Nuclear Physics and Reactor Science

Introduction to Nuclear Physics

Nuclear physics studies the structure and interactions of atomic nuclei—the dense positively charged cores of atoms containing protons and neutrons (nucleons) bound by the strong nuclear force. Nuclei are described by mass number A (total nucleons) and atomic number Z (protons): the chart of nuclides contains ~3,000 known isotopes from hydrogen-1 to oganesson-294. Nuclear binding energy—the energy holding a nucleus together—reaches a maximum at iron-56 (~8.8 MeV per nucleon), explaining why lighter nuclei fuse (gaining binding energy) and heavier nuclei fission (releasing binding energy)—both processes converting mass to energy per E = mc². The semi-empirical Bethe-Weizsäcker mass formula parameterises binding energy as volume, surface, Coulomb, asymmetry, and pairing terms—accurately reproducing nuclear masses across the chart of nuclides.

Nuclear reactions power stars, date archaeological artefacts, treat cancer, generate 10% of global electricity, and underlie both nuclear weapons deterrence and the hope of fusion energy. Marie Curie discovered polonium and radium (1898), establishing radioactive decay as a nuclear property; Rutherford discovered the nucleus (1909 gold-foil experiment) and artificial transmutation (1919); Hahn, Strassmann, and Meitner discovered neutron-induced fission (1938); Fermi demonstrated the first self-sustaining chain reaction (Chicago Pile-1, December 2, 1942)—milestones launching the nuclear age. Understanding nuclear physics requires quantum mechanics: nuclear wavefunctions, shell model (Nobel 1963 Mayer, Jensen), and collective nuclear models describing quadrupole deformations.

Radioactive Decay

Decay Modes and Laws

Radioactive nuclei are unstable against spontaneous transformation—decaying to lower-energy daughter nuclides by emitting particles or photons. Alpha decay (emission of helium-4 nucleus, 2p+2n): occurs in heavy nuclei (A>200) where Coulomb repulsion exceeds strong force; alpha particles can only escape by quantum tunnelling through the Coulomb barrier (Gamow tunnelling model)—the exponential relationship between half-life and alpha energy (Geiger-Nuttall law) was the first successful application of quantum mechanics to nuclei. Beta decay: neutron → proton + electron + antineutrino (beta-minus); proton → neutron + positron + neutrino (beta-plus); or electron capture. Gamma emission: excited nuclear states decay by photon emission—used in medical scintigraphy (Tc-99m emitting 140 keV gamma, t1/2=6 hours, ideal for imaging) and PET (F-18 positron emitter). Radioactive decay law: N(t) = N0 * exp(-lambda*t), lambda = ln2/t1/2; activity A = lambda*N.

Nuclear Reactions and Cross Sections

Nuclear reaction rates depend on cross sections—effective target areas for interaction (measured in barns: 1 barn = 10^-28 m^2)—which vary dramatically with energy and show resonances at energies matching compound nucleus excited states. Neutron cross sections are particularly important for reactor physics: thermal neutron (0.025 eV) has much higher cross sections for fission (U-235: 584 barns) than fast neutrons—the basis for thermal neutron reactors moderating neutrons. Resonance capture regions in epithermal energy range (eV to keV) are design concerns for avoiding parasitic neutron capture reducing reactivity. Nuclear reaction notation: ^A_Z X (n, p) ^A_Z+0 Y means X captures neutron, emits proton, produces Y. The Q-value (energy release per reaction) = (reactant masses - product masses) * c^2 from mass-energy conservation—positive Q means energy release, and for U-235 fission Q~200 MeV per reaction, versus D-T fusion Q=17.6 MeV.

Fission Reactors

Chain Reaction and Criticality

Self-sustaining fission chain reactions require k=1 (each fission neutron inducing exactly one new fission). k = eta*f*p*epsilon*Pnl (six-factor formula in infinite medium): eta=neutrons per fission absorption; f=thermal utilisation; p=resonance escape probability; epsilon=fast fission factor; Pnl=non-leakage probability. Reactors maintain k~1 through control rod insertion/withdrawal (neutron absorbers), moderator feedback (temperature coefficients), and delayed neutrons (0.65% of fission neutrons delayed 0.01-80 seconds—making control possible on human timescales, not microsecond prompt-neutron timescales). Pressurised water reactor (PWR—dominant worldwide): moderator=coolant is water at ~300°C/155 bar; fuel is low-enriched UO2 (3-5% U-235) in zircaloy cladding; fuel assemblies in reactor core; steam generators produce turbine steam. Negative void coefficient (when water turns to steam, losing moderation reduces reactivity—inherent safety) is required by modern designs; RBMK-1000 positive void coefficient contributed to Chernobyl accident mechanism.

