Master's Thesis · Nuclear structure theory
Four Phonon Anharmonicity and Angular Momentum Effects in Even-Even Spherical Nuclei
Aous Ahmad Abdo · with V. Zelevinsky
Spherical even-even nuclei vibrate in quantized surface ripples — quadrupole phonons. In the harmonic approximation their spectrum is a perfectly even ladder. This thesis treats the anharmonic corrections up to four phonons and solves the resulting Hamiltonian analytically, showing exactly how the degenerate multiplets split and shift.
The idea
Real nuclear vibrations interact. Writing the quartic phonon interaction in terms of the intermediate angular momenta of phonon pairs, and exploiting a hidden rotational symmetry in five-dimensional phonon space, the model becomes exactly solvable through a canonical transformation of the boson-pair operators.
The result
A closed-form energy spectrum. The ground quasi-rotational band takes the compact form
E(ν, 0) = ¼ (3ω_ν + 1/ω_ν)(ν + 5/2), ω_ν³ − ω_ν = 4(ν + k/2 + 1)λ
In the harmonic limit λ → 0 the spectrum is exactly equidistant, E = ν + 5/2; as the anharmonicity λ grows, the multiplets split and the level structure reorganizes — the effect made interactive in Chapter I.