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UT Arlington PHYS 3446 - Nuclear properties

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PHYS 3446 – Lecture #6AnnouncementsSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18AssignmentsMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu1PHYS 3446 – Lecture #6Monday, Sept. 25, 2006Dr. Jae Yu1. Nuclear properties•Mott scattering•Spin and Magnetic Moments•Stability and Instability of Nuclei•Nature of the Nuclear Force•Short Range Nature of the Nuclear Force•Shape of the Nuclear Potential•Yukawa Potential•Range of Yukawa PotentialMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu2Announcements•LPCC Workshop–10am – 5pm, Saturday, Sept. 30–CPB303 and HEP experimental areas–Need to go on shopping…–Need to know who is coming •First term exam–Date and time: 1:00 – 2:30pm, Wednesday, Oct. 4–Location: SH105–Covers: Ch 1 – Ch 3, Appendix AMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu3•At relativistic energies the magnetic moment of electron also contributes to the scattering–Neville Mott formulated Rutherford scattering in QM and included the spin effects–R. Hofstadter, et al., discovered the effect of spin, nature of nuclear (& proton) form factor in late 1950s •Mott scattering x-sec (scattering of a point particle) is related to Rutherford x-sec:•Deviation from the distribution expected for point-scattering provides a measure of size (structure)Nuclear Properties: SizesMottdds� �� �W� �=24cos2Rutherfordddq s� �� �W� �Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu4•Another way is to use the strong nuclear force of sufficiently energetic strongly interacting particles ( mesons, protons, etc)–What is the advantage of using these particles?•If the energy is high, Coulomb interaction can be neglected•These particles readily interact with nuclei, getting “absorbed” into the nucleus•Thus, probe strong interactions directly–These interactions can be treated the same way as the light absorptions resulting in diffraction, similar to that of light passing through gratings or slitsNuclear Properties: SizesMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu5•The size of a nucleus can be inferred from the diffraction pattern•All these phenomenological investigation provided the simple formula for the radius of the nucleus to its number of nucleons or atomic number, A: Nuclear Properties: Sizes1 30R r A= �How would you interpret this formula?13 1 31.2 10 A cm-� =1 31.2 fmAMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu6•Both protons and neutrons are fermions with spins•Nucleons inside a nucleus can have orbital angular momentum•In Quantum Mechanics orbital angular momenta are integers•Thus the total angular momentum of a nucleus is–Integers: if even number of nucleons in the nucleus–Half integers: if odd number of nucleons in the nucleus•Interesting facts are–All nucleus with even number of p and n are spin 0.–Large nuclei have very small spins in their ground state•Hypothesis: Nucleon spins in the nucleus are very strongly paired to minimize their overall effectNuclear Properties: Spins1 2Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu7•Every charged particle has a magnetic dipole moment associated with its spin•e, m and S are the charge, mass and the intrinsic spin of the charged particle•The constant g is called Landé factor with its value:– : for a point like particle, such as the electron– : Particle possesses an anomalous magnetic moment, an indication of having a substructure Nuclear Properties: Magnetic Dipole Moments2eg Smcm=rr2g �2g =Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu8•For electrons, e~B, where B is Bohr Magneton•For nucleons, magnetic dipole moment is measured in nuclear magneton, defined using proton mass•Measured magnetic moments of proton and neutron:Nuclear Properties: Magnetic Dipole MomentsBm =2Npem cm =h2.79p Nm m�1.91n Nm m�-2eem c=h115.79 10 MeV/T-�Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu9•What important information do you get from these?–The Landé factors of the nucleons deviate significantly from 2.•Strong indication of substructure–An electrically neutral neutron has a significant magnetic moment•Must have extended charge distributions•Measurements show that mangetic moment of nuclei lie -3N~10N–Indication of strong pairing–Electrons cannot reside in nucleusNuclear Properties: Magnetic Dipole MomentsMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu10•The number of protons and neutrons inside the stable nuclei are–A<40: Equal (N=Z)–A>40: N~1.7Z–Neutrons outnumber protons–Most are even-p + even–n•See table 2.1–Supports strong pairing Nuclear Properties: StabilityN~1.7ZN=ZN ZNnuclEven Even 156Even Odd 48Odd Even 50Odd Odd 5Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu11•In 1896 H. Becquerel accidently discovered natural radioactivity–Study of Uranium salts’ fluorescent properties•Nuclear radio activity involves emission of three radiations:  and •These can be characterized using the device on the right– : Nucleus of He– : electrons– : photonsNuclear Properties: Instability•What do you see from above?–  and  are charged particles while  is neutral.–  is mono-energetic–  has broad spectrum•What else do you see?Monday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu12•Scattering experiments help to–Determine the properties of nuclei–Learn more global information on the characteristics of the nuclear force•From what we have learned, it is clear that there is no classical analog to nuclear force–Gravitational force is too weak to provide the binding–Can’t have an electromagnetic origin •Deuteron nucleus has one neutron and one proton •Coulomb force destabilizes the nucleus Nature of the Nuclear ForceMonday, Sept. 25, 2006 PHYS 3446, Fall 2006Jae Yu13•Atomic structure is well explained by the electromagnetic interaction–Thus the range of nucleus cannot be much greater than the radius of the nucleus–Nuclear force should range ~ 10-13 – 10-12cm•Binding energy is constant per each nucleon, essentially independent of the size of the nucleus–If the nuclear force is long-ranged, like the Coulomb force–For A nucleons, there would be ½ A(A-1) pair-wise interactions–Thus, the BE which reflects all possible interactions among the nucleons would grow as a function of


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UT Arlington PHYS 3446 - Nuclear properties

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