Scintillation light produced by low-energy beams of highly-charged ions

Measurements have been performed of scintillation light intensities emitted from various inorganic scintillators irradiated with low-energy beams of highly-charged ions from an electron beam ion source (EBIS) and an electron cyclotron resonance ion source (ECRIS). Beams of xenon ions Xe$^{q+}$ with various charge states between $q$=2 and $q$=18 have been used at energies between 5 keV and 17.5 keV per charge generated by the ECRIS. The intensity of the beam was typically varied between 1 and 100 nA. Beams of highly charged residual gas ions have been produced by the EBIS at 4.5 keV per charge and with low intensities down to 100 pA. The scintillator materials used are flat screens of P46 YAG and P43 phosphor. In all cases, scintillation light emitted from the screen surface was detected by a CCD camera. The scintillation light intensity has been found to depend linearly on the kinetic ion energy per time deposited into the scintillator, while up to $q$=18 no significant contribution from the ions' potential energy was found. We discuss the results on the background of a possible use as beam diagnostics e.g. for the new HITRAP facility at GSI, Germany.Comment: 6 pages, 8 figure

Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

QED theory of the nuclear recoil effect on the atomic g factor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in \alpha Z and to first order in m/M is formulated. The complete \alpha Z-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (\alpha Z)^2 m/M for an arbitrary state of a hydrogenlike atom.Comment: 17 page

Smoothed Complexity Theory

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability). Furthermore, we discuss extensions and shortcomings of our model and relate it to semi-random models.Comment: to be presented at MFCS 201

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio of $n$ to $m$, where $m$ is the logarithm of the largest integer within $A$. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme for SSP, and implement it as a complete and exact algorithm (EnumPlus). The algorithm always equivalently reduces an instance to be low-density, and then solve it by enumeration. Through this approach, we show the possibility to design a sole algorithm that can efficiently solve arbitrary density instance in a uniform way. Furthermore, our algorithm has considerable performance advantage over previous algorithms. Firstly, it extends the density scope, in which SSP can be solved in expected polynomial time. Specifically, It solves SSP in expected $O(n\log{n})$ time when density $d \geq c\cdot \sqrt{n}/\log{n}$, while the previously best density scope is $d \geq c\cdot n/(\log{n})^{2}$. In addition, the overall expected time and space requirement in the average case are proven to be $O(n^5\log n)$ and $O(n^5)$ respectively. Secondly, in the worst case, it slightly improves the previously best time complexity of exact algorithms for SSP. Specifically, the worst-case time complexity of our algorithm is proved to be $O((n-6)2^{n/2}+n)$, while the previously best result is $O(n2^{n/2})$.Comment: 11 pages, 1 figur

Recoil correction to the ground state energy of hydrogenlike atoms

The recoil correction to the ground state energy of hydrogenlike atoms is calculated to all orders in \alpha Z in the range Z = 1-110. The nuclear size corrections to the recoil effect are partially taken into account. In the case of hydrogen, the relativistic recoil correction beyond the Salpeter contribution and the nonrelativistic nuclear size correction to the recoil effect, amounts to -7.2(2) kHz. The total recoil correction to the ground state energy in hydrogenlike uranium (^{238}U^{91+}) constitutes 0.46 eV.Comment: 16 pages, 1 figure (eps), Latex, submitted to Phys.Rev.

Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of Quantum Electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.Comment: Minor changes since previous versio

Where to restore ecological connectivity? Detecting barriers and quantifying restoration benefits

Landscape connectivity is crucial for many ecological processes, including dispersal, gene flow, demographic rescue, and movement in response to climate change. As a result, governmental and non-governmental organizations are focusing efforts to map and conserve areas that facilitate movement to maintain population connectivity and promote climate adaptation. In contrast, little focus has been placed on identifying barriers—landscape features which impede movement between ecologically important areas—where restoration could most improve connectivity. Yet knowing where barriers most strongly reduce connectivity can complement traditional analyses aimed at mapping best movement routes. We introduce a novel method to detect important barriers and provide example applications. Our method uses GIS neighborhood analyses in conjunction with effective distance analyses to detect barriers that, if removed, would significantly improve connectivity. Applicable in least-cost, circuit-theoretic, and simulation modeling frameworks, the method detects both complete (impermeable) barriers and those that impede but do not completely block movement. Barrier mapping complements corridor mapping by broadening the range of connectivity conservation alternatives available to practitioners. The method can help practitioners move beyond maintaining currently important areas to restoring and enhancing connectivity through active barrier removal. It can inform decisions on trade-offs between restoration and protection; for example, purchasing an intact corridor may be substantially more costly than restoring a barrier that blocks an alternative corridor. And it extends the concept of centrality to barriers, highlighting areas that most diminish connectivity across broad networks. Identifying which modeled barriers have the greatest impact can also help prioritize error checking of land cover data and collection of field data to improve connectivity maps. Barrier detection provides a different way to view the landscape, broadening thinking about connectivity and fragmentation while increasing conservation options

Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ\alpha Z

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $\alpha Z$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(\alpha Z)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(\alpha Z)^4$ term, while for uranium it is above the leading $(\alpha Z)^2$ correction.Comment: 6 pages, 3 tables, 1 figur