in Beta Decay

• Weak interaction governs beta decay processes
  • One of four fundamental forces in nature (along with strong, electromagnetic, gravitational)
  • Much weaker than strong and electromagnetic forces, but stronger than gravity
  • Mediated by W and Z bosons
• Beta decay serves as prime example of weak interaction
  • Changes flavor of quarks (d quark to u quark or vice versa)
  • Violates parity conservation, discovered in Wu experiment (1956)
• Characteristic time scale for weak interactions much longer than strong or electromagnetic
  • Explains relatively long half-lives of beta-decaying isotopes

Neutrino Interactions and Detection

• Neutrinos primarily interact through weak force
  • Extremely small interaction cross-section
  • Can pass through enormous amounts of matter unaffected
• Detection methods rely on rare neutrino interactions
  • Radiochemical detectors (Davis experiment)
  • Water Cherenkov detectors (Super-Kamiokande)
  • Liquid scintillator detectors (Borexino)
• Neutrino oscillations discovered in late 20th century
  • Implies neutrinos have non-zero mass
  • Requires extension of Standard Model of particle physics