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Shell model

Shell model. Extreme independent particle model!!! Does the core really remain inert?. 1d 3/2. ?. 1p 1/2. l  pairing . 2s 1/2. 1d 5/2. Shell model. 20. Core. Extreme independent particle model  only 23 rd neutron. More complete shell model  all three “valence” nucleons.

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Shell model

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  1. Shell model Extreme independent particle model!!! Does the core really remain inert? 1d3/2 ? 1p1/2 l  pairing  2s1/2 1d5/2 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  2. Shell model 20 Core • Extreme independent particle model  only 23rd neutron. • More complete shell model  all three “valence” nucleons. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  3. Shell model Discuss the energy levels of nuclei with odd number of nucleons in the 1f7/2 shell. HW 26 and 43Sc, 43Ti. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  4. Shell model Dipole Magnetic Moment HW 27Show that and examineEqs. 5.9 in Krane. In addition, work out problem 5.8 in Krane  Conclusion? Proton: gs(free) = 5.5856912 ? gl = 1 ? Neutron: gs(free) = -3.8260837 ? gl = 0 ? What about + and -? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  5. Shell model In the xy-plane: Q - r2. Electric Quadrupole Moment Refined QM  Extremes Single particle: n = 1  - ive Q Single hole: n = 2j +ive Q Number of protons in a subshell Examine Table 5.1 and Fig.5.10 in Krane <r2> for a uniformly charged sphere Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  6. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  7. Shell model Validity A < 150 190 < A < 220 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  8. Collective model • Large quadrupole moments  nucleus as a collective body (Liquid drop model). • Interactions between outer nucleons and closed shells cause permanent deformation. • Single-particle state calculated in a non-spherical potential  complicated. • Spacing between energy levels depends on size of distortion. • Doubly magic  1st excited state away from GS. • Near closure  single-particle states. • Further away from closure  collective motion of the core  excited states. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  9. A net nuclear potential due to filled core shells exists. Collective model combines both liquid drop model and shell model. Two major types of collective motion: Rotations: Rotation of a deformed shape. Vibrations: Surface oscillations. Collective model Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  10. Collective model • Rotational motion observed for non-spherical nuclei. • Deformed nuclei are mainly 150 < A < 190 and A > 220. • Ellipsoid of surface: Difference between semimajor and semiminor axes. Deformation parameter. Rav HW 28 Problems 5.11 and 5.12 in Krane. Discuss effect on quadrupole moment.  < 0  > 0 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  11. Collective model Symmetry axis Rotational States GS (even-even) 0+ Symmetry  only even I Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  12. Collective model HW 29compare measured energies of the states of the ground state rotational band to the calculations. Rigid body or liquid drop? Intermediate  Short range and saturation of nuclear force. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  13. Collective model HW 29 (continued) Higher angular momentum  centrifugal stretching  higher moment of inertia  lower energy than expected  additional evidence for lack of rigidity. 164Er Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  14. Collective model Odd-A Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  15. Collective model Vibrational States Average shape Instantaneous shape Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  16. 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, First Semester, 2007-2008 (Saed Dababneh).

  17. Collective model • = 0 monopole R(t) = Ravr +00Y00 • = 1 dipole Both monopole and dipole excitations require high energy. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  18. Collective model • = 2 quadrupole • Quantization of quadrupole vibration is called a quadrupole phonon. • A phonon carries two units of angular momentum and even parity (-12). • This mode is dominant. For most even-even nuclei, a low lying state with Jπ=2+ exists. • Octupole phonon. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  19. 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, First Semester, 2007-2008 (Saed Dababneh).

  20. Collective model Two-phonon triplet at twice the energy of the single phonon state. HW 30 Krane 5.10 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

  21. 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, First Semester, 2007-2008 (Saed Dababneh).

  22. 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, First Semester, 2007-2008 (Saed Dababneh).

  23. 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, First Semester, 2007-2008 (Saed Dababneh).

  24. Nuclear Reactions HW 31 • 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, First Semester, 2007-2008 (Saed Dababneh).

  25. Nuclear Reactions HW 31(continued) • The double valued situation occurs between TTh and the upper limit Ta\. • Double-valued in a forward cone. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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