[{"data":1,"prerenderedAt":1227},["ShallowReactive",2],{"subject:nuclear-physics":3,"course-wordcounts":75,"nav:nuclear-physics":987},{"id":4,"title":5,"blurb":6,"body":7,"brief":18,"category":56,"description":57,"draft":58,"extension":59,"meta":60,"module":15,"navigation":25,"path":61,"practice":62,"rawbody":63,"readingTime":64,"seo":69,"sources":70,"status":71,"stem":72,"summary":15,"topics":73,"__hash__":74},"course\u002F08.nuclear-physics\u002Findex.md","Nuclear Physics","What holds the nucleus together and how it comes apart — sizes and masses, the\nnuclear force, the shell and collective models, every decay mode, reactions,\nand fission and fusion.\n",{"type":8,"value":9,"toc":14},"minimark",[10],[11,12,13],"p",{},"Nuclear physics studies the structure and transformations of the atomic nucleus,\nand nearly every result traces back to one graph: the binding energy per nucleon.\nThe sequence starts with the raw facts — nuclear sizes, shapes, and masses — then\nbuilds the force that binds nucleons together and the models that organize them,\nfrom the liquid drop to the shell and collective pictures. From there it turns to\nchange: the radioactive-decay law and its half-lives, then alpha, beta, and gamma\ndecay with the interactions that drive each. Nuclear reactions supply the\nexperimental tools and the conservation laws that constrain them, and the two\ngreat energy-releasing processes — fission, with its self-sustaining chain\nreactions and reactors, and fusion, powering the stars and the synthesis of the\nelements — close the arc. A final thread follows how nuclear radiation interacts\nwith matter and the applications that follow. It follows Krane and Wong, with\nTipler & Llewellyn and Tipler & Mosca for the foundations.",{"title":15,"searchDepth":16,"depth":16,"links":17},"",2,[],[19,21,26,30,32,34,38,40,42,46,48,52,54],{"p":20},"The nucleus is a hundred-thousandth the size of its atom yet holds nearly\nall its mass, bound by a force that overwhelms the electric repulsion of\nits packed protons. Nuclear physics asks what holds it together, and how it\ncomes apart.\n",{"fig":22,"n":23,"caption":24,"large":25},"nuc-binding","001","Binding energy per nucleon: fusion climbs the left slope, fission descends\nthe right, both toward the iron peak.\n",true,{"fig":27,"n":28,"caption":29},"nuc-decay","002","Radioactive decay is exponential — the population halves over each\nsuccessive half-life.\n",{"p":31},"One curve organizes the whole subject: the \u003Cstrong>binding energy per\nnucleon\u003C\u002Fstrong>. It rises steeply through the light elements, crests at\niron — the most tightly bound matter there is — and falls away through the\nheavy ones. Everything downhill of that peak releases energy.\n",{"p":33},"Stability is never guaranteed. An unbalanced nucleus is \u003Cem>radioactive\u003C\u002Fem>:\nit transmutes toward the valley of stability at a fixed probability per unit\ntime, so a population decays exponentially and each isotope carries its own\n\u003Cstrong>half-life\u003C\u002Fstrong>, from fractions of a second to billions of years.\n",{"fig":35,"n":36,"caption":37},"nuc-modes","003","The three decay modes: an alpha cluster, a beta electron, and a gamma\nphoton leaving one nucleus.\n",{"p":39},"Decay comes in three modes. \u003Cstrong>Alpha\u003C\u002Fstrong> ejects a helium-4\ncluster; \u003Cstrong>beta\u003C\u002Fstrong> converts a neutron to a proton and emits an\nelectron; \u003Cstrong>gamma\u003C\u002Fstrong> sheds pure energy as a photon, dropping the\nnucleus to a lower state without changing what it is.\n",{"p":41},"Firing particles at nuclei drives \u003Cem>reactions\u003C\u002Fem> — the controlled\ntransmutations that build new isotopes and reveal nuclear structure, each\ngoverned by the same conservation laws of energy, momentum, and charge.\n",{"fig":43,"n":44,"caption":45},"nuc-chain","004","A fission chain reaction branches: each split releases neutrons that split\nmore nuclei.\n",{"p":47},"Split a heavy nucleus and the fragments are more tightly bound than the\nwhole — \u003Cstrong>fission\u003C\u002Fstrong> releases energy, plus spare neutrons that\ncan split more nuclei. When each fission provokes more than one further\nfission, the chain reaction sustains itself, tamed in a reactor or unleashed\nin a bomb.\n",{"fig":49,"n":50,"caption":51},"nuc-fusion","005","Fusion joins two light nuclei into a more tightly bound one, releasing the\ndifference.\n",{"p":53},"Run the curve uphill from the other end and light nuclei \u003Cstrong>fuse\u003C\u002Fstrong>\ninto heavier, more tightly bound ones — the process that powers the stars and\nforged the elements, if the reactants can first be forced through their mutual\nrepulsion.