Alpha-cluster Model for 6Li, 8Be and 12C Nuclei within the Framework of the Generator Coordinate Approach

Abstract

The ground and excited states of 6Li, 8Be and 12C nuclei are investigated using the generator- coordinate method (GCM)
involving (αd), (αα) and (3α) – clusters structures, respectively. It is assumed that the α and d particles are not structureless point particles, rather are represented by a certain four-nucleon and two-nucleon wave functions, respectively, so that the generating function depends on the possible nucleon configurations. The nucleonic wave functions are defined through the harmonic oscillator shell model (HOSM), whereas the nucleon-nucleon interaction is represented by a Gaussian-shape potential. The GCM kernels are projected out on nonorthonormal functions, instead of performing the standard Gram-Schmidt orthonormalization procedure. The total wave function is expanded in terms of these functions to obtain standard eigenvalue equation in nonorthonormal basis. Calculated spectroscopic properties are presented to be in excellent agreement with the experimental values and better than other calculation methods, such as the variational Monte Carlo (VMC), and the Green’s function Monte Carlo (GFMC).