Structure of the giant multipole resonances inNe20andSi28

Abstract

Nuclear structure wave functions for the ground and excited states of light deformed nuclei are obtained by diagonalizing a "realistic" many nucleon Hamiltonian (kinetic energy plus a Brueckner $G$ matrix based on the Hamada-Johnston potential) in a suitably truncated nonorthogonal space of angular momentum projected deformed Slater determinants being constructed out of self-consistent Hartree-Fock single nucleon orbits. Possible spurious admixtures due to the center of mass motion are eliminated at least approximately by a separate diagonalization of the center of mass Hamiltonian. Taking into account a rather large single particle basis, calculations using this method are performed for the two $\mathrm{sd}$-shell nuclei $^{20}\mathrm{Ne}$ and $^{28}\mathrm{Si}$. Besides energies and wave functions, using alternatively an oscillator and a Woods-Saxon representation, the electromagnetic ground state transitions of both parities and of various multipolarities are also calculated as well as the corresponding spectroscopic amplitudes. The results are compared, where possible, with the experimental data and the results of other calculations. Special attention is paid to the strength distributions obtained for the various multipolarities. Though completely microscopic, the model yields fair qualitative agreement with the available experimental information. Furthermore, possible improvements of the method are discussed.NUCLEAR STRUCTURE $^{20}\mathrm{Ne}$, $^{28}\mathrm{Si}$; calculated level schemes and electromagnetic transitions. Angular momentum projected Hartree-Fock and particle-hole method. Structure of the giant multipole resonances.