\n",{"p":55},"From sizes and masses through the nuclear force, the decay laws, reactions,\nfission, and fusion, the subject is one long reading of a single curve — and\nof the enormous energies stored in the gap between where a nucleus sits and\nwhere it would rather be.\n","physics","Nuclear physics studies the structure and transformations of the atomic nucleus.\nThis course runs from nuclear sizes, shapes, and masses through the nuclear force\nand the two-nucleon system, the liquid-drop, shell, and collective models, the\nradioactive-decay laws, alpha, beta, and gamma decay and their underlying\ninteractions, nuclear reactions, fission and reactors, fusion and stellar\nnucleosynthesis, and the interaction of radiation with matter and its\napplications. It follows Krane and Wong, with Tipler & Llewellyn and Tipler &\nMosca for the foundational material.\n",false,"md",{},"\u002Fnuclear-physics",[],"---\ntitle: Nuclear Physics\nstatus: available\ncategory: physics\nblurb: |\n  What holds the nucleus together and how it comes apart — sizes and masses, the\n  nuclear force, the shell and collective models, every decay mode, reactions,\n  and fission and fusion.\ndescription: |\n  Nuclear physics studies the structure and transformations of the atomic nucleus.\n  This course runs from nuclear sizes, shapes, and masses through the nuclear force\n  and the two-nucleon system, the liquid-drop, shell, and collective models, the\n  radioactive-decay laws, alpha, beta, and gamma decay and their underlying\n  interactions, nuclear reactions, fission and reactors, fusion and stellar\n  nucleosynthesis, and the interaction of radiation with matter and its\n  applications. It follows Krane and Wong, with Tipler & Llewellyn and Tipler &\n  Mosca for the foundational material.\nbrief:\n  - p: |\n      The nucleus is a hundred-thousandth the size of its atom yet holds nearly\n      all its mass, bound by a force that overwhelms the electric repulsion of\n      its packed protons. Nuclear physics asks what holds it together, and how it\n      comes apart.\n  - fig: nuc-binding\n    n: \"001\"\n    caption: |\n      Binding energy per nucleon: fusion climbs the left slope, fission descends\n      the right, both toward the iron peak.\n    large: true\n  - fig: nuc-decay\n    n: \"002\"\n    caption: |\n      Radioactive decay is exponential — the population halves over each\n      successive half-life.\n  - p: |\n      One curve organizes the whole subject: the \u003Cstrong>binding energy per\n      nucleon\u003C\u002Fstrong>. It rises steeply through the light elements, crests at\n      iron — the most tightly bound matter there is — and falls away through the\n      heavy ones. Everything downhill of that peak releases energy.\n  - p: |\n      Stability is never guaranteed. An unbalanced nucleus is \u003Cem>radioactive\u003C\u002Fem>:\n      it transmutes toward the valley of stability at a fixed probability per unit\n      time, so a population decays exponentially and each isotope carries its own\n      \u003Cstrong>half-life\u003C\u002Fstrong>, from fractions of a second to billions of years.\n  - fig: nuc-modes\n    n: \"003\"\n    caption: |\n      The three decay modes: an alpha cluster, a beta electron, and a gamma\n      photon leaving one nucleus.\n  - p: |\n      Decay comes in three modes. \u003Cstrong>Alpha\u003C\u002Fstrong> ejects a helium-4\n      cluster; \u003Cstrong>beta\u003C\u002Fstrong> converts a neutron to a proton and emits an\n      electron; \u003Cstrong>gamma\u003C\u002Fstrong> sheds pure energy as a photon, dropping the\n      nucleus to a lower state without changing what it is.\n  - p: |\n      Firing particles at nuclei drives \u003Cem>reactions\u003C\u002Fem> — the controlled\n      transmutations that build new isotopes and reveal nuclear structure, each\n      governed by the same conservation laws of energy, momentum, and charge.\n  - fig: nuc-chain\n    n: \"004\"\n    caption: |\n      A fission chain reaction branches: each split releases neutrons that split\n      more nuclei.\n  - p: |\n      Split a heavy nucleus and the fragments are more tightly bound than the\n      whole — \u003Cstrong>fission\u003C\u002Fstrong> releases energy, plus spare neutrons that\n      can split more nuclei. When each fission provokes more than one further\n      fission, the chain reaction sustains itself, tamed in a reactor or unleashed\n      in a bomb.\n  - fig: nuc-fusion\n    n: \"005\"\n    caption: |\n      Fusion joins two light nuclei into a more tightly bound one, releasing the\n      difference.\n  - p: |\n      Run the curve uphill from the other end and light nuclei \u003Cstrong>fuse\u003C\u002Fstrong>\n      into heavier, more tightly bound ones — the process that powers the stars and\n      forged the elements, if the reactants can first be forced through their mutual\n      repulsion.