Introduction to Atomic Nuclei
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1 Introduction to Atomic Nuclei Che-Ming Ko Texas A&M University The nucleus Chart of nuclides Nuclear force Nuclear structure and excitations Radioactivity and fission Nuclear reactions and accelerators Quark structure of nucleus Phases of nuclear matter Origin of the elements Applications of nuclear science 1
2 Nucleus: Discovered by Ernest Rutherford in 1911 in alpha particles scattering from atoms. It is the core of the atom, where most of its mass and all of its positive charge is concentrated. Except for 1 H, the nucleus consists of a combination of protons and neutrons. Proton: Nucleus of the hydrogen atom; carries same amount of charge (~1.6x10-19 C) as electron but opposite sign; weights (~1.67x10-27 kg or 938 MeV/c 2 ) about 2000 times heavier than the electron; has spin =1/2 ħ. (Planck constant ħ~ 1x10-34 J sec) Neutron: discovered by James Chadwick in 1933; does not have charge; spin=1/2 ħ; slightly heavier than proton; halflife~10 min ( ). Nucleon: either proton or neutron 2
3 Chart of the Nuclides ~ 300 in nature ~ 1000 artificially produced ~ 6000 to be found Magic numbers: 2, 8, 20, 28, 50, 82, 126 are neutron and/or proton numbers in nuclei with greater binding energy and stability. 3
4 Nuclear force Nucleus is bounded by strong short-range attractive force between nucleons resulting from the exchange of the pion (π), first proposed by Hideki Yukawa in 1935 but was not found until 1947 by Cecil Powell. Pion: mass ~ 1/7 of proton mass; has three different charges (e,0,-e); zero spin. Coulomb potential e - e - N Nuclear potential N e - e - N N Nuclear potential is ~ 100 times stronger than the Coulomb potential between electrons due to photon ( ) exchange. 4
5 Nuclear size can be measured from electron scattering as shown by Robert Hofstadter in Woods-Saxon form Diffuseness a~0.5 fm Surface thickness t=(4ln3)a~2.3 fm Central nuclear density ρ 0 ~Ac~A/Z Zc~0.16 fm -3 Radius R~1.2 A 1/3 fm Nuclei behave like liquid drops! 5
6 Nuclear mass can be expressed by liquid drop formula as suggested by Weizsäcker (1935); Bethe & Bacher (1936). Binding energy: Minimum energy required to dissociate a nucleus into its constituent protons and neutrons; ~ 8 MeV per nucleon. 56 Fe a v ~16 MeV, a s ~17 MeV, a sys ~25 MeV, a c ~0.7 MeV 6
7 Collective model: A large number of nucleons can execute collective motions; introduced by Bohr, Mottelson & Rainwater in ~1950 for understanding nuclear rotational and vibrational excitations. Rotational excitations J π Quadrupole vibrational excitations J π J=angular momentum (ħ) π=parity; I=moment of inertia 7
8 Shell model: Nucleons occupy shell-like orbits inside nucleus; proposed by Maria Meyer & Hans Jensen in ~1949 to explain the magic numbers and the single-particle excitations in nuclei. J π J=angular momentum (ħ) π=parity Protons and neutrons are fermions which satisfy the Pauli exclusion principle (proposed by Wolfgang Pauli in 1933) that no two fermions can 8 occupy same quantum state.
9 Radioactivity Alpha decay: the nucleus releases an alpha particle ( 4 He) Beta decay: the nucleus either emits an electron and antineutrino or a positron and neutrino Gamma decay: the nucleus lower its internal energy by emitting a photon 9
10 Fission: A nucleus can split into two large fragments; discovered by Hahn and Strassman in 1939; and explained by Meitner and Frisch as well as Bohr and Wheeler in same year. Fission occurs as a result of quantum tunneling through the fission barrier. Normally, 235 U decays by alpha emission with only ~7X10-9 probability for fission due to a high fission barrier. A thermal neutron is needed to induce the fission by exciting the nucleus, leading to a lower fission barrier thus a larger tunneling probability. 10
11 Nuclear reactions and accelerators With energetic particles (e-,p,d,π, ) from Van de Graff generator (~1931), cyclotrons (invented by Ernest Lawrence ~1939) and modern accelerators, we can study the properties of nuclei and create new isotopes, e.g. Continuous Electron Beam Accelerator Facility Thomas Jefferson National Laboratory 6 GeV (upgrade to 12 GeV) Excited states of p & n Quark effects in nuclei Relativistic Heavy Ion Collider Brookhaven National Laboratory p+p, Au+Au@100 GeV/A Quark-gluon plasma Proton structure TAMU K500 Superconducting Cyclotron Variety of beams <100 MeV/A Nuclear collective motions Exotic nuclei Hot nuclei Nuclear reactions relevant to nucleosynthesis 11
12 Quarks inside nuclei 12
13 Phases of nuclear matter As nuclei are heated, they transform from a liquid to a gas of nucleons. With further heating, nucleons are excited to their resonances (N and Δ) and emit pions (π) and kaons (K) as well as other meson resonances (ρ, ω, K*), forming a hadronic gas. At extreme high temperature, hadrons dissolve into a plasma of quarks and gluons. Under compressions, nucleons inside nuclei lose their identity and form a dense matter of quarks. Heavy ion collisions make it possible to heat and compress the nuclear matter and thus study the properties of nuclear matter under extreme conditions. 13
14 Origin of the elements 14
15 Nuclear reactions during the first three minutes kt > 800 kev: neutrons and protons were in chemical equilibrium 800 kev > kt > 60 kev: neutrons decayed freely ( 60 kev > kt > 30 kev: nucleosynthesis occurred Absence of stable nuclei at A=5 or 8 prevents the production of heavy elements during big bang nucleosynthesis. 15
16 Nuclear reactions inside stars: proposed by Hans Bethe in 1939 Hydrogen burning (7X10 6 y) Helium burning (5X10 5 y) CNO cycle Carbon burning (600 y) Neon burning (1 y) Oxygen burning (6 mon) Silicon burning (1 d) Time scales for stars of 25 solar mass 16
17 Precollapse structure of massive stars Through neutron captures and beta decays in supernova or neutron-star collisions, nuclei heavier than Fe can be produced (Burbidge, Burbidge, Fowler, and Hoyle ~ ).
18 Structure of Neutron stars 18
19 Mass-radius relations of neutron stars Mass and radius of a neutron star are sensitive to the stiffness of nuclear symmetry energy at high density 19
20 Applications of nuclear science 20
21 Radioactive dating Use naturally occurring radioactive isotopes ( 14 C) for dating objects that were once living. Smoke detectors Use alpha emitter 241 Am to ionize the air. Nuclear medicine: Use radioactive isotopes for diagnosing and treating disease ( 99m Tc, 60 Co, 131 I) as well as for generating images of brain activity ( 18 F) via Positron Emission Tomography (PET). Magnetic Resonance Imaging (MRI): Use nuclear magnetic transitions to produce 3-D images of the human body. Space exploration Use alpha particles for identifying chemical elements present in Martian rocks. Nuclear reactors: Use fission of 235 U and 239 Pu nuclei to produce electric power. 21
22 We have discussed Summary The nucleus Chart of nuclides Nuclear force Nuclear structure and excitations Radioactivity and fission Nuclear reactions and accelerators Quark structure of nucleus Phases of nuclear matter Origin of the elements Applications of nuclear science For more information, see 22
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