W. Udo Schröder, 2012 Shell Models 2 Systematic Changes in Nuclear Shapes Møller, Nix, Myers, Swiatecki, Report LBL 1993: Calculations fit to experimental deformations. Nuclear quadrupole moments (Q 0 ) are large for N, Z between magic numbers. Close to magic numbers nuclei are spherical (Q 0 0), small and tightly bound. 2 ~ Q 0
Deformed Potential s.p. Model Rotational symmetry broken Conserved quantities: nucleonic angular momentum projections on symmetry axis: = projection of orbital =±1/2= projection of spin = projection of total angular momentum Energy level degeneracy: D =2 (± axial symmetry. Anisotropic harmonic oscillator model Principal quantum number N=n x +n y +n z = number of oscillator quanta. ( x, y, z ) are different fundamental frequencies) W. Udo Schröder, 2012 Shell Models 3 Sven Gösta Nilsson (1955) z Axial Symmetry About z
Anisotropic Harmonic Oscillator Model W. Udo Schröder, 2012 Shell Models 4 | || (N,n z,) Shell Gap Deformation Parameter Ground state spin determined by last (unpaired) particle.
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: W. Udo Schröder, 2012 Shell Models 5 x,y / z After G. Musiol et al., Kern-u. Elementarteilchenphysik, VCH 1988 Increasing larger n z /smaller n xy levels bind more strongly. Shell mixing. New shells at integer axis ratio. Disappearance and reappearance of shells.