Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

Energetic neutral atom imaging of the lunar surface

Since the Moon is not shielded by a global magnetic field or by an atmosphere, solar wind plasma impinges onto the lunar surface almost unhindered. Until recently, it was assumed that almost all of the impinging solar wind ions are absorbed by the surface. However, recent Interstellar Boundary Explorer, Chandrayaan-1, and Kaguya observations showed that the interaction process between the solar wind ions and the lunar surface is more complex than previously assumed. In contrast to previous assumptions, a large fraction of the impinging solar wind ions is backscattered as energetic neutral atoms. Using the complete Chandrayaan-1 Energetic Neutral Analyzer data set, we compute a global solar wind reflection ratio of 0.16 ± 0.05 from the lunar surface. Since these backscattered neutral particles are not affected by any electric or magnetic fields, each particle's point of origin on the lunar surface can be determined in a straight-forward manner allowing us to create energetic neutral atom maps of the lunar surface. The energetic neutral atom measurements recorded by the Chandrayaan-1 Energetic Neutral Analyzer cover ˜89% of the lunar surface, whereby the lunar farside is almost completely covered. We analyzed all available energetic neutral atom measurements recorded by the Chandrayaan-1 Energetic Neutral Analyzer to create the first global energetic neutral hydrogen maps of the lunar surface.

Lunar energetic neutral atom (ENA) spectra measured by the interstellar boundary explorer (IBEX)

The solar wind continuously flows out from the Sun, filling interplanetary space and directly interacting with the surfaces of small planetary bodies and other objects throughout the solar system. A significant fraction of these ions backscatter from the surface as energetic neutral atoms (ENAs). The first observations of these ENA emissions from the Moon were recently reported from the Interstellar Boundary Explorer (IBEX). These observations yielded a lunar ENA albedo of ˜10% and showed that the Moon reflects ˜150 metric tons of neutral hydrogen per year. More recently, a survey of the first 2.5 years of IBEX observations of lunar ENAs was conducted for times when the Moon was in the solar wind. Here, we present the first IBEX ENA observations when the Moon is inside the terrestrial magnetosheath and compare them with observations when the Moon is in the solar wind. Our analysis shows that: (1) the ENA intensities are on average higher when the Moon is in the magnetosheath, (2) the energy spectra are similar above ~0.6* solar wind energy but below there are large differences of the order of a factor of 10, (3) the energy spectra resemble a power law with a "hump" at ˜0.6 * solar wind energy, and (4) this "hump" is broader when the Moon is in the magnetosheath. We explore potential scenarios to explain the differences, namely the effects of the topography of the lunar surface and the consequences of a very different Mach number in the solar wind versus in the magnetosheath.

Remote energetic neutral atom imaging of electric potential over a lunar magnetic anomaly

The formation of electric potential over lunar magnetized regions is essential for understanding fundamental lunar science, for understanding the lunar environment, and for planning human exploration on the Moon. A large positive electric potential was predicted and detected from single point measurements. Here, we demonstrate a remote imaging technique of electric potential mapping at the lunar surface, making use of a new concept involving hydrogen neutral atoms derived from solar wind. We apply the technique to a lunar magnetized region using an existing dataset of the neutral atom energy spectrometer SARA/CENA on Chandrayaan-1. Electrostatic potential larger than +135 V inside the Gerasimovic anomaly is confirmed. This structure is found spreading all over the magnetized region. The widely spread electric potential can influence the local plasma and dust environment near the magnetic anomaly.

Groundwater dating with Atom Trap Trace Analysis of 39Ar

We report on the realization of Atom Trap Trace Analysis for39Ar and its first application to dating of groundwater samples. The presented system achieves an atmospheric39Ar count rate as high as 3.58 ± 0.10 atoms/h allowing for the determination of the39Ar concentration in less than a day. We demonstrate that the measured count rates are proportional to the39Ar concentration by intercomparison with Low-Level Counting results and by measurements on prepared argon samples with defined concentration. For a geophysical application, we degas three different groundwater samples and gas chromatographically extract the argon. The39Ar ages inferred from the count rates extend over the accessible dating range and are in agreement with the Low-Level Counting results as well as with complementary isotope data.

Projected pH reductions by 2100 might put deep North Atlantic biodiversity at risk

This study aims to evaluate the potential for impacts of ocean acidification on North Atlantic deep-sea ecosystems in response to IPCC AR5 Representative Concentration Pathways (RCPs). Deep-sea biota is likely highly vulnerable to changes in seawater chemistry and sensitive to moderate excursions in pH. Here we show, from seven fully coupled Earth system models, that for three out of four RCPs over 17% of the seafloor area below 500 m depth in the North Atlantic sector will experience pH reductions exceeding −0.2 units by 2100. Increased stratification in response to climate change partially alleviates the impact of ocean acidification on deep benthic environments. We report on major pH reductions over the deep North Atlantic seafloor (depth >500 m) and at important deep-sea features, such as seamounts and canyons. By 2100, and under the high CO2 scenario RCP8.5, pH reductions exceeding −0.2 (−0.3) units are projected in close to 23% (~15%) of North Atlantic deep-sea canyons and ~8% (3%) of seamounts – including seamounts proposed as sites of marine protected areas. The spatial pattern of impacts reflects the depth of the pH perturbation and does not scale linearly with atmospheric CO2 concentration. Impacts may cause negative changes of the same magnitude or exceeding the current target of 10% of preservation of marine biomes set by the convention on biological diversity, implying that ocean acidification may offset benefits from conservation/management strategies relying on the regulation of resource exploitation.

