Higher-Order Corrections in Effective Theory of Deformed Nuclei

The low-energy excitation bands of open-shell heavy nuclei have been accounted for by collective motion of the constituting nucleons. Macroscopically, heavy nuclei can be looked upon as deformed rotors undergoing surface vibration and rotation. Traditionally, deformed nuclei are described within the Bohr-Mottelson geometric model or the interacting boson model. An effective theory that exploits spontaneous symmetry breaking has recently been developed for axially deformed nuclei. It describes the rotational and vibrational degrees of freedom in terms of Nambu-Goldstone bosons and quadrupole phonons respectively, with a power counting based on their different energy scales. A systematic way to construct the rotationally invariant Lagrangian under axial symmetry was established at next-to-leading order.

The purpose of this thesis is to extend the effective theory for deformed nuclei up to next-to-next-to-leading order. Higher-order corrections to Nambu-Goldstone modes and rotation-vibration coupling for both even-even nuclei and odd-mass nuclei are studied. For pure rotation, higher-order Nambu-Goldstone modes prove to only perturb the energy spectrum by the corresponding powers of the leading-order eigenenergy. As expected, the next-to-next-to-leading-order calculation of Nambu-Goldstone modes exhibits a higher accuracy than next-to-leading order after fitting to experimental level schemes. When vibration is coupled to rotation, the next-to-leading-order Hamiltonian correctly yields the rotational-vibrational spectrum of deformed nuclei. In the derivation of rotation-vibration coupling Hamiltonian in even-even nuclei, a perturbative method (Fukuda's inversion method) for the Legendre transformation is employed. The effect of next-to-next-to-leading-order rotation-vibration coupling yields a correction of the moment of inertia that depends on the vibrational band head. Furthermore, for odd-mass nuclei with finite ground-state spins, a gauge invariant Hamiltonian is obtained. While the rotational band encompasses a combined contribution from intrinsic spin and azimuthal angular momentum, the vibrational spectrum exhibits a feature of Landau levels with a high density of states, stemming from the velocity-dependent Lagrangian.