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‚Introduction to Nuclear and Particle Physics'

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‚Introduction to Nuclear and Particle Physics' WS2010/11: ‚‚IInnttrroodduuccttiioonn ttoo NNuucclleeaarr aanndd PPaarrttiiccllee PPhhyyssiiccss‘‘ Lectures: Elena Bratkovskaya Thursday, 14:00-16:15 Room: Phys_ 2.216 Office: FIAS 3.401; Phone: 069-798-47523 E-mail: [email protected] Script of lectures + tasks for homework: http://th.physik.uni-frankfurt.de/~brat/index.html 1 LLiitteerraattuurree 1) Walter Greiner, Joachim A. Maruhn, „Nuclear models“; ISBN 3-540-59180-X Springer-Verlag Berlin Heidelberg New York 2) „Particles and Nuclei. An Introduction to the Physical Concepts“ Bogdan Povh, Klaus Rith, Christoph Scholz, and Frank Zetsche - 2006 http://books.google.com/books?id=XyW97WGyVbkC&lpg=PR1&ots=zzIVa2OptV&dq=Bogdan%20Povh%2C%20Klaus%20Rith%2C%20Christoph%20Scholz%2C%20and%20Fr ank%20Zetsche&pg=PR1#v=onepage&q&f=false 3) "Introduction to nuclear and particle physics" Ashok Das, Thomas Ferbel - 2003 http://books.google.de/books?id=E39OogsP0d4C&printsec=frontcover&dq=related:ISBN0521621968&lr=#v=onepage&q&f=false 4) "Elementary particles" Ian Simpson Hughes - 1991 http://books.google.de/books?id=JN6qlZlGUG4C&printsec=frontcover&dq=related:ISBN0521621968&lr=#v=onepage&q&f=false 5) "Particles and nuclei: an introduction to the physical concepts" Bogdan Povh, Klaus Rith - 2004 http://books.google.de/books?id=rJe4k8tkq7sC&printsec=frontcover&dq=related:ISBN0521621968&lr=#v=onepage&q&f=false 6) "Particle physics" Brian Robert Martin, Graham Shaw - 2008 http://books.google.de/books?id=whIbrWJdEJQC&printsec=frontcover&dq=related:ISBN0521621968&lr=#v=onepage&q&f=false 7) "Nuclear and particle physics" Brian Robert Martin - 2009 http://books.google.de/books?id=ws8QZ2M5OR8C&printsec=frontcover&dq=related:ISBN0521621968&lr=#v=onepage&q&f=false 3 LLeeccttuurree 11 IInnttrroodduuccttiioonn:: uunniittss,, ssccaalleess eettcc.. NNuucclleeaarr mmooddeellss WS2010/11: ‚Introduction to Nuclear and Particle Physics‘ 4 SSccaalleess iinn tthhee UUnniivveerrssee 5 SSccaalleess iinn nnuucclleeaarr pphhyyssiiccss 6 PPhhyyssiiccaall uunniittss Common unit for length and energy: •• Length: fm (Fermi) – femtometer 1 fm = 10-15m =10-13 cm corresponds approximately to the size of the proton •• Energy: eV – electron volt 1 eV = 1.602.10-19 J is the energy gained by a particle with charge 1e by traversing a potential difference of 1V Prefixes for the decimal multiples: 1keV = 103 eV; 1MeV = 106 eV; 1GeV = 109 eV; 1TeV= 1012 eV •• Units for particle masses: MeV/c2 or GeV/c2 according to the mass-energy relation: E=mc2, the total energy E2=mc2+p2c2 ° speed of light in vacuum c=299 792 458 m/s ° Correspondence to the International System of Units (SI): 1MeV/ c2 = 1.783 .10-30 kg 7 SSyysstteemm ooff uunniittss iinn eelleemmeennttaarryy ppaarrttiiccllee pphhyyssiiccss Length and energy scales are connected by the uncertainty principle: The Planck constant h is a physical constant reflecting the sizes of quanta in quantum mechanics the reduced Planck constant : Unit system used in elementary particle physics: identical determination for masses, momentum, energy, inverse length and inverse time [m]=[p]=[E]=[1/L]=[1/t]= keV, MeV,… Typical masses: •• photon mγ=0 •• neutrino mν < 1 eV −31 •• electron me=511 keV (= 9.10938215×10 kg) −27 8 •• nucleon (proton, neutron) mp=938 MeV (=1.672621637×10 kg) AAnngguullaarr mmoommeennttuumm C Spin – S The spin angular momentum S of any physical system is quantized. The allowed values of S are: S = > s(s +1) Spin quantum numbers s is n/2, where n can be any non-negative integer: 1 3 s = 0, ,1, ,2,... 2 2 C Orbital angular momentum (or rotational momentum) – L Orbital angular momentum can only take on integer quantum numbers L = 0,1,2,... C C C Total angular momentum: J = S + L For each J exist 2J+1 projections of the angular momentum 9 SSttaattiissttiiccss:: ffeerrmmiioonnss aanndd bboossoonnss System of N particles: 1,2,…,N Wavefunction: Symmetry: Replace two particles: 1 2 Phase factor C (C2=1): •• Bosons: C= +1 •• Fermions: C= -1 Spin-statistics theorem: •• fermions have a half integer spin (1/2, 3/2, 5/2, …) •• bosons have an integer spin (0, 1, 2, …) E.g.: Bosons: photons (γ) J=1, pions (π) J=0 Fermions: e,µ,ν,p,n J=1/2, ∆-resonance J=3/2 10 EElleeccttrriicc cchhaarrggee aanndd ddiippoollee mmoommeenntt °° The electric charge is quantized : quanta – e the fine-structure constant as: 0 is the electric constant. In particle physics 0=1, so °° The Bohr magneton and the nuclear magneton are the physical constants and natural units which are used to describe the magnetic properties (magnetic dipole moment) of the electron and atomic nuclei respectively. Bohr magneton B (in SI units) : −24 B = 9.27400915×10 J/T −5 µe = 1.001159652 µB = 5.7883817555×10 eV/T < by factor 