Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

Gene expression differences in relation to age and social environment in queen and worker bumble bees

Eusocial insects provide special insights into the genetic pathways influencing aging because of their long-lived queens and flexible aging schedules. Using qRT-PCR in the primitively eusocial bumble bee Bombus terrestris (Linnaeus), we investigated expression levels of four candidate genes associated with taxonomically widespread age-related pathways (coenzyme Q biosynthesis protein 7, COQ7; DNA methyltransferase 3, Dnmt3; foraging, for; and vitellogenin, vg). In Experiment 1, we tested how expression changes with queen relative age and productivity. We found a significant age-related increase in COQ7 expression in queen ovary. In brain, all four genes showed higher expression with increasing female (queen plus worker) production, with this relationship strengthening as queen age increased, suggesting a link with the positive association of fecundity and longevity found in eusocial insect queens. In Experiment 2, we tested effects of relative age and social environment (worker removal) in foundress queens and effects of age and reproductive status in workers. In this experiment, workerless queens showed significantly higher for expression in brain, as predicted if downregulation of for is associated with the cessation of foraging by foundress queens following worker emergence. Workers showed a significant age-related increase in Dnmt3 expression in fat body, suggesting a novel association between aging and methylation in B. terrestris. Ovary activation was associated with significantly higher vg expression in fat body and, in younger workers, in brain, consistent with vitellogenin's ancestral role in regulating egg production. Overall, our findings reveal a mixture of novel and conserved features in age-related genetic pathways under primitive eusociality

Integrating network analysis, sensor tags, and observation to understand shark ecology and behavior

Group living in animals is a well-studied phenomenon, having been documented extensively in a wide range of terrestrial, freshwater, and marine species. Although social dynamics are complex across space and time, recent technological and analytical advances enable deeper understanding of their nature and ecological implications. While for some taxa, a great deal of information is known regarding the mechanistic underpinnings of these social processes, knowledge of these mechanisms in elasmobranchs is lacking. Here, we used an integrative and novel combination of direct observation, accelerometer biologgers, and recent advances in network analysis to better understand the mechanistic bases of individual-level differences in sociality (leadership, network attributes) and diel patterns of locomotor activity in a widespread marine predator, the lemon shark (Negaprion brevirostris). We found that dynamic models of interaction based on Markov chains can accurately predict juvenile lemon shark social behavior and that lemon sharks did not occupy consistent positions within their network. Lemon sharks did however preferentially associate with specific group members, by sex as well as by similarity or nonsimilarity for a number of behavioral (nonsimilarity: leadership) and locomotor traits (similarity: proportion of time swimming "fast," mean swim duration; nonsimilarity: proportion of swimming bursts/transitions between activity states). Our study provides some of the first information on the mechanistic bases of group living and personality in sharks and further, a potential experimental approach for studying fine-scale differences in behavior and locomotor patterns in difficult-to-study organisms

UV and EUV Instruments

We describe telescopes and instruments that were developed and used for astronomical research in the ultraviolet (UV) and extreme ultraviolet (EUV) regions of the electromagnetic spectrum. The wavelength ranges covered by these bands are not uniquely defined. We use the following convention here: The EUV and UV span the regions ~100-912 and 912-3000 Angstroem respectively. The limitation between both ranges is a natural choice, because the hydrogen Lyman absorption edge is located at 912 Angstroem. At smaller wavelengths, astronomical sources are strongly absorbed by the interstellar medium. It also marks a technical limit, because telescopes and instruments are of different design. In the EUV range, the technology is strongly related to that utilized in X-ray astronomy, while in the UV range the instruments in many cases have their roots in optical astronomy. We will, therefore, describe the UV and EUV instruments in appropriate conciseness and refer to the respective chapters of this volume for more technical details.Comment: To appear in: Landolt-Boernstein, New Series VI/4A, Astronomy, Astrophysics, and Cosmology; Instruments and Methods, ed. J.E. Truemper, Springer-Verlag, Berlin, 201

Regulation of healthcare ethics committees in Europe

In this article, the question is discussed if and how Healthcare Ethics Committees (HECs) should be regulated. The paper consists of two parts. First, authors from eight EC member countries describe the status quo in their respective countries, and give reasons as to the form of regulation they consider most adequate. In the second part, the country reports are analysed. It is suggested that regulation of HECs should be central and weak. Central regulation is argued to be apt to improve HECs’ accountability, relevance and comparability. To facilitate biomedical citizenship and ethical reflection, regulation should at the same time be weak rather than strict. Independence of HECs to deliberate about ethical questions, and to give solicited and unsolicited advice, should be supported and only interfered with by way of exception. One exception is when circumstances become temporary adversarial to ethical deliberation in healthcare institutions. In view of European unification, steps should be taken to develop consistent policies for both Eastern and Western European countries

A measurement of the tau mass and the first CPT test with tau leptons

We measure the mass of the tau lepton to be 1775.1+-1.6(stat)+-1.0(syst.) MeV using tau pairs from Z0 decays. To test CPT invariance we compare the masses of the positively and negatively charged tau leptons. The relative mass difference is found to be smaller than 3.0 10^-3 at the 90% confidence level.Comment: 10 pages, 4 figures, Submitted to Phys. Letts.

First Measurement of Z/gamma* Production in Compton Scattering of Quasi-real Photons

We report the first observation of Z/gamma* production in Compton scattering of quasi-real photons. This is a subprocess of the reaction e+e- to e+e-Z/gamma*, where one of the final state electrons is undetected. Approximately 55 pb-1 of data collected in the year 1997 at an e+e- centre-of-mass energy of 183 GeV with the OPAL detector at LEP have been analysed. The Z/gamma* from Compton scattering has been detected in the hadronic decay channel. Within well defined kinematic bounds, we measure the product of cross-section and Z/gamma* branching ratio to hadrons to be (0.9+-0.3+-0.1) pb for events with a hadronic mass larger than 60 GeV, dominated by (e)eZ production. In the hadronic mass region between 5 GeV and 60 GeV, dominated by (e)egamma* production, this product is found to be (4.1+-1.6+-0.6) pb. Our results agree with the predictions of two Monte Carlo event generators, grc4f and PYTHIA.Comment: 18 pages, LaTeX, 5 eps figures included, submitted to Physics Letters