\n  - p: |\n      From sizes and masses through the nuclear force, the decay laws, reactions,\n      fission, and fusion, the subject is one long reading of a single curve — and\n      of the enormous energies stored in the gap between where a nucleus sits and\n      where it would rather be.\n---\n\nNuclear physics studies the structure and transformations of the atomic nucleus,\nand nearly every result traces back to one graph: the binding energy per nucleon.\nThe sequence starts with the raw facts — nuclear sizes, shapes, and masses — then\nbuilds the force that binds nucleons together and the models that organize them,\nfrom the liquid drop to the shell and collective pictures. From there it turns to\nchange: the radioactive-decay law and its half-lives, then alpha, beta, and gamma\ndecay with the interactions that drive each. Nuclear reactions supply the\nexperimental tools and the conservation laws that constrain them, and the two\ngreat energy-releasing processes — fission, with its self-sustaining chain\nreactions and reactors, and fusion, powering the stars and the synthesis of the\nelements — close the arc. A final thread follows how nuclear radiation interacts\nwith matter and the applications that follow. It follows Krane and Wong, with\nTipler & Llewellyn and Tipler & Mosca for the foundations.\n",{"text":65,"minutes":66,"time":67,"words":68},"1 min 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Properties",1,"nuclear-properties",[993,998,1003,1009,1015],{"title":994,"path":995,"lessonNumber":990,"topics":996,"summary":997},"Nuclear Composition and Ground-State Properties","\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-constituents-nuclide-chart",[989],"The nucleus is a bound assembly of Z protons and N neutrons packed to a radius R = R0 A^(1\u002F3) at a nearly constant density of about 10^17 kg\u002Fm^3. We fix the vocabulary of nuclides, derive nuclear size from mirror-nuclide and electron-scattering data, read the binding-energy-per-nucleon curve, and model it with the liquid-drop semiempirical mass formula.\n",{"title":999,"path":1000,"lessonNumber":16,"topics":1001,"summary":1002},"Nuclear Size, Shape, and Charge Distributions","\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-size-charge-distributions",[989],"Elastic electron scattering resolves the nucleus by its de Broglie wavelength. The measured cross section is the Mott point-charge cross section modulated by a form factor, and that form factor is the Fourier transform of the charge density. Diffraction minima fix the radius, the small-angle slope fixes the mean-square radius, and the fitted Woods-Saxon profile gives a central density and a skin thickness. Mirror-nucleus Coulomb energies, muonic-atom X-rays, and optical isotope shifts give independent radii that all track R = R0 A^(1\u002F3).\n",{"title":1004,"path":1005,"lessonNumber":1006,"topics":1007,"summary":1008},"Nuclear Masses, Mass Excess, and Separation Energies","\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-masses-binding-energy",3,[989],"The atomic mass unit fixes the scale, and the mass excess collects the small binding-driven deviation from the integer mass number. Penning-trap cyclotron frequencies now measure masses to parts in a billion, and every decay and reaction Q-value is a difference of these masses. One- and two-nucleon separation energies read the binding difference between neighbouring nuclides directly, showing the even-odd pairing stagger and the sharp drops at magic numbers, and their vanishing marks the neutron and proton drip lines that bound the chart of the nuclides.\n",{"title":1010,"path":1011,"lessonNumber":1012,"topics":1013,"summary":1014},"The Semi-Empirical Mass Formula and the Valley of Stability","\u002Fnuclear-physics\u002Fnuclear-properties\u002Fsemi-empirical-mass-formula",4,[989],"Five physical terms reproduce nuclear binding across the chart: a volume term from saturation, a surface term from the deficit of edge neighbours, a Coulomb term from the electrostatic self-energy of a charged sphere, an asymmetry term from the Pauli cost of unequal proton and neutron filling, and a pairing term. The formula is quadratic in Z at fixed A, so isobars lie on a mass parabola whose minimum sets the most stable charge and whose slope dictates the direction of beta decay. The same competition between surface and Coulomb energy defines the fissility parameter and the onset of fission.\n",{"title":1016,"path":1017,"lessonNumber":1018,"topics":1019,"summary":1020},"Nuclear Spin, Magnetic Dipole, and Electric Quadrupole Moments","\u002Fnuclear-physics\u002Fnuclear-properties\u002Fnuclear-moments-multipoles",5,[989],"The ground state of a nucleus carries a definite spin and parity, a magnetic dipole moment of order the nuclear magneton, and, when its spin exceeds one-half, an electric quadrupole moment that measures its shape. The single-particle Schmidt lines predict the magnetic moment of an odd-A nucleus from the last unpaired nucleon, and the measured moments fall between them. The quadrupole moment distinguishes prolate from oblate deformation, and hyperfine structure is the experimental handle that fixes the spin and the moments from an atomic spectrum.