IMRT credentialing for prospective trials using institutional virtual phantoms: results of a joint European Organization for the Research and Treatment of Cancer and Radiological Physics Center project.

BACKGROUND AND PURPOSE Intensity-modulated radiotherapy (IMRT) credentialing for a EORTC study was performed using an anthropomorphic head phantom from the Radiological Physics Center (RPC; RPC(PH)). Institutions were retrospectively requested to irradiate their institutional phantom (INST(PH)) using the same treatment plan in the framework of a Virtual Phantom Project (VPP) for IMRT credentialing. MATERIALS AND METHODS CT data set of the institutional phantom and measured 2D dose matrices were requested from centers and sent to a dedicated secure EORTC uploader. Data from the RPC(PH) and INST(PH) were thereafter centrally analyzed and inter-compared by the QA team using commercially available software (RIT; ver.5.2; Colorado Springs, USA). RESULTS Eighteen institutions participated to the VPP. The measurements of 6 (33%) institutions could not be analyzed centrally. All other centers passed both the VPP and the RPC ±7%/4 mm credentialing criteria. At the 5%/5 mm gamma criteria (90% of pixels passing), 11(92%) as compared to 12 (100%) centers pass the credentialing process with RPC(PH) and INST(PH) (p = 0.29), respectively. The corresponding pass rate for the 3%/3 mm gamma criteria (90% of pixels passing) was 2 (17%) and 9 (75%; p = 0.01), respectively. CONCLUSIONS IMRT dosimetry gamma evaluations in a single plane for a H&N prospective trial using the INST(PH) measurements showed agreement at the gamma index criteria of ±5%/5 mm (90% of pixels passing) for a small number of VPP measurements. Using more stringent, criteria, the RPC(PH) and INST(PH) comparison showed disagreement. More data is warranted and urgently required within the framework of prospective studies.

Separation of the Ribbon from globally distributed energetic neutral Atom Flux using the first five Years of Ibex Observations

The Interstellar Boundary Explorer (IBEX) observes the IBEX ribbon, which stretches across much of the sky observed in energetic neutral atoms (ENAs). The ribbon covers a narrow (~20°-50°) region that is believed to be roughly perpendicular to the interstellar magnetic field. Superimposed on the IBEX ribbon is the globally distributed flux that is controlled by the processes and properties of the heliosheath. This is a second study that utilizes a previously developed technique to separate ENA emissions in the ribbon from the globally distributed flux. A transparency mask is applied over the ribbon and regions of high emissions. We then solve for the globally distributed flux using an interpolation scheme. Previously, ribbon separation techniques were applied to the first year of IBEX-Hi data at and above 0.71 keV. Here we extend the separation analysis down to 0.2 keV and to five years of IBEX data enabling first maps of the ribbon and the globally distributed flux across the full sky of ENA emissions. Our analysis shows the broadening of the ribbon peak at energies below 0.71 keV and demonstrates the apparent deformation of the ribbon in the nose and heliotail. We show global asymmetries of the heliosheath, including both deflection of the heliotail and differing widths of the lobes, in context of the direction, draping, and compression of the heliospheric magnetic field. We discuss implications of the ribbon maps for the wide array of concepts that attempt to explain the ribbon's origin. Thus, we present the five-year separation of the IBEX ribbon from the globally distributed flux in preparation for a formal IBEX data release of ribbon and globally distributed flux maps to the heliophysics community.

Backscattered energetic neutral atoms from the Moon in the Earth's plasma sheet observed by Chandarayaan-1/Sub-keV Atom Reflecting Analyzer instrument

We present the observations of energetic neutral atoms (ENAs) produced at the lunar surface in the Earth's magnetotail. When the Moon was located in the terrestrial plasma sheet, Chandrayaan-1 Energetic Neutrals Analyzer (CENA) detected hydrogen ENAs from the Moon. Analysis of the data from CENA together with the Solar Wind Monitor (SWIM) onboard Chandrayaan-1 reveals the characteristic energy of the observed ENA energy spectrum (the e-folding energy of the distribution function) ∼100 eV and the ENA backscattering ratio (defined as the ratio of upward ENA flux to downward proton flux) <∼0.1. These characteristics are similar to those of the backscattered ENAs in the solar wind, suggesting that CENA detected plasma sheet particles backscattered as ENAs from the lunar surface. The observed ENA backscattering ratio in the plasma sheet exhibits no significant difference in the Southern Hemisphere, where a large and strong magnetized region exists, compared with that in the Northern Hemisphere. This is contrary to the CENA observations in the solar wind, when the backscattering ratio drops by ∼50% in the Southern Hemisphere. Our analysis and test particle simulations suggest that magnetic shielding of the lunar surface in the plasma sheet is less effective than in the solar wind due to the broad velocity distributions of the plasma sheet protons.

First πK atom lifetime and πK scattering length measurements

The results of a search for hydrogen-like atoms consisting of π∓K±π∓K± mesons are presented. Evidence for πK atom production by 24 GeV/c protons from CERN PS interacting with a nickel target has been seen in terms of characteristic πK pairs from their breakup in the same target (178±49178±49) as well as in terms of produced πK atoms (653±42653±42). Using these results, the analysis yields a first value for the πK atom lifetime of View the MathML sourceτ=(2.5−1.8+3.0) fs and a first measurement of the S-wave isospin-odd πK scattering length View the MathML source|a0−|=13|a1/2−a3/2|=(0.11−0.04+0.09)Mπ−1 (aIaI for isospin I).

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1 /| x | 2 . The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if R is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.