Nuclear Waste and Safety

Nuclear fission produces radioactive fission products (Kr, Xe, Sr, Cs, I isotopes—short to medium half-lives) and actinides (U, Pu, Am, Cm—long half-lives from neutron capture transmutation). High-level waste (HLW) from reprocessing or spent fuel remains radiotoxic for ~10,000–1,000,000 years requiring deep geological disposal. Yucca Mountain (US—stalled), WIPP (US, for defence TRU waste), and Onkalo (Finland—world's first licensed deep geological repository) are disposal approaches. Three Mile Island (1979), Chernobyl (1986), and Fukushima Daiichi (2011) shaped global nuclear safety culture and regulation. Life-cycle carbon emissions from nuclear (~12 g CO2eq/kWh) are comparable to wind and solar and well below gas (~490) and coal (~820), making nuclear important in low-carbon electricity generation: 413 operating reactors provide ~10% of global electricity as of 2025.

Examples and Applications

Example 1: Radiocarbon Dating

Radiocarbon dating (Willard Libby, Nobel 1960) exploits the known production rate of C-14 (t1/2 = 5,730 years) in the atmosphere by cosmic ray spallation (N-14 + n → C-14 + p) and its incorporation into living organisms at atmospheric concentrations. After death, C-14 decays without replacement—measuring residual C-14/C-12 ratio (by decay counting or accelerator mass spectrometry for microgram samples) determines time since death. Calibration curve (IntCal20) corrects for known atmospheric C-14 variations (from solar activity, ocean circulation, fossil fuel dilution) enabling calendar-year dating accuracy of ±20-50 years for samples up to ~50,000 years old. AMS dating dated the Shroud of Turin (~1260-1390 CE medieval), Ötzi the Iceman mummy (~3,300 BCE), and established the timeline of human migrations from Africa and peopling of the Americas. Bomb radiocarbon from 1950s-1960s nuclear tests—doubling atmospheric C-14—provides a tracer for dating post-1950 samples and measuring cell turnover rates in human tissues including brain neurons.

Example 2: Medical Radioisotopes

Nuclear medicine uses radioisotopes for diagnosis (SPECT, PET) and therapy (targeted radionuclide therapy). Technetium-99m (6-hour half-life, 140 keV gamma) produced from Mo-99 generators is used in 80% of nuclear medicine imaging procedures—bone scans, cardiac perfusion, renal function, thyroid, lung PE studies. F-18-FDG (fluorodeoxyglucose, 110-minute T1/2, positron emitter → 511 keV annihilation photons detected by PET) images metabolically active tumours and brain function. Therapeutic: I-131 (8-day T1/2, beta + gamma) for thyroid cancer (thyroid tissue avidly concentrates iodine—selective irradiation); Lu-177 DOTATATE for somatostatin receptor-expressing NETs achieved 11-month PFS improvement in NETTER-1 trial (approval 2018); Ac-225 (alpha emitter)-labelled PSMA ligands for metastatic prostate cancer in Phase III trials. Cyclotrons at hospital sites produce short-lived diagnostics (C-11, N-13, О-15, Ga-68) needed for local clinical PET imaging.

Example 3: Neutron Activation Analysis

Neutron activation analysis (NAA) irradiates samples in a research reactor, converting stable isotopes to radioactive ones by neutron capture; the characteristic gamma-ray spectrum of activated nuclides identifies and quantifies elemental composition to parts-per-billion sensitivity with minimal sample preparation. NAA provided the first definitive evidence of the Cretaceous-Paleogene (K-Pg) impactor from the worldwide iridium anomaly at the K-Pg boundary (Alvarez et al. 1980)—iridium is rare in Earth's crust but characteristic of meteoritic material—leading to the asteroid impact hypothesis for the Cretaceous mass extinction. NAA analysis of Napoleon Bonaparte's hair revealed elevated arsenic levels supporting the arsenic poisoning hypothesis. Forensic NAA of hair and nail samples can provide exposure history timeline due to sequential deposition. Modern NAA replaced by laser ablation ICP-MS for many applications but remains definitive for light elements and accuracy.

Example 4: Advanced Nuclear Reactors

Generation IV reactor concepts under development aim to improve safety, sustainability, and proliferation resistance beyond current light water reactors. High-temperature gas-cooled reactors (HTGR): graphite-moderated, helium-cooled, TRISO fuel particles with ceramic coating preventing fission product release even at 1600°C—passive safety through ceramic fuel. Molten salt reactors (MSR): fuel dissolved in fluoride salt coolant at atmospheric pressure, passive draining to freeze plug subcritical tanks on power loss—Jiang Chen-1 Chinese MSR design commissioned; Terrestrial Energy, Moltex in Canada. Sodium fast reactors (SFR): liquid sodium coolant, no moderator, fast spectrum enabling plutonium and minor actinide burning reducing waste longevity. Small modular reactors (SMRs, <300 MWe): factory-manufactured, transportable, faster deployment—NuScale VOYGR, Rolls-Royce SMR, Kairos Power, X-Energy among 70+ applicants in licensing review. SMRs target industrial heat applications and remote communities currently dependent on diesel.

