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Collective model

Collective model. Vibrational States. Average shape. Instantaneous shape. Collective model. Symmetry. Instantaneous coordinate. Spherical harmonics. r 0 A 1/3. Amplitude. http://wwwnsg.nuclear.lu.se/basics/excitations.asp?runAnimation=beta10. = 1 dipole. = 2 quadrupole. = 3

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Collective model

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  1. Collective model Vibrational States Average shape Instantaneous shape Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  2. Collective model Symmetry Instantaneous coordinate Spherical harmonics r0A1/3 Amplitude http://wwwnsg.nuclear.lu.se/basics/excitations.asp?runAnimation=beta10 • = 1 dipole • = 2 quadrupole • = 3 octupole • = 0 monopole . Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  3. Collective model • = 0 monopole R(t) = Ravr +00Y00 • = 1 dipole Both monopole and dipole excitations require high energy. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  4. Collective model • = 2 quadrupole • Quantization of quadrupole vibration is called a quadrupole phonon. • A phonon carries two units of angular momentum. • This mode is dominant. For most even-even nuclei, a low lying state with Jπ=2+ exists. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  5. Collective model l = 4  = +4, +3, +2, +1, 0, -1, -2, -3, -4 l = 2  = +2, +1, 0, -1, -2 l = 0  = 0 Triplet 0+, 2+, 4+ Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  6. Collective model Two-phonon triplet at twice the energy of the single phonon state. HW 24 Krane 5.10 Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  7. Nuclear Reactions • X(a,b)Y • First in 1919 by Rutherford: • 4He + 14N  17O + 1H • 14N(,p)17O • Incident particle may: change direction, lose energy, completely be absorbed by the target…… • Target may: transmute, recoil…… • b =   Capture reaction. • If B.E. permits  fission (comparable masses). • Different exit channels a + X  Y1 + b1 •  Y2 + b2 •  Y3 + b3 ……. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  8. Nuclear Reactions • Recoil nucleus Y could be unstable   or  emission. • One should think about: • Reaction dynamics and conservation lawsi.e. conditions necessary for the reaction to be energetically possible. • Reaction mechanism and theories which explain the reaction. • Reaction cross sectioni.e. rate or probability. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  9. Nuclear Reactions • Conservation Laws • Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??)……. b pb  a pa X  +ve Q-value  exoergic reaction. -ve Q-value  endoergic reaction. pY Y +ve Q-value  reaction possible if Ta 0. -ve Q-value  reaction not possible if Ta 0. (Is Ta > |Q| sufficient?). Conservation of momentum …… Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  10. Nuclear Reactions HW 25 • Conservation of momentum. • We usually do not detect Y. • Show that: • The threshold energy (for Ta): (the condition occurs for  = 0º). • +ve Q-value  reaction possible if Ta 0. • Coulomb barriers…….!!! • -ve Q-value  reaction possible if Ta> TTh. double valued !? solve for Q Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  11. Nuclear Reactions HW 25(continued) • The double valued situation occurs between TTh and the upper limit Ta\. • Double-valued in a forward cone. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  12. Nuclear Reactions Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  13. Nuclear Reactions Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  14. Nuclear Reactions Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  15. Nuclear Reactions Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  16. Nuclear Reactions • If the reaction reaches excited states of Y 58Ni(,p)61Cu even less …. less proton energy Highest proton energy See Figures 11.4 in Krane Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  17. Nuclear Reactions • Neutron scattering • Inelastic Q = -Eex (=-E*). • Elastic Q = 0. HW 26 Discuss the elastic and inelastic scattering of neutrons using the relations you derived in HW 25. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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