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CoulEx

Nuclear s.p . Models The Deformed Shell Model. CoulEx. Systematic Changes in Nuclear Shapes. Møller , Nix, Myers, Swiatecki , Report LBL 1993: Calculations fit to experimental deformations.

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CoulEx

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  1. Nuclear s.p. Models The Deformed Shell Model CoulEx

  2. Systematic Changes in Nuclear Shapes Møller, Nix, Myers, Swiatecki, Report LBL 1993: Calculations fit to experimental deformations. Nuclear quadrupole moments (Q0) are large for N, Z between “magic” numbers. Close to magic numbers nuclei are spherical (Q0≈0), small and tightly bound. e2 ~ Q0 Shell Models

  3. Deformed Potential s.p. Model Sven Gösta Nilsson (1955) Axial Symmetry About z z Rotational symmetry broken  Conserved quantities: nucleonic angular momentum projections on symmetry axis: L= projection of orbital S=±1/2= projection of spin W=L+S= projection of total angular momentum Energy level degeneracy: DW=2 (± W ) axial symmetry. Anisotropic harmonic oscillator model  Principal quantum numberN=nx+ny+nz= number of oscillator quanta. (wx, wy, wz) are different fundamental frequencies) S L Shell Models

  4. Anisotropic Harmonic Oscillator Model |W|p Shell Gap |W|p(N,nz,L) Shell Models Deformation Parameter Ground state spin determined by last (unpaired) particle.

  5. Shell Stabilized Deformation Why are not all nuclei spherical? Observation: As nucleons are added to spherical (magic, closed-shell) nuclei, deformation increases  microscopic origin in nuclear structure & stability.Approximate trends: Shell Models Increasing d larger nz /smaller nxylevelsbind more strongly.  Shell mixing. New shells at integer axis ratio.  Disappearance and reappearance of shells. wx,y/wz After G. Musiol et al., Kern-u. Elementarteilchenphysik, VCH 1988

  6. End Def. Shell Model Shell Models

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