Example 5: Nuclear Weapons Physics

Nuclear weapons exploit supercritical fission chain reactions (k >> 1) producing exponential energy release. Gun-type assembly (U-235, Little Boy): one piece fired into another to achieve supercriticality—~64 kg U-235 (~90% enriched). Implosion design (Pu-239, Fat Man): chemical explosive lenses simultaneously compress a subcritical sphere to supercritical density—~6 kg Pu-239 with ~100 conventional explosive detonators. Thermonuclear (hydrogen) weapons: fission primary ignites fusion secondary (Li-6 D converted to tritium by fission neutrons, then D-T fusion)—no theoretical yield limit. Physics enablers: neutron initiator (polonium-beryllium or electronic), tamper (reflecting neutrons and providing inertial confinement), staging. Non-proliferation regime: Treaty on Non-Proliferation of Nuclear Weapons (NPT, 191 states), IAEA safeguards (verification of civilian programme declarations), CTBT (Comprehensive Test Ban Treaty—monitoring through seismic/infrasound/hydroacoustic/radionuclide IMS network), and export controls (Nuclear Suppliers Group) form the interlocking regime—though North Korea and India/Pakistan demonstrate its limitations.

Example 6: Cosmic Nucleosynthesis

The abundances of elements in the universe are determined by nuclear reactions in various cosmic settings—a triumph connecting nuclear physics to cosmology and astrophysics. Big Bang nucleosynthesis (BBN, t=3-20 minutes): proton-neutron ratio froze at n/p=1/7 after weak interactions froze out; nucleosynthesis produced ~75% H, ~25% He-4, trace D, He-3, Li-7—measurements matching BBN predictions constrain the baryon density of the universe. Stellar nucleosynthesis (Hans Bethe, Nobel 1967): hydrogen burning (pp chain in low-mass stars; CNO cycle in massive stars), helium burning (triple-alpha process: 3 He4 → C-12 through Hoyle state resonance), successive shell burning of C, Ne, O, Si in massive stars to iron group. Explosive nucleosynthesis: supernovae produce elements heavier than iron through rapid neutron capture (r-process); neutron star mergers confirmed as r-process site by kilonova optical/IR emission following GW170817 gravitational wave detection (2017).

Example 7: Radiation Shielding and Dosimetry

Radiation protection aims to limit human exposure to ionising radiation below harm thresholds while enabling its beneficial uses. Absorbed dose (Gray = J/kg) weighted by radiation effectiveness (quality factor Q: gamma/beta Q=1, protons Q=2, alpha Q=20, neutrons Q=5-20) gives effective dose (Sievert = Gy * Q). ICRP dose limits: 20 mSv/year occupational; 1 mSv/year public; natural background ~2.4 mSv/year globally (radon contributes ~1.2 mSv/year indoors). Shielding calculations use half-value layer (HVL—thickness reducing intensity by half) and tenth-value layer: for 6 MeV X-rays, HVL in concrete ~15 cm; for alpha particles, a sheet of paper; for neutrons, hydrogenous materials (polyethylene, water) moderate and absorb. ALARA principle (As Low As Reasonably Achievable) guides radiation protection practice, balancing protection against cost. Monte Carlo N-Particle (MCNP) code calculates particle transport through complex geometries for reactor shielding design, medical accelerator vault design, and space mission radiation environment modelling.

Example 8: Nuclear Structure—Shell Model

The nuclear shell model (independently by Maria Goeppert Mayer and J. Hans D. Jensen, 1949, Nobel 1963) explains magic numbers (2, 8, 20, 28, 50, 82, 126 protons or neutrons—nuclei with extra stability) through filled nuclear shells, analogous to atomic electron shells but with spin-orbit coupling ~100× stronger than atomic spin-orbit splitting, ordering the orbitals differently. Doubly magic nuclei (Z=N=magic number: He-4, O-16, Ca-40, Ca-48, Pb-208) resist deformation, have high excitation energies to first excited state, and are the most stable nuclei. Shell model calculations using modern effective interactions (GXPF1A for the pf-shell, USD for sd-shell, SDPF-U spanning shells) reproduce nuclear energy levels, transition rates, and beta-decay properties with high accuracy. Exotic nuclei near the r-process path—neutron-rich isotopes produced in supernovae—have modified shell structure (quenching of shell gaps far from stability), measured by radioactive beam facilities (RIKEN RIBF, CERN-ISOL ISOLDE, FRIB at MSU) essential for constraining r-process nucleosynthesis models.

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