\n",{"module":1022,"moduleNumber":16,"slug":1023,"lessons":1024},"The Nuclear Force","nuclear-force-deuteron",[1025,1030,1035,1040],{"title":1026,"path":1027,"lessonNumber":990,"topics":1028,"summary":1029},"The Nuclear Force and the Shell Model","\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnuclear-force-shell-overview",[1022],"The strong force between nucleons is short-range, charge-independent, saturated, and repulsive at its core, about a hundred times stronger than Coulomb. Yukawa explained it as an exchange of massive mesons, tying the force's range to the meson mass through the uncertainty principle. Layered on top, an independent-particle shell model with strong spin-orbit coupling reproduces the magic numbers 2, 8, 20, 28, 50, 82, 126.\n",{"title":1031,"path":1032,"lessonNumber":16,"topics":1033,"summary":1034},"The Deuteron and the Tensor Force","\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fthe-deuteron",[1022],"The deuteron is the only bound two-nucleon state: one shallow level at 2.22 MeV, no excited states. A square-well fit fixes a depth near 35 MeV over a 2 fm range, yet the wavefunction leaks so far past the edge that most of the probability lies outside the force. Its spin-1 ground state, magnetic moment close to the sum of the free-nucleon moments, and small but nonzero electric quadrupole moment together force a D-state admixture and a non-central tensor force.\n",{"title":1036,"path":1037,"lessonNumber":1006,"topics":1038,"summary":1039},"Nucleon-Nucleon Scattering and the Interaction's Structure","\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fnucleon-nucleon-scattering",[1022],"Scattering probes the nuclear force above threshold. Partial-wave analysis reduces low-energy data to a single s-wave phase shift, and the effective-range expansion packages that into a scattering length and an effective range. The triplet channel binds (the deuteron) while the singlet is only virtual, which together explain the anomalously large free neutron-proton cross section. Comparing pp, nn, and np results establishes charge symmetry and charge independence, and polarization experiments expose the spin-orbit and tensor pieces.\n",{"title":1041,"path":1042,"lessonNumber":1012,"topics":1043,"summary":1044},"Meson Exchange, the Yukawa Potential, and Isospin","\u002Fnuclear-physics\u002Fnuclear-force-deuteron\u002Fmeson-theory-isospin",[1022],"Yukawa's massive-field propagator turns the range of the nuclear force into a meson mass: the exchanged quantum's Compton wavelength is the range. One-pion exchange fixes the long-range tail, complete with the tensor structure the deuteron demanded, while heavier mesons build the intermediate attraction and the repulsive core. Charge independence becomes an isospin symmetry, the force is diagonalized by the total isospin through a tau-dot-tau interaction, and the whole picture sits inside QCD as a residual color force between color-neutral nucleons.\n",{"module":1046,"moduleNumber":1006,"slug":1047,"lessons":1048},"Nuclear Models","nuclear-models",[1049,1054,1059,1064],{"title":1050,"path":1051,"lessonNumber":990,"topics":1052,"summary":1053},"The Fermi Gas Model","\u002Fnuclear-physics\u002Fnuclear-models\u002Ffermi-gas-model",[1046],"Treating the nucleus as two degenerate Fermi gases of protons and neutrons confined in a common well fixes the Fermi momentum near 250 MeV\u002Fc and the Fermi energy near 33 MeV from the nuclear density alone. The average kinetic energy per nucleon is about 20 MeV, the well depth is the Fermi energy plus the separation energy, and unequal proton and neutron Fermi levels reproduce the asymmetry term of the mass formula.\n",{"title":1055,"path":1056,"lessonNumber":16,"topics":1057,"summary":1058},"The Liquid-Drop Model and Collective Deformation","\u002Fnuclear-physics\u002Fnuclear-models\u002Fliquid-drop-collective-coordinates",[1046],"Deforming a charged liquid drop into a spheroid raises its surface energy and lowers its Coulomb energy; the two effects compete through the deformation parameter to set a stability minimum and a fission barrier. The ratio of Coulomb to twice the surface energy is the fissility Z-squared over A, which crosses one near 49 and marks the point where the sphere is unstable. The same surface tension that restores small deformations quantizes into collective vibrations, carrying the static mass formula into dynamic collective motion.