Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method

The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape towards the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. To describe open quantum systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow Shell Model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an $\alpha$+ n + n cluster system. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly-bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method, if it can be applied, can provide an additional information about partial energy widths associated with individual thresholds.Comment: 15 pages, 16 figure

The Friedrichs-Model with fermion-boson couplings II

In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by applying standard methods of representation of bound and resonant states.Comment: 13 page

Particle-unstable nuclei in the Hartree-Fock theory

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let

Needs to Achieve Improved Fire Protection as regards the Implementation and Development of the EN Eurocodes

The work reported is a deliverable within the framework of the Administrative Arrangement between DG ENTR and JRC on support to the implementation, harmonization and further development of the Eurocodes. The report encompasses the results achieved during the three-year work on Sub-task 5.2 'Needs for fire protection' of the Administrative Arrangement with DG ENTR. The report consists of three self-contained sections, namely: - Research needs to achieve improved fire design using the Eurocodes, - Implementation and use of fire-parts of the Eurocodes, and - Survey on the progress in the National implementation of the Eurocodes fire design parts. The present report has been prepared by the JRC in collaboration with the two ad-hoc groups on fire design convened by the JRC and in consultation with DG ENTR, Member States and individual experts and organizations involved in fire design.JRC.G.5-European laboratory for structural assessmen

Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method

Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.Comment: submitted to Phys. Rev. C, 12 pages, 7 figure

Decay Rate of Triaxially-Deformed Proton Emitters

The decay rate of a triaxially-deformed proton emitter is calculated in a particle-rotor model, which is based on a deformed Woods-Saxon potential and includes a deformed spin-orbit interaction. The wave function of the $I=7/2^{-}$ ground state of the deformed proton emitter $^{141}$Ho is obtained in the adiabatic limit, and a Green's function technique is used to calculate the decay rate and branching ratio to the first excited 2$^{+}$ state of the daughter nucleus. Only for values of the triaxial angle $\gamma$ $<5^{\circ}$ is good agreement obtained for both the total decay rate and the 2$^{+}$ branching ratio.Comment: 19 pages, 4 figure

Modified two-potential approach to tunneling problems

One-body quantum tunneling to continuum is treated via the two-potential approach, dividing the tunneling potential into external and internal parts. We show that corrections to this approach can be minimized by taking the separation radius inside the interval determined by simple expressions. The resulting two-potential approach reproduces the resonance energy and its width, both for narrow and wide resonances. We also demonstrate that, without losing its accuracy, the two-potential approach can be modified to a form resembling the R-matrix theory, yet without any uncertainties of the latter related to the choice of the matching radius.Comment: 7 two-column pages, 3 figures, extra-explanation added, Phys. Rev. A, in pres

Plasma amyloid concentration in Alzheimer's disease: performance of a high-throughput amyloid assay in distinguishing Alzheimer's disease cases from controls

BACKGROUND: Collection of cerebrospinal fluid (CSF) for measurement of amyloid-β (Aβ) species is a gold standard in Alzheimer's disease (AD) diagnosis, but has risks. Thus, establishing a low-risk blood Aβ test with high AD sensitivity and specificity is of outmost interest. OBJECTIVE: We evaluated the ability of a commercially available plasma Aβ assay to distinguish AD patients from biomarker-healthy controls. METHOD: In a case-control design, we examined plasma samples from 44 AD patients (A + N+) and 49 controls (A-N-) from a memory clinic. AD was diagnosed using a combination of neuropsychological examination, CSF biomarker analysis and brain imaging. Total Aβ40 and total Aβ42 in plasma were measured through enzyme-linked immunosorbent assay (ELISA) technology using ABtest40 and ABtest42 test kits (Araclon Biotech Ltd.). Receiver operating characteristic (ROC) analyses with outcome AD were performed, and sensitivity and specificity were calculated. RESULTS: Plasma Aβ42/40 was weakly positively correlated with CSF Aβ42/40 (Spearman's rho 0.22; p = 0.037). Plasma Aβ42/40 alone was not able to statistically significantly distinguish between AD patients and controls (AUC 0.58; 95% CI 0.46, 0.70). At a cut-point of 0.076 maximizing sensitivity and specificity, plasma Aβ42/40 had a sensitivity of 61.2% and a specificity of 63.6%. CONCLUSION: In this sample, the high-throughput blood Aβ assay was not able to distinguish well between AD patients and controls. Whether or not the assay may be useful in large-scale epidemiological settings remains to be seen

Localization of shadow poles by complex scaling

Through numerical examples we show that the complex scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be revealed and the Riemann sheets on which they reside can be identified.Comment: 6 pages, Latex with Revtex, 3 figures (not included) available on reques