V. Dose

Bayesian inference in physics: case studies

This report describes the Bayesian approach to probability theory with emphasis on the application to the evaluation of experimental data. A brief summary of Bayesian principles is given, with a discussion of concepts, terminology and pitfalls. The step from Bayesian principles to data processing involves major numerical efforts. We address the presently employed procedures of numerical integration, which are mainly based on the Monte Carlo method. The case studies include examples from electron spectroscopies, plasma physics, ion beam analysis and mass spectrometry. Bayesian solutions to the ubiquitous problem of spectrum restoration are presented and advantages and limitations are discussed. Parameter estimation within the Bayesian framework is shown to allow for the incorporation of expert knowledge which in turn allows the treatment of under-determined problems which are inaccessible by the traditional maximum likelihood method. A unique and extremely valuable feature of Bayesian theory is the model comparison option. Bayesian model comparison rests on Ockhams razor which limits the complexity of a model to the amount necessary to explain the data without fitting noise. Finally we deal with the treatment of inconsistent data. They arise frequently in experimental work either from incorrect estimation of the errors associated with a measurement or alternatively from distortions of the measurement signal by some unrecognized spurious source. Bayesian data analysis sometimes meets with spectacular success. However, the approach cannot do wonders, but it does result in optimal robust inferences on the basis of all available and explicitly declared information.

Atomic Adsorption of Oxygen on Cu(111) and Cu(110)

We have studied angle-resolved inverse photoemission (ħω = 9.7 eV) after room temperature adsorption of oxygen on Cu(111) and Cu(110). On Cu(111) exposure to 500 L induces a band (3.0 eV aboveEFatΓ) which shows clear dispersion (1.0 eV) to higher energies for off normal incidence. Since no LEED superstructure is seen for that system, our results present strong evidence for the presence of short-range surface order. Two adsorbate bands are identified (2.8 eV and 6.3 eV atΓ) on Cu(110)p(2×1)-O. Our results are in good agreement with a long-bridge adsorption site.

Bilayer growth in a metallic system: Fe on Cu( 100)

Abstract During epitaxial growth of Fe on Cu(100) the normalized Auger signal of Fe was taken as a function of evaporation time. This curve shows evidence for a layer-by-layer growth mode and clearly rules out other possible growth modes. Rutherford backscattering spectrometry was used to determine thicknesses of a one- and two-layer film quantitatively with an accuracy of ± 0.3 ML. These data together with the Auger analysis unveil a bilayer-by-bilayer growth mode for the first two bilayers.

Improved resolution in VUV isochromat spectroscopy

The energy resolution of a VUV isochromat spectrometer employing the traditional energy selective Geiger counter can be significantly improved. The variance of the optical resolution function with the usual CaF2 entrance window is (240 meV)2. With SrF2 we obtain (113 meV)2 at room temperature and (73 meV)2 at 70°C. A direct confirmation of these data, which were derived from a moment analysis of the threshold behaviour of an Au isochromat is provided by a measurement of image potential states at Cu(001).

Exchange splitting of an oxygen 2p-derived band at Ni(110)

Abstract Employing spin-resolved inverse photoemission we have observed an exchange splitting of the unoccupied oxygen-induced band in the chemisorption system (2 × 1)-O/Ni(110). At the centre of the surface Brillouin zone the splitting between the oxygen 2p-derived majority and minority band— referred to the magnetization vector of nickel-was found to be 80±20 meV. This effect is a manifestation of the strong magnetic correlation between the oxygen and nickel bands. The size of the splitting is surprising as earlier experimental work indicated a substantial reduction of the surface magnetization due to chemisorption. For the empty 2π∗-derived band of CO on Ni(110) no such splitting has been observed.

Analysis of long-term time series of the beginning of flowering by Bayesian function estimation

The identification of changes in long-term phenological time series is a prerequisite for the analysis and interpretation of phenological observations as bio-indicator of climate change. The new method for the analysis of phenological time series based on Bayesian concepts, recently presented by DOSE and MENZEL (2004), is employed to the analysis of three long term observational flowering records in Germany (1900-2003) as well as of a 600 year record of cherry flowering in Kyoto, Japan. The onset of these phenological phases in relation to reported temperature variations is discussed, considering three different models for function estimation: The one-change-point-model is preferred in all data sets to the less sophisticated alternatives, the linear model and the constant model. The three time series covering the 20 th century at Geisenheim have a clear maximum of change point probability mid of the 1980s; the record from Kyoto spanning the last 6 centuries has a broad maximum at the beginning of the 20 th century. After these maxima, the resulting rates of change indicate advancing onset of flowering, reaching - with a considerable uncertainty range - higher rates at Geisenheim (up to -1.7 days/year in 2003) compared to Kyoto (-0.1 days/year in 1998). Thus, our analysis allows us to quantify these shifts in phenological phases, which turn out to be strongly dependent on spring temperature. Consequently, they mirror the marked temperature rise in the 20 th century (Kyoto), especially its enhancement in the last 2-3 decades as reflected by the Geisenheim time series.

Unoccupied electronic states and surface barriers at Cu surfaces

The surface potential barrier shape of the low-index faces of copper was determined by an analysis of inverse photoemission and two-photon photoemission measurements making use of the one-step model of photoemission. The barrier potentials obtained in this way allow for a consistent description of the energetic positions and effective masses of all known surface states for the various faces. It is found, in agreement with previous theoretical predictions that the most open surface, Cu(110), exhibits the strongest saturation of the image potential with an image plane lying nearest to the topmost atomic layer and with the weakest image force outside the crystal. A comparison with theoretical slab calculations shows that in these calculations the position of the image plane is always significantly further outside the crystal than derived in the present study. Dynamical effects in the effective potential are found to be negligible for electronic states up to 6 eV above the Fermi level EF,but are probably responsible for systematic discrepancies between theory and experiment for unoccupied bulk states in the energy range 10-15 eV above EF.

Unoccupied electronic surface resonance at Cu(001)

Abstract Theoretical calculations of inverse photoemission spectra from Cu(001) employing the familiar one step model suggest the existence of a surface resonance at 1.8 eV above the Fermi level. This theoretical prediction has been verified by comparison of experimental inverse photoemission spectra from clean and Co-covered Cu(001).

Critical point energies in hcp and fcc cobalt from appearance potential spectra

Appearance potential spectra have been measured for (low-temperature) hcp and (high-temperature) fcc cobalt. The measurements allowed a determination of the transition temperatures of (690±6) K for the hcp → fcc transition and (653±12) K for the fcc → hcp transition in good agreement with earlier findings. Critical-point energies are (6.7±0.3) eV for the M point in hcp cobalt and (5.6±0.3) eV for the L7 and (8.9±0.3) eV for the X7, K8 critical points in fcc cobalt, respectively.

Momentum-Resolved Bremsstrahlung Isochromat Spectroscopy of Silver Surfaces

Angle-resolved bremsstrahlung isochromat spectra of the Ag(100), Ag(110) and Ag(111) surfaces have been measured. Our work extends and complements several earlier investigations of other authors. The data are summarized in the form of final state dispersionsE(k∥). Comparison is made to the available theoretical and experimental information. The results for the bulk as well as for the surface-specific features are in excellent to reasonable agreement among each others and with recent calculations.