Symplectic effective field theory for nuclear structure studies

Abstract

A symplectic effective field theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self-consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for $^{20}\mathrm{Ne}$, $^{22}\mathrm{Ne}$, and $^{22}\mathrm{Mg}$ are presented that yield energy spectra, $B(E2)$ values, and matter radii in good agreement with experimentally measured results.