Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #5 Monday, Sept. 18, 2006 Dr. Jae Yu 1.Nuclear Phenomenology 2.Properties of Nuclei Labeling Masses Sizes Nuclear Spin and Dipole Moment Stability and Instability of Nuclei 3.Nature of the Nuclear Force

Monday, Sept. 18, 2006PHYS 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 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.

Monday, Sept. 18, 2006PHYS 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  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  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

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 4 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 (=N p +N n ) –Examples Nucleus Labeling HydrogenHelium Oxygen Nitrogen Carbon Fluoride or

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 5 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 Np and NnNn Types of Nuclei Ref:

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 6 How many protons and neutrons does nucleus have? –N p =Z and N n =A-Z So what should the mass of look like? –Where m p =938.27MeV/c 2 and m n =939.56MeV/c 2 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 Nuclear Properties: Masses of Nuclei

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 7 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 Nuclear Properties: Binding Energy

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 8 BE per nucleon is Nuclear Properties: Binding Energy 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.

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 9 de Broglie’s wavelength: –Where is the Planck’s constant –And is the reduced wavelength Assuming 8MeV was given to a nucleon (m n ~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. Nuclear Properties: Binding Energy

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 10 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 R Au <3.2x cm or R Ag <2x cm Nuclear Properties: Sizes

Monday, Sept. 18, 2006PHYS 3446, Fall 2006 Jae Yu 11 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 Nuclear Properties: Sizes