bluuebunny/crossref_metadata_2025 huggingface dataset:
Relativistic Equations of Motion with Forces Depending on Particle Velocity in Media
Authors: Cavalleri G.
Published: August 2005

The relativistic equation of motion with a resistance force of Newtonian type cannot be simply given by Fr = m0dvr/dτ+λvr. It is shown that the relativistic form corresponding to the classical equation of motion with a resistance force proportional to the nth power of the velocity is given by Fr = m0dvr/dτ+λ(zvr − ur)[(zvs − us)(zvs − us)](n−1)/2, where ur, is the four-velocity of the fluid and z = −vsu3/c2. This equation may be considered as “physical,” because it can be reduced to particular exact (i.e., relativistic) equations describing real motions. Other mathematically correct (i.e., relativistically covariant) equations which reduce, for low velocities, to the same classical expression, cannot.
Kinematics of Finite, Rigid-Body Displacements
Authors: Beatty Millard F.
Published: August 2005

Elementary vector and matrix methods are used to prove several fundamental theorems that bear on the foundation of kinematics of finite, rigid-body displacements. Euler's theorem, the parallel axis theorem, invariance of axial projected displacements, Chasles' theorem, and other equivalent displacement theorems are proved. The composition of several screw displacements is investigated, and it is shown that the resultant screw is unique.
Hysteresis Loop
Authors: Weltin Hans
Published: August 2005

A rugged lecture and laboratory apparatus is described with which it is possible to obtain data and plot a hysteresis loop in only a few minutes.
An Experiment in Elementary Particle Physics for the Elementary Laboratory
Authors: Whiteside H. , Palmieri J. N. , Burnstein R. A.
Published: August 2005

An experiment in elementary particle physics is described which is suitable for either the introductory or the advanced undergraduate laboratory. By making quantitative measurements on bubble chamber photographs and using the laws of relativistic mechanics, the student can make a complete analysis of the events studied. This analysis includes the identification of several “unknown” particles and the estimation of their lifetimes. A second part of the experiment involves scanning and recognition of various events produced by K−, p interactions. The necessary photographs are included to allow the experiment to be performed by the reader.
Eigenfunctions of the Hydrogen Atom in Momentum Space
Authors: Klein James J.
Published: August 2005

The Schrödinger problem of the hydrogen atom is solved using toroidal coordinates in momentum space. The wavefunctions are expressible in terms of Jacobi polynomials and ordinary trigonometric functions.
Mathematical Education for Scientists and Engineers
Authors: Serbin Hyman
Published: August 2005

Mathematical education for scientists and engineers is defined as including not only the education required to understand currently accepted theories, but also the mathematical background which may become useful in future research. This broader requirement is confronted with the dilemma that the professional academic mathematicians emphasize the axiomatic and rigorously deductive aspects of their work. On the other hand, it is a serious error to teach mathematics from the standpoint of the applications; to do so is to forsake mathematical abstraction as an end in itself. The pure mathematicians are separated into two groups, the “creative” and the “critical,” depending on the degree of rigor. Modern mathematicians in the overwhelming majority fall within the critical school. Creative mathematicians postulate properties (sometimes implicitly) which have not been proved and arrive at new results without establishing the complete logical sequence from fundamental axioms. Mathematical education for applications should be taught by creatively oriented mathematicians. According to this point of view, the essential mathematical features of abstraction and rigor are still maintained.
Simple Derivation of the Bloch Equation
Authors: ter Haar D.
Published: August 2005

It is shown how one can derive Bloch's induction equation from the equation of motion of the density matrix by coarse-graining in time. The relaxation of the magnetization is assumed to be due to a fluctuating magnetic field acting upon the spins. The derivation does not provide any new information but is sufficiently simple that it may be used as a lecture application of the density matrix.
A Simple Mössbauer-Effect Apparatus
Authors: Adler Alan D. , Hane Michael
Published: August 2005

A circular-drive Mössbauer-effect apparatus is described in which the absorber rotates at a fixed speed and the vector character of velocity is used to observe the Mössbauer effect by observing the absorber at varying angles to the emitter. A complete Mössbauer absorption spectrum is thereby recorded without changing the absorber rotation speed.
Transference Numbers in Ionized Gases
Authors: Fisher L. H. , Varney R. N.
Published: August 2005

