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Nuclear Size

Nuclear Size. Alpha particle (+2e). Gold nucleus (+79e). d. Not exactly for Au!!!. Quite old!!!. Nuclear Size. Closest approach “d”. E  = E Coulomb  d = 2kZe 2 /E  What about the recoil nucleus? HW 7 Show that where m N : mass of the nucleus m  : mass of alpha

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Nuclear Size

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  1. Nuclear Size Alpha particle (+2e) Gold nucleus (+79e) d Not exactly for Au!!! Quite old!!! Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  2. Nuclear Size • Closest approach “d”. • E = ECoulomb d = 2kZe2/E • What about the recoil nucleus? • HW 7Show that • where mN : mass of the nucleus • m : mass of alpha • What are the values of d for 10, 20, 30 and 40 MeV  on Au? • How does this explain … ? Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  3. Nuclear Shape • Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure  Nuclear radius. • Deformations…! Consequences….!! • Is there a sharp spherical wall…???!!! • HW 8 • if it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by: Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  4. Nuclear Binding Energy Btot(A,Z) = [ ZmH+ Nmn- m(A,Z) ] c2 Bm Bave(A,Z) = Btot(A,Z) / A HW 9Krane 3.9 Atomic masses from: HW 10Krane 3.12 http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all Separation Energy Neutron separation energy: (BE of last neutron) Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2 = Btot(A,Z) - Btot(A-1,Z)HW 11Prove that HW 12 Similarly, find Sp and S. HW 13 Krane 3.13 HW 14 Krane 3.14 Magic numbers Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  5. Nuclear Binding Energy Magic numbers Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  6. Nuclear Binding Energy In general X  Y + a Sa(X) = (ma + mY –mX) c2 = BX –BY –Ba The energy needed to remove a nucleon from a nucleus ~ 8 MeV  average binding energy per nucleon (Exceptions???). Mass spectroscopy  B. Nuclear reactions  S. Nuclear reactionsQ-value Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  7. Nuclear Binding Energy Surface effect Coulomb effect ~200 MeV  Fission HWc 4 Think of a computer program to reproduce this graph. Fusion  Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  8. Nuclear Binding Energy • HW 15 • A typical research reactor has power on the order of 10 MW. • Estimate the number of 235U fission events that occur in the reactor per second. • b) Estimate the fuel-burning rate in g/s. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  9. Nuclear Binding Energy Is the nucleon bounded equally to every other nucleon? C ≡ this presumed binding energy. Btot = C(A-1)  A  ½ Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!!Clearly wrong … !  wrong assumption finite range of strong force, and force saturation. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  10. Nuclear Binding Energy Lead isotopes Z = 82 For constant Z Sn (even N) > Sn (odd N) For constant N Sp (even Z) > Sp (odd Z) Remember HW 14 (Krane 3.14). 208Pb (doubly magic)  can then easily remove the “extra” neutron in 209Pb. 208Pb Neutron Separation Energy Sn (MeV) Neutron Number N Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  11. Nuclear Binding Energy Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !)  Stability (e.g. -particle, N=2, Z=2). Sn (A, Z, even N) – Sn (A-1, Z, N-1) This is the neutron pairing energy. even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei. Symmetry? Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  12. Abundance Systematics HWc 1\ • Compare: • even Z to odd Z. • even N to odd N. • even A to odd A. • even-even to even-odd to odd-even to odd-odd. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  13. Neutron Excess Z = N Odd A Even A Remember HWc 1. Asymmetry Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

  14. Neutron Excess Remember HWc 1. Asymmetry Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

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