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UT Arlington PHYS 3446 - Lecture Notes

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Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu1PHYS 3446 – Lecture #5Monday, Sept. 18, 2006Dr. Jae Yu1. Nuclear Phenomenology2. Properties of Nuclei• Labeling• Masses•Sizes• Nuclear Spin and Dipole Moment• Stability and Instability of Nuclei3. Nature of the Nuclear ForceMonday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu2Announcements• We will have a private lecture from Dr. H. Weerts this Wednesday– Current director of HEP division of Argonne National AcceleratorLaboratory– 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.Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu3Nuclear 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 α particles (E>25MeV), especially for low Z target nuclei.• In 1920’s, James Chadwick found – Serious discrepancies between Coulomb scattering expectation andthe elastic scattering of α 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 Î Nuclei consist of nucleons, protons and neutronsMonday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu4• 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)– ExamplesNucleus Labeling X11HApnNN+42HeHydrogen Helium16 8OOxygen14 7NNitrogen12 6CCarbon19 9FFluorideXAZ=AXorMonday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu5• 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 Npand NnTypes of Nuclei 12 6C13 6C613C713N613C713N25 51Mn26 51Fe235 92U238 92U238 94Pu238 92URef: http://www.fas.org/nuke/intro/nuke/plutonium.htmMonday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu6• 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/c2and 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 apartNuclear Properties: Masses of NucleiAZX()ZAMX=(),MAZpZm+AZX(),MAZ=()nAZm−()pnZmAZm<+−Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu7• 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 nucleusNuclear Properties: Binding Energy(),MAZ∆=()2.,BE M AZ c=∆(),MAZ()pnZmAZm−−−Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu8• BE per nucleon isNuclear Properties: Binding EnergyBA=()2,MAZ cA−∆=()()()2,pnZmAZmMAZcA+− −=• Rapidly increase with A till A~60 at which point BE~9MeV.• A>60, the B.E gradually decrease Î For most the large A nucleus, BE~8MeV.BEA−Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu9• 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.Nuclear Properties: Binding Energy=p====2mT==22cmc T= p=1971.62 940 8Mev fmfm−≈≈⋅⋅Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu10• 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<2x10-12cmNuclear Properties: Sizes2min0'ZZerE=Monday, Sept. 18, 2006 PHYS 3446, Fall 2006Jae Yu11• 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 Î 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 nucleusNuclear Properties:


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UT Arlington PHYS 3446 - Lecture Notes

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