When a potential difference is applied between two electrodes immersed in an electrolyte containing one-ion-type of each polarity, the ratio of the current densities at any point due to the positive and negative charges within the body of the solution is given by the ratio of the drift velocities of the charged carriers. The charge species with the greater drift velocity is associated with the larger fraction of the current density. The fractions of the current density due to the motion of positive and negative charges within the body of the solution are for the most part independent of position, potential difference, and of electrode geometry. These statements apply only when the densities of positive and negative charges are equal. In contrast to the case of electrolytes, there are many cases in gaseous electronics at low current densities where charge neutrality does not hold. In these cases, the fractions of current densities of negative and positive charges are functions of position, electrode geometry, charge production, and loss mechanisms in the gas, and boundary conditions (essentially charge production and loss mechanisms at the electrodes). In a number of cases, these fractions can be calculated without knowledge of the charge carrier velocities in marked contrast to the electrolytic case. In gaseous electronics, it is not true that the more rapidly moving charge species is necessarily responsible for the larger share of the current, either crossing a given plane or averaged over the interelectrode separation. The spatially averaged current fractions furnish revealing information about discharges and are equal to the fractions of currents in an external metallic circuit associated with the motion of the respective ion species. These points are illustrated by a number of steady-state examples encompassing the principal phenomena of gaseous electronics. The discussion is carried out in terms of transference numbers, but it has been found necessary to generalize the concept of transference numbers usually used in chemistry.
Application of the Cornu Spiral to the Semitransparent Half Plane
Authors: Givens M. Parker , Goffe William L.
Published: August 2005

A simple approach is presented to the problem of Fresnel diffraction by an uniform half plane of arbitrary transmission and phase delay. A simple extension of the Cornu spiral allows this graphical device to provide a ready solution for this situation as well as for the opaque half plane. A laboratory experiment for advanced undergraduates may be used to confirm the validity of the method.
Lehmann-Symanzik-Zimmermann Formalism in the One-Boson Lee Model
Authors: Scarfone Leonard M.
Published: August 2005

The one-boson Lee model of a solvable field theory with nontrivial charge and mass renormalization provides an elementary example of the Lehmann-Symanzik-Zimmermann formalism. The basic quantities of interest in this method of calculation are the vacuum expectation values of time-ordered Heisenberg operators and by studying the analytic properties of the Fourier transforms of these functions, the first nontrivial subspace of the model is solved without resorting to eigenvalue equations. The full Lee model was recently analyzed with this technique and it seems pedagogically appropriate to carry out an analogous calculation in an even more elementary context.
Descartes on the Refraction and the Velocity of Light
Authors: Burke John G.
Published: August 2005

A critical analysis is made of Descartes's ideas concerning the nature of light and its refraction in order to ascertain the logic of his conclusion that light travels with a greater velocity in water than in air. The conclusions are (1) that Descartes was not an adherent of an emission theory but conceived of light as a pressure in a transparent medium, (2) that he believed this pressure was transmitted from the light source at an incredibly rapid but nevertheless finite velocity, and (3) that he was led to his erroneous conclusion concerning the velocity of light in rare and dense media by confusing the pressure and the velocity of the light propagation in the explanation of his experimental results.
Whaples's Proof of Existence of Temperature
Authors: Lu Pau-Chang
Published: August 2005

Whaples's highly abstract proof that the zeroth law of thermodynamics leads to the existence of empirical temperature functions is paraphrased so as to make it more accessible to physicists. An understanding of Whaples's work is all the more important if one recognizes that it may be the only correct proof.
Optical Near Field of a He-Ne Laser
Authors: Caulfield H. J. , Eden D. D.
Published: August 2005

Although there is widespread recognition that near-field (Fresnel) diffraction can occur with laser light, this fact seems not to have led to previous systematic study of near-field diffraction at simple apertures. Near-field diffraction at circular apertures is studied in detail. The number of Fresnel zones present in the diffraction pattern is given by n = ca2/λX, where a is the radius of the circle, λ is the wavelength, X is the distance from the aperture, and c is a numerical factor which is unity for collimated light, less than unity convergent light, and greater than unity for divergent light. The near-field beam for collimated light diverges noticeably only for λX/a2 > 0.25 and reaches the far-field divergence for λX/a2 > 0.7. Several practical applications of near-field diffraction are suggested.
Quantum-Mechanical Harmonic Oscillator (A Computer-Produced Film)
Authors: Bork Alfred M.
Published: August 2005