\n",{"title":1060,"path":1061,"lessonNumber":1006,"topics":1062,"summary":1063},"The Shell Model: Single-Particle States and Spin-Orbit Coupling","\u002Fnuclear-physics\u002Fnuclear-models\u002Fshell-model-single-particle",[1046],"A harmonic-oscillator well reproduces the first three magic numbers but fails above twenty; adding a strong inverted spin-orbit term that drives the stretched j equals l plus one-half level down closes the gaps at 28, 50, 82, and 126. The filled shells couple to zero, so the last unpaired nucleon fixes the ground-state spin and parity, and its single-particle magnetic moment falls on the Schmidt lines. Configuration mixing sets the limits of the extreme single-particle model.\n",{"title":1065,"path":1066,"lessonNumber":1012,"topics":1067,"summary":1068},"The Collective Model: Rotations, Vibrations, and Deformed Nuclei","\u002Fnuclear-physics\u002Fnuclear-models\u002Fcollective-model-rotations-vibrations",[1046],"Deformed nuclei rotate with energies proportional to I times I plus one, giving the ground-state band its characteristic level ratios, while near-spherical nuclei vibrate in quantized surface phonons that build one- and two-phonon multiplets. The Nilsson model tracks single-particle levels as the well deforms, moments of inertia fall between the rigid and irrotational limits, backbending marks the sudden alignment of a broken pair, and giant resonances are the bulk dipole and quadrupole modes of the whole nucleus.\n",{"module":1070,"moduleNumber":1012,"slug":1071,"lessons":1072},"Radioactive Decay","radioactive-decay",[1073,1078],{"title":1074,"path":1075,"lessonNumber":990,"topics":1076,"summary":1077},"Radioactivity and Decay Modes","\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-law-modes",[1070],"Unstable nuclei decay at a rate proportional to how many remain, giving the exponential law N(t) = N0 e^(-lambda t) with half-life t = 0.693\u002Flambda. We work through the three common modes: alpha decay as Coulomb-barrier tunneling with the Geiger-Nuttall rule, beta decay whose continuous spectrum demands the neutrino, and gamma de-excitation, and follow a decay chain across the chart of nuclides.\n",{"title":1079,"path":1080,"lessonNumber":16,"topics":1081,"summary":1082},"Serial Decay, the Bateman Equations, and Radioactive Equilibrium","\u002Fnuclear-physics\u002Fradioactive-decay\u002Fdecay-kinetics-equilibrium",[1070],"A radioactive parent that decays into a radioactive daughter obeys a coupled pair of rate equations whose solution is the Bateman formula. Depending on the half-life ordering the chain settles into secular equilibrium (equal activities), transient equilibrium (a fixed activity ratio), or no equilibrium. Constant production under irradiation drives the activity toward a saturation value equal to the production rate, competing decay modes split the total decay constant into partial constants, and the natural decay series in secular equilibrium underpin radiometric dating.\n",{"module":1084,"moduleNumber":1018,"slug":1085,"lessons":1086},"Alpha Decay","alpha-decay",[1087,1092],{"title":1088,"path":1089,"lessonNumber":990,"topics":1090,"summary":1091},"Alpha Decay and the Gamow Theory of Tunneling","\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-decay-gamow-theory",[1084],"The alpha Q-value turns positive above mass number 150 because the emitted helium-4 is exceptionally tightly bound. Emission proceeds by quantum tunneling through the Coulomb barrier: a WKB integral from the nuclear surface to the outer turning point gives the Gamow factor, and multiplying its penetrability by the assault frequency yields half-lives spanning more than twenty orders of magnitude. The leading term reproduces the Geiger-Nuttall relation, log t½ proportional to the daughter charge over the square root of Q.\n",{"title":1093,"path":1094,"lessonNumber":16,"topics":1095,"summary":1096},"Fine Structure, Angular Momentum, and Hindrance Factors","\u002Fnuclear-physics\u002Falpha-decay\u002Falpha-fine-structure-hindrance",[1084],"A single parent emits several alpha groups of slightly different energy, each feeding a distinct level of the daughter, so the alpha spectrum maps the daughter's low-lying states. Emission with orbital angular momentum L raises the barrier by a centrifugal term and is allowed only when angular-momentum and parity selection rules permit. Comparing the measured partial half-life to the Gamow estimate defines a hindrance factor near unity for even-even ground-state transitions and large for odd-A decays that must rearrange the unpaired nucleon.\n",{"module":1098,"moduleNumber":1099,"slug":1100,"lessons":1101},"Beta Decay and the Weak Interaction",6,"beta-decay",[1102,1107,1112,1117],{"title":1103,"path":1104,"lessonNumber":990,"topics":1105,"summary":1106},"Beta Decay Energetics and the Neutrino","\u002Fnuclear-physics\u002Fbeta-decay\u002Fbeta-decay-energetics-neutrino",[1098],"Beta decay converts a neutron into a proton or the reverse, adjusting Z at fixed A along an isobaric mass parabola. We write the three processes (beta-minus, beta-plus, electron capture), reduce every Q-value to a difference of neutral atomic masses, and read the continuous electron spectrum as the fingerprint of a third, nearly massless particle. Pauli's neutrino, its detection by Reines and Cowan, and the endpoint bound on its mass close the lesson.