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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

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

anisotropic harmonic oscillator model
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.

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.

wx,y/wz

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