Interacting Boson Model — Nuclear Shape Phases

The IBM (Arima-Iachello) describes nuclei via s and d bosons. The symmetry triangle connects three dynamical symmetries: U(5) (spherical vibrator), SU(3) (axially deformed rotor), and O(6) (γ-unstable). Explore energy spectra and E2 transitions across the triangle.

IBM Parameters

χ (SU3 vs O6): -1.32 η (U5 mixing): 0.50 N bosons: 6

H = ε n̂_d + κ Q̂·Q̂
Q̂_μ = (d†s+s†d̃)_μ + χ(d†d̃)_μ
U(5): ε≫κ → vibrator E~nd
SU(3): χ=-√7/2 → rotor E~L(L+1)
O(6): χ=0 → γ-unstable
E2: T̂(E2)=e₂Q̂

Phase: SU(3) limit