William J. Thompson

An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements

Teaching Special Relativity Phys. Teach. 47, 485 (2009) Student Selection of the Textbook for an Introductory Physics Course Phys. Teach. 45, 416 (2007) The Perceived Value of College Physics Textbooks: Students and Instructors May Not See Eye to Eye Phys. Teach. 44, 338 (2006) Electromagnetism Am. J. Phys. 73, 574 (2005) Introduction to Electrodynamics Am. J. Phys. 73, 574 (2005)

Proton-induced Thermonuclear Reaction Rates for A = 20–40 Nuclei

Proton-induced reaction rates on 26 stable and 29 unstable target nuclei in the mass A = 20–40 region have been evaluated and compiled. Recommended reaction rates, assuming that all interacting nuclei are in the ground state, are presented in tabular form on a temperature grid in the range T = 0.01–10.0 GK. Most reaction rates involving stable targets were normalized to a set of measured standard resonance strengths in the sd shell. For the majority of reaction rates, experimental information from transfer reaction studies has been used consistently. Our results are compared with recent statistical model (Hauser-Feshbach) calculations. Reaction rate uncertainties are presented and amount to several orders of magnitude for many of the reactions. Several of these reaction rates and/or their corresponding uncertainties deviate from results of previous compilations. In most cases, the deviations are explained by the fact that new experimental information became available recently. Examples are given for calculating reaction rates and reverse reaction rates for thermally excited nuclei from the present results. The survey of literature for this review was concluded in 2000 August.

Least‐squares fitting when both variables contain errors: Pitfalls and possibilities

Least‐squares fitting is reviewed, in tutorial form, when both variables contain significant errors. Various error models are described; corresponding appropriate weighting is discussed; and the interpretation of weighting is clarified by a physically intuitive description and by graphical results. Resources in the literature on least‐squares fitting that are suitable for physics and astronomy students are reviewed. Algorithms for straight‐line fitting, indicate practical solution methods, are summarized and numerical comparisons are given. Also described are several readily available computer programs that allow fitting for both straight‐line and nonlinear situations and that are appropriate for both research and teaching applications.

Explosive hydrogen burning of 27Si, 31S, 35Ar, and 39Ca in novae and X-ray bursts

Stellar reaction rates for proton captures on the nuclei 27Si, 31S, 35Ar, and 39Ca are estimated from the most recent nuclear structure information available. Reliable mirror-state correspondences are found by using the isobaric multiplet mass equation. An improved method for calculating proton partial widths is applied. Systematic comparisons of excitation energies, spectroscopic factors, proton partial widths, and γ-ray partial widths for states of the same isospin multiplet are presented. Stellar reaction-rate uncertainties are deduced, and our reaction rates are compared to previous estimates. Reaction network calculations are performed to investigate implications of the new reaction rates for nucleosynthesis in novae and X-ray bursts. Our recommended reaction rates are varied within their assigned uncertainties, and we find only minor effects on the nuclear energy generation and the final abundances after the outbursts. Thus, contrary to previous claims, we find no compelling reason for measuring the proton capture reactions on 27Si, 31S, 35Ar, and 39Ca by using radioactive ion beams.

Estimating small signals by using maximum likelihood and Poisson statistics

Estimation of small signals from counting experiments with backgrounds larger than signals is solved using maximum likelihood estimation for situations in which both signal and background statistics are Poissonian. Confidence levels are discussed, and Poisson, Gauss and least-squares fitting methods are compared. Efficient algorithms that estimate signal strengths and confidence levels are devised for computer implementation. Examples from simulated data and a low count rate experiment in nuclear physics are given.

