Quasimolecular resonances in the alpha +20Ne system

Abstract

By introducing a Lagrangian depending on a complex scalar field, a quantum analogue of the classical large amplitude collective motion in nuclei (solitonic excitations of the nuclear surface), successfully used for the evaluation of the preformation factors in alpha and cluster decays, was formulated. We have shown that in the classical limit the corresponding Lagrange equation, which is a modified nonlinear Schrodinger (MNLS) equation with soliton and breather solutions, becomes a Korteweg-de Vries (KdV) equation with only soliton solutions. By using a non-perturbative weak-coupling procedure we have quantized the normal modes of the soliton and breather solutions. We have shown that, in the third order approximation, the corresponding Hamiltonian becomes diagonal with a spectrum similar to a sum of nonlinear harmonic oscillator spectra. In this way an additional degree of freedom and new quantum numbers are introduced. This formulation, applied for the description of the quasimolecular spectra, explains some of the observed levels and also predicts positions and spins of other levels, of both even and odd parities, with the parameters having the same values for all levels.