\n",{"title":1108,"path":1109,"lessonNumber":16,"topics":1110,"summary":1111},"Fermi's Theory: Kurie Plots and ft Values","\u002Fnuclear-physics\u002Fbeta-decay\u002Ffermi-theory-beta-decay",[1098],"Fermi treated beta decay as a point-contact weak transition and read its rate from the golden rule. The electron spectrum then follows from phase space and the Coulomb Fermi function; the Kurie plot straightens it to a line whose intercept is the endpoint. Integrating the spectrum gives the comparative half-life ft, whose logarithm sorts transitions into superallowed, allowed, and forbidden classes governed by the Fermi and Gamow-Teller selection rules.\n",{"title":1113,"path":1114,"lessonNumber":1006,"topics":1115,"summary":1116},"The Weak Interaction and Parity Violation","\u002Fnuclear-physics\u002Fbeta-decay\u002Fweak-interaction-parity-violation",[1098],"Beta decay violates mirror symmetry. The Wu experiment on polarized cobalt-60 showed electrons emitted preferentially against the nuclear spin, a pseudoscalar correlation forbidden if parity were conserved. The result fixes the weak charged current as left-handed V minus A, forces neutrinos to be left-handed and antineutrinos right-handed (measured by Goldhaber), and places beta decay within the electroweak theory as W-boson exchange turning a down quark into an up quark.\n",{"title":1118,"path":1119,"lessonNumber":1012,"topics":1120,"summary":1121},"Double Beta Decay and Neutrino Mass","\u002Fnuclear-physics\u002Fbeta-decay\u002Fdouble-beta-decay-neutrino-mass",[1098],"For even-A isobars the pairing term splits the mass parabola into two curves, and a handful of even-even nuclides sit below their odd-odd neighbor yet above the next even-even one: single beta decay is forbidden but second-order double beta decay is allowed. The two-neutrino mode is a standard-model process with the longest measured lifetimes in nature; the neutrinoless mode would require the neutrino to be its own antiparticle and its rate measures the effective Majorana mass, the sharpest probe of the absolute neutrino mass scale.\n",{"module":1123,"moduleNumber":1124,"slug":1125,"lessons":1126},"Gamma Decay",7,"gamma-decay",[1127,1132,1137],{"title":1128,"path":1129,"lessonNumber":990,"topics":1130,"summary":1131},"Multipole Radiation and Selection Rules","\u002Fnuclear-physics\u002Fgamma-decay\u002Fgamma-multipole-radiation",[1123],"Gamma decay carries a nucleus from an excited state to a lower one by emitting a photon of definite angular momentum and parity. We correct the photon energy for nuclear recoil, expand the radiation field into electric and magnetic multipoles, and read off how the transition rate collapses with each increase in multipole order. The Weisskopf single-particle estimates set the scale, and angular-momentum and parity conservation fix which multipole dominates.\n",{"title":1133,"path":1134,"lessonNumber":16,"topics":1135,"summary":1136},"Internal Conversion and Isomers","\u002Fnuclear-physics\u002Fgamma-decay\u002Finternal-conversion-isomers",[1123],"A nucleus can shed excitation energy without emitting a photon by handing it directly to an atomic electron. We define the internal-conversion coefficient, trace its growth with atomic number, multipole order, and decreasing energy, and treat the electron-only E0 transitions and internal pair formation. When the lowest allowed multipole is high and the energy low, the gamma rate falls so far that the excited state survives as a metastable isomer.\n",{"title":1138,"path":1139,"lessonNumber":1006,"topics":1140,"summary":1141},"Angular Correlations and the Mössbauer Effect","\u002Fnuclear-physics\u002Fgamma-decay\u002Fangular-correlations-mossbauer",[1123],"Two gammas emitted in cascade are not independent in direction: detecting the first selects magnetic substates of the intermediate level and makes the second anisotropic, so the correlation function fixes the intermediate spin. The same nuclear resonance that recoil normally destroys is recovered when the emitter is locked in a lattice, giving the Mössbauer effect and its part-in-a-trillion resolution of isomer shifts and hyperfine fields.