The 8-mm loop cartridge film described here is intended for teaching beginning quantum mechanics in the physics curriculum. It displays the solution of the time-independent Schrödinger equation (the energy eigenvalue equation) for the harmonic oscillator problem for linearly increasing values of energy, including noneigenvalues, and for two choices of boundary conditions at the origin. The film was made, with the exception of the titles, on a digital computer and a computer recorder. The possibility of other similar films is discussed briefly.
Additivity of Mass in Newtonian Mechanics
Authors: Feather N.
Published: August 2005

The term “Newtonian particle” is introduced to designate the ultimate entities of which gross bodies are assumed to be constituted in Newton's mechanics. It is shown that the principle of mass-additivity can be validated more convincingly in that system if the mutual forces between pairs of Newtonian particles are noncentral than if these forces are central forces. On the basis of this conclusion the action and reaction pairs of the third law are identified as wrench-pairs rather than simple force-pairs.
Advanced Laboratory Experiments on Optical Pumping of Rubidium Atoms—Part I: Magnetic Resonance
Authors: Nagel Michael , Haworth F. E.
Published: August 2005

The construction and operation of a simple apparatus for optical pumping experiments using rubidium vapor are described. The experiments are intended to involve students with the concepts of resonance, atomic orientation, nuclear magnetic moments, and the precession of atomic magnetic moments. An outline of the elementary theory is included.
Mach's Critique of Newtonian Mechanics
Authors: Bunge Mario
Published: August 2005

Mach's reinterpretation of Newtonian mechanics is examined and found ambivalent. His criticism of absolute time and absolute space was sound whereas his attempt to replace Newton's whole theory by an allegedly empirical statement and a definition was logically untenable. The whole program of reducing mechanics to kinematics is found to be unfeasible for logical reasons. The impossibility of deriving masses and forces from observations alone is discussed in detail. The driving force behind Mach's ideas on the foundations of mechanics is shown to be his empiricist philosophy which, while allowing him to impugn inscrutables, also suggested him to minimize the role of ideas. It is recalled that the discussion of the foundations of mechanics proceeds nowadays in a way far removed from Mach's operationalistic approach, namely via the axiomatic reconstruction of classical theories on the basis of undefined but meaningful concepts.
WKB Treatment of Bound States in an Electric-Dipole Potential
Authors: Fox Kenneth , Turner J. E.
Published: August 2005

The WKB method is applied to the problem of bound states of an electron in the field of a finite dipole. A necessary condition for binding is derived which suggests that bound states may exist only if the dipole moment is larger than a certain minimum value. It is also shown that the number of bound states given by the WKB method is comparable to the exact number for the one- and three-dimensional square-well potentials.
Orbital Angular Momentum in Quantum Mechanics
Authors: Whippman M. L.
Published: August 2005

Various methods of proving that half-integral values of the orbital angular momentum do not occur are discussed and a complete proof is given.
Simple Mössbauer Spectrometer using X-Ray Film
Authors: Kankeleit E.
Published: August 2005

A simple and inexpensive Mössbauer spectrometer has been constructed which employs an x-ray film for detection of the gamma ray. Using enriched absorbers hyperfine interactions can easily be demonstrated for the 14.4 keV transition in Fe57.
Simple Demonstration of Photoconductivity in CdS
Authors: Mullaney Paul F.
Published: August 2005

This communication describes a simple demonstration of photoconduction in CdS. The method is a quasi-stationary one. From an analysis of the photocurrent as a function of the light intensity, some of the major features of the photoconductive process can be demonstrated.
Momentum Books
Authors: Michels Walter C.
Published: August 2005

A brief history of Momentum Books, a series of paperback volumes published by D. Van Nostrand Company for the Commission on College Physics, is given. The usage of the books, as measured by sales figures, is given and an appeal is made for comments that will guide the future development of the series.
Classical Derivation of the Magnetic Hyperfine Anomaly
Authors: Sorensen Raymond A.
Published: August 2005

