The 2-site Hubbard and $\mathsf{t}$-$\mathsf{J}$ models

The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Greens function formalism. The exact solution of the t-J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response properties have been studied as functions of the external parameters and compared between the two models and with some numerical and exact results. It has been shown that the 2-site Hubbard model already contains the most relevant energy scales of the Hubbard model: the local Coulomb interaction U and the spin-exchange one . As a consequence of this, for some relevant properties (kinetic energy, double occupancy, energy, specific heat and entropy) and as regards the metal-insulator transition issue, it has resulted possible to almost exactly mime the behavior of larger systems, sometimes using a higher temperature to get a comparable level spacing. The 2-site models have been also used as toy models to test the efficiency of the Greens function formalism for composite operators. The capability to reproduce the exact solutions, obtained by the exact diagonalization technique, gives a firm ground to the approximate treatments based on this formalism.Received: 16 July 2003, Published online: 30 January 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.)     

Photodissociation and photoionization of sodium coated C $_\mathsf{60}$ clusters

At the Prague Asterix Laser System Center (PALS) the Asterix iodine laser delivering up to 700 J/0.5 ns is used as a pump source for X-ray laser experiments and applications. The prepulse technique was applied which is known to improve the neon-like X-ray laser output at the J = 0-1 transition dramatically. Since Zn slab targets were used the operating wavelength was 21.2 nm. A prepulse having up to 20 J precedes the main pulse by 10 ns. The main beam and the prepulse beam are focussed by two different optical systems separately and their foci are superimposed at the target surface. By implementing a half-cavity set-up for double-pass amplification using a Mo/Si multilayer mirror - which can be used for more than 100 shots - the X-ray laser output was more than 10 times stronger than at the single pass in a 30 mm long plasma. Double-pass amplification was observed to be most efficient when the pump pulse duration was at least 150 ps longer than the round trip time ( ≈ 260 ps) in the half-cavity. Under this fundamental condition the X-ray laser reached saturation in the double-pass regime containing approx. 4 mJ energy which has been proved to be enough for future applications. In this contribution, the X-ray laser features like divergence in two dimensions, the beam quality (symmetry), the pointing angle and the integrated intensity giving an estimation of the output energy are investigated over 110 shots. To characterize the stability of the X-ray laser the shot distribution, the mean value and the standard deviation for these parameters are evaluated. For 18 shots in a series - what was achievable during one day - the corresponding values are given, and a statistical analysis carrying out a chi-squared test characterize the Zn X-ray laser as a robust tool suitable for applications. In the future it is planned to allocate X-ray laser beam time to external research groups. Received 17 May 2002 / Received in final form 10 September 2002 Published online 6 November 2002 RID="a" ID="a"e-mail: praeg@fzu.cz     

Ion trap nuclear resonance on $\mathsf{^{151}Eu^ + }$

Laser-microwave double resonance techniques applied to a cloud of a natural mixture of Eu ⁺ isotopes confined in a Penning trap has been used to induce and detect nuclear Zeeman transitions. In spite of the complex level structure of Eu ⁺ and overlapping spectra from the two isotopes five different transitions could be observed from which the nuclear magnetic moment can be derived. We obtain for ¹⁵¹ Eu ⁺ g _I = 1.377 34(6) demonstrating the potential for high accuracy of the technique. The experiment can be considered as a feasibility test that precise spectroscopy data using the ion storage technique can be obtained of very complex ions and under unfavourable conditions.Received: 13 June 2003, Published online: 12 August 2003PACS: 32.60. + i Zeeman and Stark effects - 32.10.Dk Electric and magnetic moments, polarizability     

Insulating surface layer on single crystal K $\mathsf{_{3}}\mathsf{C}\mathsf{_{60}}$

Using angle-dependent photoemission spectra of core and valence levels we show that metallic, single crystal K³C₆₀ is terminated by an insulating or weakly-conducting surface layer. We attribute this to the effects of strong intermolecular correlations combined with the average surface charge state. Several controversies on the electronic structure are thereby resolved.Received: 16 July 2004, Published online: 5 November 2004PACS: 71.20.Tx Fullerenes and related materials; intercalation compounds - 73.20.-r Electron states at surfaces and interfaces - 79.60.Bm Clean metal, semiconductor, and insulator surfaces     

$\mathsf{La_{0.5}Sr_{0.5}CoO_{3}}$: A ferromagnet with strong irreversibility

Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper bound follows from “n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from “n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the lower ones. Received 22 October 2002 / Received in final form 4 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: jschnack@uos.de     

Thermal evolution of cluster assembled $\mathsf{Ni_3Al}$ materials modelled at the atomic scale

Diffusion properties of Ni₃Al cluster assembled nanostructured materials are investigated at the atomic scale. Two different model samples are considered, at equilibrium at 300 K. One is obtained by modelling cluster compaction under 2 GPa external pressure and the second by accumulating low energy deposited clusters on a Ni surface. They differ essentially by their density, the latter sample presenting an interconnected network of nanopores, which is not observed in the former. At elevated temperatures, cluster coalescence is observed in both, as well as an intense atomic diffusion at the internal surfaces and nanograin interfaces. A method is presented which allows, in a good approximation, to distinguish between the two phenomena and to estimate diffusion coefficients. At temperatures above 400 K, it is found for both samples, irrespective to their density, that the diffusion activation energy at the internal surfaces and interfaces is as low as in a liquid while the grain cores remain crystalline.Received: 20 June 2003, Published online: 16 September 2003PACS: 61.43.Bn Structural modeling: serial-addition models, computer simulation - 36.40.-c Atomic and molecular clusters - 61.46. + w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals