A unitary correlation operator method

The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy- and mass-number-independent correlated two-body Hamiltonian reproduces all "exact" many-body calculations surprisingly well.Comment: 43 pages, several postscript figures, uses 'epsfig.cls'. Submitted to Nucl. Phys. A. More information available at http://www.gsi.de/~fm

A method for generating realistic correlation matrices

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS638 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Method for High Accuracy Multiplicity Correlation Measurements

Multiplicity correlation measurements provide insight into the dynamics of high energy collisions. Models describing these collisions need these correlation measurements to tune the strengths of the underlying QCD processes which influence all observables. Detectors, however, often possess limited coverage or reduced efficiency that influence correlation measurements in obscure ways. In this paper, the effects of non-uniform detection acceptance and efficiency on the measurement of multiplicity correlations between two distinct detector regions (termed forward-backward correlations) are derived. An analysis method with such effects built-in is developed and subsequently verified using different event generators. The resulting method accounts for acceptance and efficiency in a model independent manner with high accuracy thereby shedding light on the relative contributions of the underlying processes to particle production.Comment: 28 pages, 13 figures. Updated for having pseudorapidity dependent efficiency gradient

Probing jet properties via two particle correlation method

The formulae for calculating jet fragmentation momentum, $$, and parton transverse momentum,$$, and conditional yield are discussed in two particle correlation framework. Additional corrections are derived to account for the limited detector acceptance and inefficiency, for cases when the event mixing technique is used. The validity of our approach is confirmed with Monte-carlo simulation.Comment: Proceeding for HotQuarks2004 conference. 11 pages, 8 figures, corrected for typo

Tensor correlations in the Unitary Correlation Operator Method

We present a unitary correlation operator that explicitly induces into shell model type many-body states short ranged two-body correlations caused by the strong repulsive core and the pronounced tensor part of the nucleon-nucleon interaction. Alternatively an effective Hamiltonian can be defined by applying this unitary correlator to the realistic nucleon-nucleon interaction. The momentum space representation shows that realistic interactions which differ in their short range behaviour are mapped on the same correlated Hamiltonian, indicating a successful provision for the correlations at high momenta. Calculations for He4 using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. For heavier nuclei like O16 and Ca40 where exact many-body calculations are not possible we compare our results with other approximations. The correlated single-particle momentum distributions describe the occupation of states above the Fermi momentum. The Unitary Correlation Operator Method (UCOM) can be used in mean-field and shell model configuration spaces that are not able to describe these repulsive and tensor correlations explicitly.Comment: 73 pages, 65 figure

Calculation of acoustic parameters by a filter-correlation method

This paper presents the filter correlation method, a technique for extracting consistent and accurate estimates of attenuation parameters from acoustic waveform data. The method minimizes problems associated with short time windows and multipath secondary arrivals. The method comprises two stages: a causal passband filter stage followed by a cross-correlation step. The results of the filter-correlation estimator are compared to those of the spectral difference approach for short time series with and without a secondary multipath arrival. Preliminary analyses of acoustic data collected on cored marine silts and clays show the attenuation properties of these materials cannot be described by a constant Q mechanism. The filter correlation method refines estimates of frequency-dependent velocity, revealing a small but systematic anisotropy between measurements made parallel and transverse to the sediments\u27 bedding plane. The observed velocity anisotropy can be modeled by assuming layered porosity variations in the cored sediments. No systematic anisotropy in attenuation was observed