It is shown that all the qualitative effects of magnetic hyperfine interaction can be obtained nonrelativistically.
Total Binding Energy of Electrons in a Neutral Atom
Authors: Mitler Henri E.
Published: August 2005

A very simple derivation is given for a well-known expression for the total ionization energy of an atom.
Kinematics of Finite, Rigid-Body Displacements
Authors: Thurnauer Peter G.
Published: August 2005

Several classical theorems on finite, rigid-body displacements are proved analytically by matrix algebraic methods in terms of a formalism which describes a rigid body directly in terms of its mass density and a fundamental kinematical property of a rigid body under arbitrary displacements. Particular emphasis is placed on the pedagogical value of studying rigid-body kinematics as a means to understanding certain basic concepts employed in the general theory of physical transformations.
Two-Kilobar Hydrostatic-Pressure System for Teaching and Research
Authors: Stajdohar Ralph E. , Towle Laird C.
Published: August 2005

The design and construction of a simple hydrostatic-pressure system suitable for the undergraduate laboratory are described. Operation of the apparatus is illustrated by measurements of the effect of pressure on the dielectric constant of several liquids. The system can be used for a wide range of advanced undergraduate experiments, an assortment of which is suggested in an appendix.
On Geometrical Symmetry
Authors: Karl G.
Published: August 2005

An algebraic procedure leading to all the geometric symmetry operations of a given set of points is described.
Olbers', Halley's, or Whose Paradox?
Authors: Jaki Stanley L.
Published: August 2005

The problem of the darkness of the night sky, or Olbers' paradox, as currently referred to, received but sporadic attention on the part of astronomers and cosmologists until the formulation of the steady-state theory in 1948. The frequent references by the proponents of that theory to Olbers' views on the paradox are, however, at a baffling variance with the contents of Olbers' original paper published in 1826. This situation is a telling illustration of the scientists' often unscientific handling of the data of scientific history.
Shock-Wave Convergence Demonstrated by Surface Waves on Water
Authors: Gerhard Sherman L.
Published: August 2005

Airplanes in supersonic flight along curved paths produce, on the concave side of the path, shock waves that converge to a focus or else form cusps. At these places especially intense sonic booms occur. Since shock waves in air are invisible, a visual demonstration of their behavior may be of interest. The logarithmic spiral that an airplane in supersonic flight must follow to produce a shock wave converging at a given point on the ground was scaled to dimensions suitable for producing analogous surface waves on water in a ripple tank. An apparatus was built to move the wave-generating stylus along the spiral path at the proper speed. Prints of successive frames of motion pictures of the resulting wave are shown. The application of this technique to demonstrate shock waves produced by other curved paths is discussed.
Accidental Degeneracy of the Coulomb Interaction
Authors: Aldrovandi R. , Alcaras J. A. C. , Ferreira P. Leal
Published: August 2005

A treatment of the bound states for the hydrogen atom is given, based on the Schrödinger equation in momentum representation. The work runs parallel to Fock's treatment of the integral equation in momentum space. The problem is reduced to an eigenvalue equation for the Laplace-Beltrami operator in a momentum space of constant curvature, from which Balmer formula and the eigenfunctions are easily derived.
Locus of Magnetization for a Spin-1 Quadrupolar Nucleus
Authors: Albert Richard H.
Published: August 2005

The path traced out by the terminus of the magnetization vector for a spin-1 nucleus subjected to a nonvanishing electric-field gradient is calculated quantum mechanically. Certain special combinations of angular momentum operators are used to simplify the work.
Alternative to the Orthodox Interpretation of Quantum Theory
Authors: Pearle Philip
Published: August 2005

An alternative calculational procedure for quantum theory is presented, employing three features which differ from the corresponding features of orthodox quantum theory. These are: (1) the state vector is never to be “reduced”; (2) quantum theory only makes predictions about ensembles of identical experiments (not about individual experiments); and (3) the measuring apparatus must always be included in the state vector. What is new about this alternative theory is the demonstration that Features 2 and 3 (which have hitherto been discussed separately) can be consistently combined to yield an interpretation of quantum theory which has the additional advantage of Feature 1. It is shown that alternative and orthodox theories yield identical predictions for any practical experiment. However, two classes of experiments (which are impractical) for which the orthodox and alternative theories yield different predictions are described. Therefore, it is, in principle, possible to decide which theory Nature has chosen to obey. It is concluded that there is no reason, based upon experimental evidence, for preferring one theory over the other.
The Divergent Labortory
Authors: Ivany J. W. George , Parlett Malcolm R.
Published: August 2005

A report, by an education professor and a psychologist, on the Opening Conference of the CCP Summer Workshop on Introductory Laboratory. This report investigates and interprets the conference discussion of the pedagogical goals of laboratory, the importance and role of the teaching assistant, the student for whom the laboratory is designed, and contrasts two pedagogical styles, those of “autonomy” and “control,” which seem to underlie the different attitudes toward the laboratory.
Students Do Not Think Physics Is “Relevant.” What Can We Do About It?
Authors: Crane H. R.
Published: August 2005

The “noncalculus” introductory physics courses in our large universities are populated almost exclusively by captives, i.e., students who are satisfying a requirement. In the students' view, the courses do not justify themselves on their own merits. With the increasing self-determination students are exercising in curriculum matters, the captive audience is due to decrease. This may be averted by reform of the courses, long overdue. The reasons the courses do not seem relevant or worthwhile to the students are examined, and a number of remedies are proposed. Particular evils pointed out are the types of problems and tests given, which generally defeat any effort to direct attention to the more interesting and relevant aspects of the course. An appeal is made for a stockpile of imaginative problems and tests, as a first step toward reform.
Influence of Band Structure on the Thermal Properties of Metals
Authors: Glasser M. L. , Lucas A. A.
Published: August 2005

The assumption that a three-dimensional band structure is separable greatly simplifies the calculation of various properties of solids. In this paper this approach is demonstrated for thermodynamic properties of metals within the independent-particle model. A detailed application is made to the influence of a band gap on the temperature dependence of the magnetic susceptibility and specific heat.
Group Theory and Normal Modes
Authors: Nussbaum Allen
Published: August 2005

This article—which is tutorial in its approach—gives explicit directions for determining the normal modes of a symmetrical vibrating system through the use of group theory. The example considered is the planar, homonuclear, equilateral molecule. The eigenvalues are first determined from the secular equation by a numerical, empirical method. After a brief review of the applicable concepts from group theory, it is shown how the projection operator method may be used to solve the same problem in a direct way.
Diffusion: A Relativistic Appraisal
Authors: Kelly Don C.
Published: August 2005

The classic equation describing diffusion, δn/δt = D∇2n, is not consistent with the principles of special relativity. Specifically, its solutions permit the diffusive flow of particles to proceed at speeds in excess of the speed of light. A careful derivation, proceeding from the covariant form of the Boltzmann equation, results in a diffusion equation which exhibits the correct causal behavior. This equation assumes a particularly simple form, v−1(δ2n/δt2) + (δn/δt) = D∇2n, when the collision frequency for momentum transfer, v, is independent of particle speed. The general solution for diffusion in one dimension is presented, revealing the causal character of the diffusive flow.
Vibrations of a Circular Membrane
Authors: Casperson L. W. , Nicolet M-A.
Published: August 2005

A setup is described in which the eigenfrequencies of a circular membrane agree closely with the theoretical values. The usual difficulty with air damping is removed by using as a membrane a mesh of proper design, driven magnetically.
Apparatus for the Study of Charged Particles and Droplets
Authors: Berg T. G. Owe , Gaukler T. A.
Published: August 2005

An apparatus has been constructed for the free suspension of charged particles and droplets in the range 5–200 μ and for their study with respect to charge and mass and their variations with time in various gaseous environments. The apparatus and its functioning are described and illustrated by various applications. It is thought to be a useful research tool in physics, physical chemistry, and other disciplines and also to be useful in laboratory courses on the graduate and undergraduate levels.
The Additive Coloration of Alkali Halides
Authors: Jirgal G. H. , Shaw M. D. , Noble G. A.
Published: August 2005

A description is given of the construction and use of a furnace specifically designed to produce F-centers in alkali halide crystals by additive coloration. The method described avoids corrosion or contamination during the coloration process. Examination of the resultant crystals is discussed and several experiments using additively colored crystals are mentioned.
Optical Resource Letter on Colorimetry
Authors: Wyszecki Günter
Published: August 2005

These Optical Resource Letters are patterned after the materials that have been developed by the AAPT Committee on Resource Letters and previously published in the American Journal of Physics. Since they contain information of direct interest to most teachers of physics, we are pleased to have the permission of the Journal of the Optical Society of America to reprint them in AJP. The purpose is to provide, in an important field of optics, briefly annotated references which should be of value to teachers, researchers, engineers, and technicians interested in the subject area. No claim is made for completeness or exhaustiveness of coverage; rather, it is hoped that the references quoted will be helpful in themselves, and will be representative, or at least suggestive, of the broad literature on this subject. The letter E following an item number indicates that the reference is on a more-or-less elementary level; the letter A indicates an advanced level.

The present Optical Resource Letter, OC-1, was prepared under the direction of the OSA Ad Hoc Committee on Resource Letters: K. M. Baird, H. E. Breed, M. A. Jeppesen, J. M. Stone, and S. S. Ballard (Chairman).

Additional copies are available from the Executive Office of the Optical Society of America, 2100 Pennsylvania Avenue, N. W., Washington, D. C. 20037. Request Optical Resource Letter OC-1, and please enclose a stamped, return-addressed envelope.
A Quantitative Transmission Line Experiment
Authors: Johnston D. C. , Silbernagel B. G.
Published: August 2005

Modification of a commercially available strip-type transmission line is described, which makes possible reproducible measurements of standing waves on the line. The experimental data yield values for the characteristic impedance, phase velocity and line wavelength of radiation in the transmission line, and the dielectric constant of material in the line. Interpretation at several levels of difficulty is discussed and quantitative agreement between experiment and theory is obtained.
Classification of Electromagnetic and Gravitational Fields
Authors: Ludwig Garry
Published: August 2005

The connection between the three main methods of obtaining the Petrov classification is examined. Spinor techniques are used extensively. A five-dimensional complex linear space is introduced whose elements are Weyl tensors. It is found that not only Weyl tensors of type N and type III, but also some Weyl tensors of type I are null vectors in this space. In analogy with the electromagnetic case we would expect these null vectors to correspond to “pure” gravitational radiation.
Fermion Operator Ordering and the Quantum c-Number Correspondence
Authors: Mehta C. L. , Jaiswal A. K.
Published: August 2005

The linearly ordered and the exponentially ordered forms of an arbitrary spin 12-Fermion operator are defined and evaluated. As an application an expression for exp (αb̂) exp (βb̂†) is evaluated which resembles the usual Baker-Hausdorff identity. It is shown that the trace of the product of two Fermion operators can be expressed as a three-dimensional integral over c-number functions. Further the quantum equations of motion are also expressible as equations involving c-number functions.
A Proposed Electromagnetic Momentum-Energy 4-Vector for Charged Bodies
Authors: Butler J. W.
Published: August 2005

The conventional electromagnetic momentum- and energy-density expressions (E × H/c) and [12(E2+H2)], respectively (Heaviside-Lorentz units in free space), are known not to lead to a momentum-energy 4-vector for the fields of charged bodies. Yet the rest of classical electrodynamics is a covariant theory. This is a most remarkable anomaly. The reason for this anomaly is shown herein to lie in the procedure used to derive Poynting's theorem, which is shown not to be covariant in the presence of sources. A 4-vector is derived to represent the 4-momentum dGμ contained within a volume element dV of the electromagnetic field of a charged body with a 4-velocity uμ ≡ (γv, iγc): dGμ = [γ(E2−H2)dV/2c2]uμ, where γ ≡ (1 − v2/c2)−1/2. This proposed 4-vector is shown to remove several paradoxes associated with the predictions of the conventional momentum and energy density expressions. And the proposed 4-vector is also shown to be in agreement with the results of several experiments.
Operational Approach to Space and Time Measurements in Flat Space
Authors: Anderson James L. , Gautreau Ronald
Published: August 2005