Proton scattering from 9Be between 6 and 30 MeV and the structure of 9Be

Abstract Differential cross-section excitation functions at lab scattering angles 86.9°, 120.0°, 140.0° and 160.0° were measured for 9Be(p, po)9Be, 9Be(p, p2)9Be and 9Be(p, d0)8Be at proton lab energies from 6 to 15 MeV in 100 keV steps. A broad anomaly was observed in the 9Be(p, p0)9Be excitation functions. Differential cross-section angular distributions were measured for 9Be(p, p0)9Be and 9Be(p, p2)9Be at lab energies of 13.0, 14.0, 15.0, 21.35 and 30.3 MeV and for 9Be(p, d0)8Be at 13.0, 14.0, 15.0 and 21.35 MeV. Angular distributions of polarization analysing powers for 9Be( p ,p0)9Be, 9Be(p, p2)9Be and 9Be( p , d0)8Be were measured at 8.0, 11.0, 12.0, 13.0 and 15.0 MeV. A spherical optical-model (SOM) analysis of the elastic scattering angular distribution data from 13.0 to 30.3 MeV showed that an energy dependence of only VR and Ws (volume real and surface imaginary depths) is sufficient to reproduce the measurements. Coupled-channels (CC) analyses were made with a quadrupole-deformed optical-model potential and strong coupling of 3 2 − , 5 2 − and 7 2 − levels of a K = 3 2 ground-state rotational band of 9Be. The 9Be(p, p0)9Be and 9Be(p, p2)9Be data from 13.0 to 30.3 MeV were analyzed simultaneously at each energy, varying only VR and Ws with energy, for a potential deformation of β = 1.1. Both SOM and CC analyses indicated the same energy dependence in VR, while Ws averaged 3.5 MeV lower in CC than in SOM, with both energy dependences consistent with previous analyses of nucleon scattering from 1p shell nuclei.

Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems

Symmetry in Quantum Systems Mathematical and Quantum-Theoretical Preliminaries Rotational Invariance and Angular Momentum Angular Momentum Eigenstates Angular Momentum for Quantum Systems Finite Rotations of Angular Momentum Eigenstates Combining Two Angular-Momentum Eigenstates Irreducible Spherical Tensors Recombining Several Angular-Momentum Eigenstates Electromagnetic Multipole Fields Tables of Formulas Computer Programs.

The collected works of john w. tukey

We describe novel, analytical, data-analysis, and Monte-Carlo-simulation studies of strongly heteroscedastic data of both small and wide range.Many different types of heteroscedasticity and fixed or variable weighting are incorporated through error-variance models.Attention is given to parameter bias determinations, evaluations of their significances, and to new ways to correct for bias.The error-variance models allow for both additive and independent power-law errors, and the power exponent is shown to be able to be well determined for typical physicalsciences data by the rapidly-converging, general-purpose, extended-least-squares program we use.The fitting and error-variance models are applied to both low-and high-heteroscedasticity situations, including single-response data from radioactive decay.Monte-Carlo simulations of data with similar parameters are used to evaluate the analytical models developed and the various minimization methods em-ployed, such as extended and generalized least squares.Logar...

Isospin-forbidden T = 32 resonances in 25Al, 29P and 33Cl, and the systematics of isospin mixing☆

Abstract The two lower T = 3 2 states in 25Al and the lowest T = 3 2 states in 29P and 33Cl were observed as isospin-forbidden proton elastic-scattering resonances. The widths of these states were deduced by combining polarisation analysing-power data in the vicinity of these resonances with high-resolution cross-section data in an analysis incorporating the effects of finite beam resolution (≈ 650 eV), Doppler broadening, and straggling of the incident beam in the target. A new estimate of Γ for the lowest T = 3 2 state in 21Na was obtained by re-analysing previously measured data. The elastic-proton reduced widths γp2 of the T = 3 2 states observed in scattering from T = 0 nuclei with 8 ≦ A ≦ 40 are well represented by the formula γp2 = cA2.4 where c = 0.128 ± 0.007 eV for target nuclei with A = 8n + 4 and c = 0.023 ± 0.009 eV for A = 8n, where n is integral. Possible mechanisms for this behavior of γp2 which is not predicted by previous calculations, are discussed.

Spheroidal wave functions

Spheroidal wave functions occur in many scientific and engineering contexts, from atomic nuclei to the cosmos-scattering by nonspherical nuclei, wave functions of diatomic molecules, analysis of band-limited random noise, orthogonal frequency division multiplexing, and anisotropy of the cosmic microwave background radiation. Therefore, visualizing these functions and computing them reliably can be useful and interesting.