1836 nuclear magneton N : N B proton: p= 2.79 N neutron: n= -1.91 N ~ -2/3 p 11 FFuunnddaammeennttaall iinntteerraaccttiioonnss Interaction Current Theory Mediators Relative Range Strength (m) Strong Quantum chromodynamics(QCD) gluons 1038 10−15 Electromagnetic Quantum electrodynamics(QED) photons 1036 Weak Electroweak Theory W and Z bosons 1025 10−18 Gravitation General Relativity(GR) gravitons 1 (not yet discovered) Particle Electromagnetic Week Strong Statistic interraction interraction interraction Photon + (+) B Lepton + + F Baryon + + + F Meson + + + B B=Bosons F=Fermions Quarks + + + F Gluons + B 12 SSttrruuccttuurree ooff aattoommss ((hhiissttoorryy)) The existance of atomic nucleus was discovered in 1911 by Ernest Rutherford, Hans Geiger and Ernest Marsden leads to the downfall of the plum pudding model (J.J. Thomson) of the atom, and the development of the Rutherford (or planetary) model. J.J. Thomson (1904) ‚plum pudding model‘ : the atom is composed of electrons surrounded by a soup of uniformly distributed positive charge (protons) to balance the electrons' negative charges Ernest Rutherford (1871-1937) Experiment 1909-1911: Rutherford bombarded gold foils with α-particles (ionized helium atom) α-particles Observed results: a small portion of Expected results from plum pudding the particles were deflected by large model : alpha particles passing through angles, indicating a small, concentrated the atom practically undisturbed. the atom practically undisturbed. positive charge ‚core‘ positive charge ‚core‘ 13 NNuucclleeaarr mmooddeellss Rutherford (or planetary) model: the atom has very small positive 'core' – nucleus - containing protons with negatively charged electrons orbiting around it (as a solar sytem - planets around the sun). the atom is 99.99% empty space ! The nucleus is approximately 100,000 times smaller than the atom. The diameter of the nucleus is in the range of 1.75 fm (1.75×10−15 m) for hydrogen (the diameter of a single proton) to about 15 fm for the heaviest atoms Experimental discovery of the neutrons – James Chadwick in 1932 (the existance of neutral particles (neutrons) has been predicted by Rutherford in 1921) Experimentally found:: The nucleus consists of protons and neutrons Neutron: charge = 0, spin 1/2 mn=939.56 MeV (mp=938.27 MeV) − Mean life time τn = 885.7 s ~ 15 minutes n → p + e +ν e 14 NNuucclleeaarr ffoorrccee The atomic nucleus consists of protons and neutrons (two types of baryons) bound by the nuclear force (also known as the residual strong force). The baryons are further composed of subatomic fundamental particles known as quarks bound by the strong interaction. The residual strong force is a minor residuum of the strong interaction which binds quarks together to form protons and neutrons. Properties of nuclear forces : 1. Nuclear forces are short range forces. For a distance of the order of 1 fm they are quite strong. It has to be strong to overcome the electric repulsion between the positively charged protons. 2. Magnitude of nuclear force is the same for n-n, n-p and p-p as it is charge independent. 3. These forces show the property of saturation. It means each nucleon interacts only with its immediate neighbours. 4. These forces are spin dependent forces. 5. Nuclear forces do not obey an inverse square law (1/r2). They are non-central non-conservative forces (i.e. a noncentral or tensor component of the force does not conserve orbital angular momentum, which is a constant of motion under central forces). 15 NNuucclleeaarr YYuukkaawwaa ppootteennttiiaall Interactions between the particles must be carried by some quanta of interactions, e.g. a photon for the electromagnetic force. Hideki Yukawa (1907–1981): Nuclear force between two nucleons can be considered as the result of exchanges of virtual mesons (pions) between them. Yukawa potential (also called a screened Coulomb potential): e−mr V(r) = −g2 r Yukawa potential with a hard core: where g is the coupling constant (strength of interraction). repulsive core Since the field quanta (pions) are massive (m) the nuclear force has a certain range, i.e. V0 for large r. At distances of a few fermi, the force between two nucleons is weakly attractive, indicated by a negative potential. At distances below 1 fermi (rN ~1.12 fm): the force becomes attraction strongly repulsive (repulsive core), preventing nucleons merging. The core relates to the quark structure of the nucleons. 16 GGlloobbaall PPrrooppeerrttiieess ooff NNuucclleeii A - mass number gives the number of nucleons in the nucleus Z - number of protons in the nucleus (atomic number) N – number of neutrons in the nucleus A = Z + N A In nuclear physics, nucleus is denoted as Z X , where X is the chemical symbol of the 1 12 197 element, e.g. 1 H − hydrogen, 6 C − carbon, 79 Au− gold Different combinations of
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