The problem of making the space-time measurements that constitute an arbitrary reference frame is discussed within the framework of special relativity. An operational approach to such measurements is presented that does not require any special assumptions concerning the behavior of clocks and measuring rods but rather makes use of simple systems, material particles, and light signals to construct models of such measuring devices. With the help of a collection of free particles (which can be characterized operationally) and light signals we show how to construct inertial frames and how the usual kinematic results of special relativity can be obtained from a knowledge of the properties of these systems. Our main concern is with the properties of accelerated reference frames and we give an operational procedure for constructing a uniformly accelerated frame. With its help we show that the observed trajectory of a free particle in such a frame does not agree with the trajectory of a uniformly accelerated particle as observed in an inertial frame, except in a sufficiently small region of space-time. Finally we show that measurements made in an accelerated reference frame correspond in all respects to measurements made by a stationary observer in what is usually called a static homogeneous gravitational field.
The Poorman's Macroscopic Scattering Analyzer
Authors: Hageseth Gaylord T. , McCormack Francis J.
Published: August 2005

A scattering apparatus has been developed which is quite useful for teaching concepts in atomic and nuclear physics. The apparatus permits the students the opportunity for actually measuring differential cross sections, back angle scattering cross sections, capture cross sections, threshold energies and resonant energies. The classical mechanics problem involved in this scattering apparatus is discussed.
Motion in a Schwarzschild Field I. Precession of a Moving Gyroscope
Authors: Parker L.
Published: August 2005

A simple hypothesis is used to obtain, in lowest order, the precessional angular velocity of a slowly moving gyroscope in a Schwarzschild gravitational field. The hypothesis is that, at least to first approximation, the motion of the spin vector in a small displacement is the sum of two effects: (1) the motion the spin would have if it moved by parallel transfer in the curved 3-space, and (2) the motion of the spin as calculated directly from the principle of equivalence, treating the gravitational field in the vicinity of the gyroscope as though it were uniform. The precessional angular velocity obtained is in agreement with the general relativistic result. In another paper it will be shown that the same hypothesis also leads to the general relativistic result for the lowest order deflection of light by the central mass. These derivations are useful because they help to show how the motion of the spin vector can be understood from a 3 + 1 dimensional viewpoint.
Motion in a Schwarzschild Field II. Deflection of Light
Authors: Parker L.
Published: August 2005

The total angular precession of the spin vector of a photon (or neutrino) as it moves through the gravitational field of a non-rotating spherically symmetric mass is obtained, in lowest order, by means of an hypothesis previously applied to a slowly moving gyroscope. Since the spin vector of the photon must point along its path in the asymptotic region, as is well known from other considerations, it follows that the total angular precession of the spin vector must equal the total angular deflection of the path. The deflection obtained is in agreement with the general relativistic result.
Ferroelectricity Experiment for Advanced Laboratory
Authors: Schmidt V. Hugo
Published: August 2005

An experiment suitable for a junior or senior physics laboratory is described, in which the spontaneous polarization and coercive field for Rochelle salt are measured from the ferroelectric hysteresis loops, over the temperature range −18° to +24°C in which this crystal is ferroelectric. The suitability of triglycine sulfate for this experiment is discussed. The apparatus is also useful in demonstrating the relation of capacitance to electrode geometry, and in determining dielectric constants.
Temperature-Dependent, Indirect-Exchange Interaction between Magnetic Ions
Authors: Darby M. I.
Published: August 2005

Using first-order perturbation theory by analogy with the screening of a point charge by an electron gas, it is shown how the Ruderman-Kittel-Kasuya-Yosida indirect exchange interaction can be generalized to be temperature-dependent. An approximate expression is obtained for the molecular field in this case, and its application is briefly discussed.
Ballistics of the Modern-Working Recurve Bow and Arrow
Authors: Schuster Burton G.
Published: August 2005

A model of the working recurve bow amenable to analytic solution is developed. The equations of motion of the bow and arrow system are obtained and numerically integrated by computer. It is shown that subject to the approximations, the system is 100% efficient. Variations of the transfer of energy between bow and arrow are discussed in terms of bow parameters and the effects on the archer. A discussion of first-order exterior ballistics and arrow penetration indicates the equipment characteristics most desirable for both the target archer and hunter, subject to the archer's own capabilities.
Contribution to Isotope Shifts by the Charge Distribution within a Neutron: A Naive, First-Order Perturbation Approach
Authors: Ter Bush Robert
Published: August 2005

