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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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
Sven Gösta Nilsson (1955)
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)
Ground state spin determined by last (unpaired) particle.
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:
Increasing d larger nz /smaller nxylevelsbind more strongly. Shell mixing. New shells at integer axis ratio. Disappearance and reappearance of shells.
After G. Musiol et al., Kern-u. Elementarteilchenphysik, VCH 1988