\n",{"module":1143,"moduleNumber":1144,"slug":1145,"lessons":1146},"Nuclear Reactions",8,"nuclear-reactions",[1147,1152,1157],{"title":1148,"path":1149,"lessonNumber":990,"topics":1150,"summary":1151},"Nuclear Reactions, Fission, and Fusion","\u002Fnuclear-physics\u002Fnuclear-reactions\u002Freaction-kinematics-cross-sections",[1143],"A nuclear reaction X(x, y)Y is governed by its Q value and its cross section, the effective target area for a given process. Splitting the curve of binding energy near iron in either direction releases energy: fission of heavy nuclei by neutron capture and a chain reaction, and fusion of light nuclei that powers the Sun and needs Lawson's density-confinement criterion to be practical.\n",{"title":1153,"path":1154,"lessonNumber":16,"topics":1155,"summary":1156},"The Compound Nucleus and Resonance Reactions","\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fcompound-nucleus-resonances",[1143],"Low-energy reactions proceed through a long-lived intermediate state whose decay forgets how it formed. Bohr's independence hypothesis factorizes the cross section into a formation step and a branching ratio, an isolated level gives the single-level Breit-Wigner line shape with total width Γ tied to the lifetime by Γτ = ħ, and at high excitation overlapping levels merge into a statistical continuum described by evaporation spectra and the Hauser-Feshbach average.\n",{"title":1158,"path":1159,"lessonNumber":1006,"topics":1160,"summary":1161},"Direct Reactions and the Optical Model","\u002Fnuclear-physics\u002Fnuclear-reactions\u002Fdirect-reactions-optical-model",[1143],"A complex optical potential replaces the many-body target by a single particle moving in an average field whose imaginary part removes flux into non-elastic channels, reproducing the diffraction pattern of elastic scattering. Direct reactions bypass the compound nucleus, transferring a nucleon in one step: stripping and pickup deposit or remove a single nucleon, the angle of the first peak in the distorted-wave angular distribution fixes the transferred orbital angular momentum, and its magnitude gives the spectroscopic factor.\n",{"module":1163,"moduleNumber":1164,"slug":1165,"lessons":1166},"Nuclear Fission",9,"fission",[1167,1172],{"title":1168,"path":1169,"lessonNumber":990,"topics":1170,"summary":1171},"The Fission Barrier and Fragment Energetics","\u002Fnuclear-physics\u002Ffission\u002Ffission-barrier-dynamics",[1163],"Fission is the large-amplitude collective deformation of a heavy nucleus into two fragments. The liquid-drop model sets a barrier from the competition between rising surface energy and falling Coulomb energy under quadrupole deformation, with the fissility parameter Z²\u002FA measuring how close a nucleus is to instability. Bohr-Wheeler theory separates spontaneous from neutron-induced fission, the fragment mass yield is double-humped and asymmetric, about 200 MeV is released per event, and shell corrections add a second minimum that produces fission isomers.\n",{"title":1173,"path":1174,"lessonNumber":16,"topics":1175,"summary":1176},"Chain Reactions and Reactor Physics","\u002Fnuclear-physics\u002Ffission\u002Fchain-reactions-reactor-physics",[1163],"A self-sustaining chain reaction is a fixed point of neutron bookkeeping: the multiplication factor k counts the neutrons in one generation per neutron in the last, and criticality is k = 1. The four-factor formula tracks a neutron through fast fission, resonance escape, thermal utilization, and reproduction; moderation slows fission neutrons to the thermal energies where the fission cross section is largest; and the small delayed-neutron fraction sets the timescale that makes a reactor controllable. Breeding converts fertile U-238 and Th-232 into new fissile fuel.\n",{"module":1178,"moduleNumber":1179,"slug":1180,"lessons":1181},"Fusion and Nucleosynthesis",10,"fusion-nucleosynthesis",[1182,1187,1192],{"title":1183,"path":1184,"lessonNumber":990,"topics":1185,"summary":1186},"Fusion Reactions and Confinement","\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Ffusion-reactions-confinement",[1178],"Light nuclei release energy when they fuse because binding per nucleon rises steeply toward the iron peak, but the Coulomb barrier suppresses the rate at reactor temperatures. The thermonuclear rate is a convolution of the Maxwell distribution with the tunneling probability, sharply peaked at the Gamow energy. The deuterium-tritium reaction has the lowest barrier and largest cross section; sustained energy gain requires the Lawson triple product of density, temperature, and confinement time, reached by magnetic or inertial confinement.\n",{"title":1188,"path":1189,"lessonNumber":16,"topics":1190,"summary":1191},"Stellar Nucleosynthesis","\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fstellar-nucleosynthesis",[1178],"Main-sequence stars burn hydrogen to helium through the proton-proton chain and the CNO cycle, both releasing 26.7 MeV per helium nucleus. Helium burning bridges the mass-5 and mass-8 gaps by the triple-alpha process through the Beryllium-8 and Hoyle resonances, and successive carbon-to-silicon burning stages climb to the iron peak, where fusion stops. The elements beyond iron are built by slow and rapid neutron capture, and the solar neutrino flux confirms the reactions directly.