Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials

We analyze the spin-orbit coupling term in the nuclear energy density functional in terms of a zero-range NN-contact interaction and finite-range contributions from two-pion exchange. We show that the strength of the spin-orbit contact interaction as extracted from high-precision nucleon-nucleon potentials is in perfect agreement with that of phenomenological Skyrme forces employed in non-relativistic nuclear structure calculations. Additional long-range contributions from chiral two-pion exchange turn out to be relatively small. These explicitly density-dependent contributions reduce the ratio of the isovector to the isoscalar spin-orbit strength significantly below the Skyrme value 1/3. We perform a similar analysis for the strength function of the $(\vec \nabla \rho)^2$-term and find values not far from those of phenomenological Skyrme parameterizations.Comment: 10 pages, 3 figures, accepted for publication in Physical Review C70 (2004

Yucca Mountain Project Getter Program Results (Year 1) I-I29 and Other Anions of Concern

Although high level nuclear wastes (HLW) contain a daunting array of radioisotopes, only a restricted number are long-lived enough to be problematic, and of these many are either effectively insoluble or are likely to be scavenged from solution by minerals indigenous to all aquifers. Those few constituents likely to travel significant distances through aquifers either form colloids (and travel as particulates) or anions--which are not sorbed onto the predominantly negatively charged mineral surfaces. Iodine ({sup 129}I) is one such constituent and may travel as either iodide (I{sup -}) or iodate (IO{sub 3}{sup -}) depending on whether conditions are mildly reducing or oxidizing. Conventionally, {sup 99}Tc (traveling as TcO{sub 4}{sup 0}) is regarded as being of greater concern since it is both more abundant and has a shorter half life (e.g., has a higher specific activity). However, it is unclear whether TcO{sub 4}{sup -} will ever actually form in the mildly reducing environments thought likely within degrading HLW canisters. Instead, technetium may remain reduced as highly insoluble Tc(lV), in which case {sup 129}I might become a significant risk driver in performance assessment (PA) calculations. In the 2004-2005 time frame the US Department of Energy (DOE)--Office of Civilian Radioactive Waste Management (OCRUM), Office of Science and Technology International (S&T) funded a program to identify ''getters'' for possible placement in the invert beneath HLW packages in the repository being planned by the Yucca Mountain Project (YMP). This document reports on progress made during the first (and only) year of this activity. The problem is not a new one and the project did not proceed in a complete vacuum of information. Potential leads came from past studies directed at developing anion getters for a near surface low-level waste facility at Hanford, which suggested that both copper-containing compounds and hydrotalcite-group minerals might be promising. Later work relating to closing HLW tanks (Hanford and Savannah River) added layered bismuth hydroxides to the list of candidates. In fact, even in the first year the project had considerable success in meeting its objectives (Krumhansl, et al., 2005). ''Batch Kd'' testing was used to screen a wide variety of materials from the above-mentioned groups. Some materials tested were, in fact, archived samples from prior studies but a significant amount of effort was also put into synthesizing new--and novel--phases. A useful rule of thumb in judging getter performance is that the ''Kd'' , should exceed a value of roughly 1000 before it's placement can materially decrease the potential dose at a hypothetical (distant) point of compliance (MacNeil, et al., 1999). Materials from each of the groups met these criteria for both iodide and iodate (though, of course, the actual chemistry operating in ''batch Kd'' runs is unknown, which casts a rather long shadow over the meaning of such comparisons). Additionally, as a sideline, a few materials were also tested for TcO{sub 4}{sup -} and occasionally Kd values in excess of 10{sup 3} were also found for this constituent. It is to be stressed that the ''batch Kd'' test was used as a convenient screening tool but in most cases nothing is known about the chemical processes responsible for removing iodine from the test solutions. It follows that the real meaning of such tests is just as a relative measure of iodine scavenging ability, and they may say nothing about sorption processes (in which case evaluating a Kd is irrelevant). Numerous questions also remain regarding the longevity and functionality of materials in the diverse environments in, and around, the proposed YMP repository. Thus, although we had a highly successful first year, we are still far from being able to either qualify any material for placement in the repository, or quantify a getter's performance for use in PA assessments

Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

The UK risk assessment scheme for all non-native species

1. A pest risk assessment scheme, adapted from the EPPO (European and Mediterranean Plant Protection Organisation) scheme, was developed to assess the risks posed to UK species, habitats and ecosystems by non-native taxa. 2. The scheme provides a structured framework for evaluating the potential for non-native organisms, whether intentional or unintentional introductions, to enter, establish, spread and cause significant impacts in all or part of the UK. Specialist modules permit the relative importance of entry pathways, the vulnerability of receptors and the consequences of policies to be assessed and appropriate risk management options to be selected. Spreadsheets for summarising the level of risk and uncertainty, invasive attributes and economic impact were created. In addition, new methods for quantifying economic impact and summarising risk and uncertainty were explored. 3. Although designed for the UK, the scheme can readily be applied elsewhere

Shell evolution of N = 40 isotones towards 60Ca: First spectroscopy of 62Ti

Excited states in the isotone 62Ti were populated via the 63V62Ti reaction at ∼200 MeV/nucleon at the Radioactive Isotope Beam Factory and studied using γ-ray spectroscopy. The energies of the and transitions, observed here for the first time, indicate a deformed 62Ti ground state. These energies are increased compared to the neighboring 64Cr and 66Fe isotones, suggesting a small decrease of quadrupole collectivity. The present measurement is well reproduced by large-scale shell-model calculations based on effective interactions, while ab initio and beyond mean-field calculations do not yet reproduce our findings. The shell-model calculations for 62Ti show a dominant configuration with four neutrons excited across the gap. Likewise, they indicate that the island of inversion extends down to , disfavoring a possible doubly magic character of the elusive 60Ca

Measurements of d+p Elastic Scattering Analyzing Powers at 80 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Chiral three-nucleon forces and bound excited states in neutron-rich oxygen isotopes

We study the spectra of neutron-rich oxygen isotopes based on chiral two- and three-nucleon interactions. First, we benchmark our many-body approach by comparing ground-state energies to coupled-cluster results for the same two-nucleon interaction, with overall good agreement. We then calculate bound excited states in 21,22,23O, focusing on the role of three-nucleon forces, in the standard sd shell and an extended sdf7/2p3/2 valence space. Chiral three-nucleon forces provide important one- and two-body contributions between valence neutrons. We find that both these contributions and an extended valence space are necessary to reproduce key signatures of novel shell evolution, such as the N = 14 magic number and the low-lying states in 21O and 23O, which are too compressed with two-nucleon interactions only. For the extended space calculations, this presents first work based on nuclear forces without adjustments. Future work is needed and open questions are discussed.Comment: 6 pages, 4 figures, published versio

Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro