The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.Comment: 10 pages, 4 figure

Dielectronic Resonance Method for Measuring Isotope Shifts

Longstanding problems in the comparison of very accurate hyperfine-shift measurements to theory were partly overcome by precise measurements on few-electron highly-charged ions. Still the agreement between theory and experiment is unsatisfactory. In this paper, we present a radically new way of precisely measuring hyperfine shifts, and demonstrate its effectiveness in the case of the hyperfine shift of $4s\_{1/2}$ and $4p\_{1/2}$ in $^{207}\mathrm{Pb}^{53+}$. It is based on the precise detection of dielectronic resonances that occur in electron-ion recombination at very low energy. This allows us to determine the hyperfine constant to around 0.6 meV accuracy which is on the order of 10%

Students’ analogical reasoning in novel situations: theory-like misconceptions or p-prims?

Over the past 50 years there has been much research in the area of students' misconceptions. Whilst this research has been useful in helping to inform the design of instructional approaches and curriculum development it has not provided much insight into how students reason when presented with a novel situation and, in particular, the knowledge they draw upon in an attempt to make predictions about that novel situation. This article reports on a study of Greek students, aged from 10 to 17 years old, who were asked to make predictions in novel situations and to then provide, without being told whether their predictions were correct or incorrect, explanations about their predictions. Indeed, their explanations in such novel situations have the potential to reveal how their ideas, as articulated as predictions, are formed as well as the sources they draw upon to make those predictions. We also consider in this article the extent to which student ideas can be seen either as theory-like misconceptions or, alternatively, as situated acts of construction involving the activation of fragmented pieces of knowledge referred to as phenomenological primitives (p-prims). Our findings suggest that in most cases students' reasoning in novel situations can be better understood in terms of their use of p-prims and that teaching might be made more effective if teachers were more aware of the p-prims that students were likely to be using when presented with new situations in physics

Isotope shift calculations for atoms with one valence electron

This work presents a method for the ab initio calculation of isotope shift in atoms and ions with one valence electron above closed shells. As a zero approximation we use relativistic Hartree-Fock and then calculate correlation corrections. The main motivation for developing the method comes from the need to analyse whether different isotope abundances in early universe can contribute to the observed anomalies in quasar absorption spectra. The current best explanation for these anomalies is the assumption that the fine structure constant, alpha, was smaller at early epoch. We test the isotope shift method by comparing the calculated and experimental isotope shift for the alkali and alkali-like atoms Na, MgII, K, CaII and BaII. The agreement is found to be good. We then calculate the isotope shift for some astronomically relevant transitions in SiII and SiIV, MgII, ZnII and GeII.Comment: 11 page

Isotope shift in the electron affinity of chlorine

The specific mass shift in the electron affinity between ^{35}Cl and ^{37}Cl has been determined by tunable laser photodetachment spectroscopy to be -0.51(14) GHz. The isotope shift was observed as a difference in the onset of the photodetachment process for the two isotopes. In addition, the electron affinity of Cl was found to be 29138.59(22) cm^{-1}, giving a factor of 2 improvement in the accuracy over earlier measurements. Many-body calculations including lowest-order correlation effects demonstrates the sensitivity of the specific mass shift and show that the inclusion of higher-order correlation effects would be necessary for a quantitative description.Comment: 16 pages, 6 figures, LaTeX2e, amsmat

Measurement with Persons: A European Network

The European ‘Measuring the Impossible’ Network MINET promotes new research activities in measurement dependent on human perception and/or interpretation. This includes the perceived attributes of products and services, such as quality or desirability, and societal parameters such as security and well-being. Work has aimed at consensus about four ‘generic’ metrological issues: (1) Measurement Concepts & Terminology; (2) Measurement Techniques: (3) Measurement Uncertainty; and (4) Decision-making & Impact Assessment, and how these can be applied specificallyto the ‘Measurement of Persons’ in terms of ‘Man as a Measurement Instrument’ and ‘Measuring Man.’ Some of the main achievements of MINET include a research repository with glossary; training course; book; series of workshops;think tanks and study visits, which have brought together a unique constellation of researchers from physics, metrology,physiology, psychophysics, psychology and sociology. Metrology (quality-assured measurement) in this area is relativelyunderdeveloped, despite great potential for innovation, and extends beyond traditional physiological metrology in thatit also deals with measurement with all human senses as well as mental and behavioral processes. This is particularlyrelevant in applications where humans are an important component of critical systems, where for instance health andsafety are at stake

