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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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systematic changes in nuclear shapes
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

deformed potential s p model
Deformed Potential s.p. Model

Sven Gösta Nilsson (1955)

Axial Symmetry

About 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)



Shell Models

anisotropic harmonic oscillator model
Anisotropic Harmonic Oscillator Model


Shell Gap


Shell Models

Deformation Parameter

Ground state spin determined by last (unpaired) particle.

shell stabilized deformation
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.


After G. Musiol et al., Kern-u. Elementarteilchenphysik, VCH 1988