1. PHYS 3446 – Lecture #5 Monday, Sept. 18, 2006 Dr. JaeYu • Nuclear Phenomenology • Properties of Nuclei • Labeling • Masses • Sizes • Nuclear Spin and Dipole Moment • Stability and Instability of Nuclei • Nature of the Nuclear Force PHYS 3446, Fall 2006 Jae Yu

2. Announcements • We will have a private lecture from Dr. H. Weerts this Wednesday • Current director of HEP division of Argonne National Accelerator Laboratory • Current member of HEPAP-P5 advisory panel • Former spokesperson of the DØ experiment • Expert in strong interactions • Sorry, I still don’t have e-mail from three of you • Please come by my office after the class to add you on the list • Workshop on Sept. 30 • 10am – 5pm, CPB303 and HEP experimental areas • Food and refreshments • Quiz in the class next Monday • First term exam on Wednesday, Oct. 4. PHYS 3446, Fall 2006 Jae Yu

3. Nuclear Phenomenology • What did Rutherford scattering experiment do? • Demonstrated the existence of a positively charged central core in an atom • The formula did not quite work for high energy a particles (E>25MeV), especially for low Z target nuclei. • In 1920’s, James Chadwick found • Serious discrepancies between Coulomb scattering expectation and the elastic scattering of a particle on He. • None of the known effects, including quantum effect, described the discrepancy. • Clear indication of something more than Coulomb force involved in the interactions • Chadwick’s discovery neutron in 1932  Nuclei consist of nucleons, protons and neutrons PHYS 3446, Fall 2006 Jae Yu

4. Nucleus Labeling • What are good quantities to label nuclei of an atom X? • Electrical Charge or atomic number Z (number of protons) • Most chemical properties depends on charge • Total number of nucleons A (=Np+Nn) • Examples or Hydrogen Helium Carbon Nitrogen Fluoride Oxygen PHYS 3446, Fall 2006 Jae Yu

5. Types of Nuclei • Isotopes: Nuclei with the same Z but different A • Same number of protons but different number of neutrons • Have similar chemical properties • Isobars: Nuclei with same A but different Z • Same number of nucleons but different number of protons • Different Chemical properties • Isomers or resonances of the ground state: Excited nucleus to a higher energy level • Mirror nuclei: Nuclei with the same A but with switched Np and Nn PHYS 3446, Fall 2006 Jae Yu Ref: http://www.fas.org/nuke/intro/nuke/plutonium.htm

6. Nuclear Properties: Masses of Nuclei • How many protons and neutrons does nucleus have? • Np=Z and Nn=A-Z • So what should the mass of look like? • Where mp=938.27MeV/c2 and mn=939.56MeV/c2 • However measured mass turns out to be • The energy difference is used as binding energy, keeping the nucleus together • One of reasons why nuclei are not falling apart PHYS 3446, Fall 2006 Jae Yu

7. Nuclear Properties: Binding Energy • The mass deficit • Is always negative and is proportional to the nuclear binding energy • How are the BE and mass deficit related? • What is the physical meaning of BE? • A minimum energy required to release all nucleons from a nucleus PHYS 3446, Fall 2006 Jae Yu

8. Nuclear Properties: Binding Energy • BE per nucleon is • Rapidly increase with A till A~60 at which point BE~9MeV. • A>60, the B.E gradually decrease  For most the large A nucleus, BE~8MeV. PHYS 3446, Fall 2006 Jae Yu

9. Nuclear Properties: Binding Energy • de Broglie’s wavelength: • Where is the Planck’s constant • And is the reduced wavelength • Assuming 8MeV was given to a nucleon (mn~940MeV), its wavelength is • Makes sense for nucleons to be inside a nucleus since the size is smaller than the nucleus. • Could they be electrons with 8MeV? • The wavelength is ~10fm, a whole lot larger than a nucleus. PHYS 3446, Fall 2006 Jae Yu

10. Nuclear Properties: Sizes • Sizes of subatomic particles are not as clearly defined as normal matter • Must be treated quantum mechanically via • probability distributions or expectation values • Atomic size is the average coordinate of the outermost electron and calculable via QM using Coulomb potential • Not calculable for nucleus since the potential is not known • Must rely on experimental measurements • For Rutherford scattering of low E projectile • DCA provides an upper bound on the size of a nucleus • These result in RAu<3.2x10-12cm or RAg<2x10-12cm PHYS 3446, Fall 2006 Jae Yu

11. Nuclear Properties: Sizes • Scatter very high E projectiles for head-on collisions • As E increases DCA becomes 0. • High E particles can probe deeper into nucleus • Use electrons to probe the charge distribution (form factor) in a nucleus • What are the advantages of using electrons? • Electrons are fundamental particles  No structure of their own • Electrons primarily interact through electromagnetic force • Electrons do not get affected by the nuclear force • The radius of charge distribution can be regarded as an effective size of the nucleus PHYS 3446, Fall 2006 Jae Yu