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The high-spin structures and isomers of the N = 81 isotones 135 Xe and 137 Ba are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Both nuclei are populated (i) in 136 Xe+ 238 U and (ii) 136 Xe+ 208 Pb MNT reactions employing the high-resolution Advanced Gamma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA, (iii), in the 136 Xe+ 198 Pt MNT reaction employing the γ-ray array GAMMASPHERE in combination with the gas-detector array CHICO, and (iv) via a 11 B+ 130 Te fusion-evaporation reaction with the HORUS γ-ray array at the University of Cologne. The high-spin level schemes of 135 Xe and 137 Ba are considerably extended to higher energies. The 2058-keV (19/2 − ) state in 135 Xe is identified as an isomer, closing a gap in the systematics along the N = 81 isotones. Its half-life is measured to be 9.0(9) ns, corresponding to a reduced transition probability of B(E2, 19/2 − → 15/2 − ) = 0.52(6) W.u. The experimentally-deduced reduced transition probabilities of the isomeric states are compared to shell-model predictions. Latest shell-model calculations reproduce the experimental findings generally well and provide guidance to the interpretation of the new levels.

The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for Nр8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons . The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for Nр8 and ϭNϩ1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling /N. In this case a few selected larger clusters (7рNр43) in the strongly correlated limit (U/t→ϩϱ) are considered. It is shown that the /N dependence of the spin-flip energy ⌬ sf shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. the magnetic moments and magnetic order on cluster geometry have precluded one so far from applying accurate firstprinciples methods to study this problem.An alternative approach, which has provided numerous significant results, is to consider a model that is simple enough to allow an exact or at least very accurate solution of the many-body problem, and that at the same time contains enough complexity to be able to shed light on the physics of real systems ͑e.g., 3d TM͒. The most popular and probably most simple physical model for describing correlated itinerant electrons on a lattice is given by the well-known Hubbard Hamiltonian 19where, as usual, c i † (c i ) refers to the creation ͑annihilation͒ operator for an electron at site i with spin , and n i ϭc i † c i is the corresponding number operator. In this model the dynamics of the valence electrons is ruled by the interplay of two simple terms. The first term is the kineticenergy operator, which describes the hopping of the electrons between nearest-neighbor sites i and j (tϾ0) leading to electron delocalization and bond formation. The second term takes into account the intra-atomic Coulomb repulsion U (Uу0), which is the dominant contribution from the electron-...