CP-odd Phase Correlations and Electric Dipole Moments

We revisit the constraints imposed by electric dipole moments (EDMs) of nucleons and heavy atoms on new CP-violating sources within supersymmetric theories. We point out that certain two-loop renormalization group corrections induce significant mixing between the basis-invariant CP-odd phases. In the framework of the constrained minimal supersymmetric standard model (CMSSM), the CP-odd invariant related to the soft trilinear A-phase at the GUT scale, theta_A, induces non-trivial and distinct CP-odd phases for the three gaugino masses at the weak scale. The latter give one-loop contributions to EDMs enhanced by tan beta, and can provide the dominant contribution to the electron EDM induced by theta_A. We perform a detailed analysis of the EDM constraints within the CMSSM, exhibiting the reach, in terms of sparticle spectra, which may be obtained assuming generic phases, as well as the limits on the CP-odd phases for some specific parameter points where detailed phenomenological studies are available. We also illustrate how this reach will expand with results from the next generation of experiments which are currently in development.Comment: 31 pages, 21 eps figures; v2: additional remarks on 2-loop threshold corrections and references added; v3: typos corrected, to appear in Phys. Rev.

Electric dipole moments of Hg, Xe, Rn, Ra, Pu, and TlF induced by the nuclear Schiff moment and limits on time-reversal violating interactions

We have calculated the atomic electric dipole moments (EDMs) induced in ^{199}Hg, ^{129}Xe, ^{223}Rn, ^{225}Ra, and ^{239}Pu by their respective nuclear Schiff moments S. The results are (in units 10^{-17}S(e {fm}^{3})^{-1}e cm): d(^{199}Hg)=-2.8, d(^{129}Xe)=0.38, d(^{223}Rn)=3.3, d(^{225}Ra)=-8.5, d(^{239}Pu)=-11. We have also calculated corrections to the parity- and time-invariance-violating (P,T-odd) spin-axis interaction constant in TlF. These results are important for the interpretation of atomic and molecular experiments on EDMs in terms of fundamental P,T-odd parameters.Comment: 16 page

High accuracy calculation of 6s -> 7s parity nonconserving amplitude in Cs

We calculated the parity nonconserving (PNC) 6s -> 7s amplitude in Cs. In the Dirac-Coulomb approximation our result is in a good agreement with other calculations. Breit corrections to the PNC amplitude and to the Stark-induced amplitude $\beta$ are found to be -0.4% and -1% respectively. The weak charge of $^{133}$Cs is $Q_W=-72.5 \pm 0.7$ in agreement with the standard model.Comment: 4 pages, LaTeX2e, uses revtex4.cls, submitted to PR

Atomic Parity Nonconservation: Electroweak Parameters and Nuclear Structure

There have been suggestions to measure atomic parity nonconservation (PNC) along an isotopic chain, by taking ratios of observables in order to cancel complicated atomic structure effects. Precise atomic PNC measurements could make a significant contribution to tests of the Standard Model at the level of one loop radiative corrections. However, the results also depend upon certain features of nuclear structure, such as the spatial distribution of neutrons in the nucleus. To examine the sensitivity to nuclear structure, we consider the case of Pb isotopes using various recent relativistic and non-relativistic nuclear model calculations. Contributions from nucleon internal weak structure are included, but found to be fairly negligible. The spread among present models in predicted sizes of nuclear structure effects may preclude using Pb isotope ratios to test the Standard Model at better than a one percent level, unless there are adequate independent tests of the nuclear models by various alternative strong and electroweak nuclear probes. On the other hand, sufficiently accurate atomic PNC experiments would provide a unique method to measure neutron distributions in heavy nuclei.Comment: 44 pages, INT Preprint DOE/ER/40561-050-INT92-00-1