\n",{"title":1193,"path":1194,"lessonNumber":1006,"topics":1195,"summary":1196},"Big-Bang Nucleosynthesis","\u002Fnuclear-physics\u002Ffusion-nucleosynthesis\u002Fbig-bang-nucleosynthesis",[1178],"In the first three minutes the expanding universe forged the light elements. The weak interaction froze the neutron-to-proton ratio near one in six when the reaction rate fell below the expansion rate, and free-neutron decay lowered it to about one in seven before the deuterium bottleneck broke. Almost every surviving neutron ended in helium-4, fixing the primordial helium mass fraction near 0.25, with trace deuterium, helium-3, and lithium-7. The deuterium abundance measures the cosmic baryon density.\n",{"module":1198,"moduleNumber":1199,"slug":1200,"lessons":1201},"Radiation and Applications",11,"radiation-matter-applications",[1202,1207,1212,1217,1222],{"title":1203,"path":1204,"lessonNumber":990,"topics":1205,"summary":1206},"Stopping Power and the Range of Charged Particles","\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fcharged-particle-stopping-power",[1198],"A heavy charged particle loses energy in a dense sequence of small Coulomb collisions with atomic electrons, at a rate the Bethe-Bloch formula fixes from the particle's charge and speed and the medium's electron density and mean excitation energy. The rate scales as the inverse square of the speed, so most energy is deposited at the end of the track in the Bragg peak, and integrating the reciprocal rate gives a sharp range. Electrons differ: they also radiate, and above a critical energy bremsstrahlung dominates. Fast particles above the phase velocity of light in the medium emit Cherenkov radiation.\n",{"title":1208,"path":1209,"lessonNumber":16,"topics":1210,"summary":1211},"Interactions of Photons and Neutrons","\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fphoton-neutron-interactions",[1198],"Photons are removed from a beam in single events, so their intensity falls exponentially with a linear attenuation coefficient built from three processes: the photoelectric effect at low energy, Compton scattering at intermediate energy, and pair production above twice the electron rest energy, each with its own atomic-number and energy dependence. Neutrons carry no charge and interact only with nuclei, moderating by elastic scattering and being captured with a cross section that rises as one over speed away from resonances.\n",{"title":1213,"path":1214,"lessonNumber":1006,"topics":1215,"summary":1216},"Radiation Detectors and Nuclear Spectroscopy","\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fradiation-detectors",[1198],"Every detector converts the energy a radiation deposits into a measurable electrical signal. Gas counters read the ionization directly, in three operating regions set by the applied voltage; scintillators convert the energy to light read out by a photomultiplier; semiconductor detectors collect electron-hole pairs and give the best energy resolution because so many carriers are made per event. The resolution is governed by the number of independent charge carriers, and the pulse-height spectrum of a gamma line shows a full-energy photopeak, a Compton continuum with its edge, and escape peaks.\n",{"title":1218,"path":1219,"lessonNumber":1012,"topics":1220,"summary":1221},"Dosimetry, Radiation Biology, and Protection","\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fdosimetry-radiation-biology",[1198],"Absorbed dose is the energy deposited per unit mass, measured in gray. Equal absorbed doses do unequal biological damage because densely ionizing radiation deposits its energy along short tracks: weighting the dose by a radiation factor gives the equivalent dose, and weighting by tissue sensitivity gives the effective dose, both in sieverts. Deterministic effects have a threshold and a severity that grows with dose; stochastic effects are assumed to follow a linear-no-threshold probability. Natural background dominates the dose to the population, and protection rests on time, distance, and shielding.\n",{"title":1223,"path":1224,"lessonNumber":1018,"topics":1225,"summary":1226},"Applications — Dating, Analysis, and Nuclear Medicine","\u002Fnuclear-physics\u002Fradiation-matter-applications\u002Fnuclear-applications-dating-medicine",[1198],"Charged particles lose energy continuously and stop at a well-defined range with a Bragg peak, while gamma rays are attenuated exponentially. These interactions define radiation detectors and dosimetry (gray and sievert) and drive the applications: neutron activation analysis, magnetic resonance imaging, PET, and radiometric dating with carbon-14 and long-lived rock clocks.\n",1786059479770]