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The Shell Model of the Nucleus 5. Nuclear moments. The Collective Model of the Nucleus

The Shell Model of the Nucleus 5. Nuclear moments. The Collective Model of the Nucleus. [Sec. 6.2, 6.4, 6.5, 6.6, 6.7 Dunlap]. The Bohr-Mottelson Collective Model of the Nucleus. James Rainwater (1917 – 1986) U.S.A. Aage Bohr (1922 – Denmark. Ben Mottelson (1926 – USA / Denmark.

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The Shell Model of the Nucleus 5. Nuclear moments. The Collective Model of the Nucleus

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  1. The Shell Model of the Nucleus5. Nuclear moments.The Collective Model of the Nucleus [Sec. 6.2, 6.4, 6.5, 6.6, 6.7 Dunlap]

  2. The Bohr-Mottelson Collective Model of the Nucleus James Rainwater (1917 – 1986) U.S.A Aage Bohr (1922 – Denmark Ben Mottelson (1926 – USA / Denmark Between about 1950 – 1955, Bohr and Mottelson followed the idea on collective nuclear motion suggested by Rainwater. All three received the 1975 Nobel Prize – “For their work on the connection of collective nuclear motion with single particle motion”

  3. Electric nuclear moments The electrostatic energy associated with charge distribution (r) in electric potential (r) is: ELECTRIC CHARGE ELECTRIC DIPOLE ELECTRIC QUADRUPOLE - - + + + + -

  4. Electric and Magnetic nuclear moments “For symmetry reasons the electric dipole moment of the nucleus (as well as all other static multipole moments with odd parity; for example – magnetic monopole, magnetic quadrupole or electric octupole) must VANISH. WHY? Because the both the strong and the electric forces are invarient under the parity operation – which means we should never get different nuclear properties under space inversion

  5. The nuclear Quadrupole moment Q PROLATE“Cigar” OBLATE“Dou-nut” Unlike atoms – nuclei can easily distort from spherical state. Unlike atoms the potential the nucleons move in is formed by the nucleons themselves. [In an atom it is the potential coming from the nucleus that dominates]

  6. The nuclear Quadrupole moment Q Quadrupole Moment (Barns) Magic Numbers

  7. The regions of sphericity Limits of manmade nuclides QUESTION – will mankind ever make this double magic?

  8. Quadrupole moment on the Shell model A proton or neutron removed from a closed shell configuration make a PROLATE ellipsoid An extra proton or neutron added to a closed shell configuration makes an OBLATE ellipsoid

  9. Quadrupole moment on the Shell model missing Odd proton extra QM expression missing Advanced treatment Odd neutron For a uniformly charged sphere: extra

  10. Deformation effects shell states Nilsson Model In a nonspherical nucleus a definite direction is defined – the direction 3 along the axis. The total angular momentum j is projected along the 3rd axis to give a new quantum no. K. = ± j, ±(j-1), ± (j-2) etc. This phenomenon also splits the degeneracy previously seen for spherical (closed shell) nuclei

  11. The Nilsson Shell Model Plot for Deformed Nuclei

  12. Irrotational collective rotation of the nucleus Nuclear collective rotation occurs around an axis perpendicular to the symmetry axis “3” The rotation is called irrotational because the nucleus is not quite solid – It is largely the “skin” of “outer shape” of the nucles that is rotating

  13. Collective rotational motion Consider energy of a rigid rotator with moment of inertia  J  and

  14. The nucleus can also vibrate Breathing mode – First observed in 1977 – very high energy Requires nuclear fluid compressibility Quadrupole Deformation Rotating wave with Sherical Harmonic Wavefunction – circulates – or vibrates the nucleus. Spin = 2, Parity = +

  15. Nuclear vibrations are bosonic

  16. High energy photon The giant dipole resonance p  n PHOTON CROSS SECTION (mb) PHOTON ENERGY (MeV)

  17. s • The magnetic moment of the nucleus comes about because • We have charged particles – protons moving around the center of the nucleus (i.e. p, d, f, g etc states) • Both protons and neutrons have their own INTRINSIC magnetic moments. s For the PROTON we must add the mag mom due to ORBITAL motion to get the full mag. Mom. For the NEUTRON we can write down a similar equation but define that gln=0 z j l proton Nuclear magnetic moments After time averaging rapid motion about j then See SEC 6.6

  18. Magnetic dipole moments MAGNETIC MOMENT (nuc magnetons) JACKNIFE ODD NEUTRON STRETCH Shown are the “Schmidt lines” NUCLEAR SPIN J

  19. Magnetic dipole moments Shown are the “Schmidt Lines” named after German physicist T. Schmidt who discovered these lines empirically in 1937. MAGNETIC MOMENT (nuc magnetons) ODD PROTON STRETCH ODD NEUTRON JACKNIFE NUCLEAR SPIN J

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