The double ionization energy (DIE) spectra are calculated for the spin-polarized aluminum and sodium clusters by means of the all-electron spin-polarized $GW+T$-matrix method based on the many-body perturbation theory. Our method using the one- and two-particle Green’s functions enables us to determine the whole spectra at once in a single calculation. The smaller is the size of the cluster, the larger the difference between the minimal double ionization energy and the twice of the ionization potential. This is because the strong Coulomb repulsion between two holes becomes dominant in small confined geometry. Due to Pauli’s exclusion principle, the parallel spin DIE is close to or smaller than the antiparallel spin DIE except for ${\text{Na}}_4$ that has well-separated highest and second highest occupied molecular-orbital levels calculated by the spin-dependent $GW$ calculation. In this paper, we compare the results calculated for aluminum and sodium clusters and discuss the spin-polarized effect and the cluster size dependence of the resulting spectra in detail.

• Received 7 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.165411