The contribution of the charge distribution within a neutron to the isotope shift is estimated by means of a first-order perturbation approach employing a simplistic model of the neutron. This “neutron shift,” (ΔE)N′,N, of an isotope with neutron number N′ relative to that with neutron number N is shown to be given by (ΔE)N′,N≅−|e|2ρe(N′−N)r02/10ε0, where −|e|ρe is the electronic charge density at the nucleus, and r0 is the effective radius of the negative charge cloud of the neutron as determined from electron-scattering data. A specific case, the neutron shift of Cs135 relative to Cs133, is worked out, and the neutron shift is seen to be small compared to the “volume-effect” shift, but of comparable magnitude to the experimental error associated with the measurement of the latter.
Some Thermodynamic Relations for Superconducting Ellipsoids
Authors: Zoller Paul , Dillinger J. R.
Published: August 2005

Under the assumption that no latent heat is associated with the phase changes that occur when a superconducting ellipsoid of type I material (or type II material) enters or leaves the intermediate (or mixed) state in a constant uniform applied field, we expect finite jumps in the specific heat at constant applied field, when these phase changes occur. The jumps are related to the magnetization curves at constant temperature.
A Student Exercise on the Decay Scheme of In116m
Authors: Banta H. E. , Gleason G. I.
Published: August 2005

Indium offers unique advantages in the teaching of radioisotope techniques: among others, enough activity for meaningful measurements may be excited with an isotopic neutron source. Semiconductor gamma detectors permit assignment of levels to an accuracy previously available only with bent crystal monochromators. Coincidence measurements on the gammas lend confidence in the structure of the decay scheme. Semiconductor detector measurements on the betas, along with beta-gamma coincidences, establish the Qβ for the decay. Peak integration and stripping allow assignment of relative abundances to the gammas. These abundances and the decay scheme allow assignment of relative abundances to the beta groups. The whole is suggested as a student exercise for a modern physics laboratory.
Approaches to Electromagnetic Induction
Authors: Scanlon P. J. , Henriksen R. N. , Allen J. R.
Published: August 2005

The first part of this article is a discussion of some ambiguities and sources of confusion in the presentation of electromagnetic induction in introductory texts. Particular attention is paid to the use of special relativity theory in these presentations. The second part of the paper discusses various examples of electromagnetic induction that have acquired reputations as “exceptions to the flux rule”. The origin of these exceptions is traced to an inappropriate choice of contour or its motions. We explicitly show that in these examples no exceptions occur, and give a general prescription for evaluating induced emf's.
Materials for a Radar Ranging Experiment
Authors: Fowler J. M.
Published: August 2005

This demonstration-experiment was developed as part of a one-semester course for upperclass nonscience students. Materials are offered which allow student data taking and analysis of radar moon echoes.
Solution to the Fresnel Zone Plate Problem
Authors: Childers H. Malcolm , Stone David E.
Published: August 2005

The diffraction problem for the Fresnel half-period zone plate is solved. The zone plate behaves as a lens with marked chromatism which can be taken advantage of for use in a spectrometer. The multiplicity of foci associated with the zone plate are examined in detail, and it is shown that the spectral range that can be focused without overlap is 3λmin≥λmax. The wavelength resolution is λ/Δλ ≈ (m+1)/0.445, where m is the number of transparent half-period zones. For m = 300, this corresponds to a 34-wave number resolution at 20 microns. The intensity at the focus is given approximately by 4I (m+1)2, where I is the intensity at the zone plate. The transmitted power that falls within the airy disk is proportional to the area of the zone plate.
Optical Diffraction from a Two-Dimensional Array of Spheres
Authors: de Fontaine D. , Jackson K. A. , Miller C. E.
Published: August 2005

A helium-neon laser has been used to produce diffraction from a monolayer of 2.68-μ-diam polymer spheres. Diffraction patterns characteristic of single crystals, polycrystals, crystal aggregates, and gases or liquids have been obtained, and can be directly correlated with the microscopic structure of the monolayer. Experimental verification is reported for the prediction by Bienenstock and Bagley that small-angle scattering from small crystallites becomes negligible when the crystallites are brought together in a density packed structure.
The Electromagnetic Shift of Landau Levels and the Magnetic Moment of the Electron
Authors: Arunasalam V.
Published: August 2005

The change in the magnetic moment of the electron due to zero-point vibrations of the quantized radiation field is calculated from nonrelativistic quantum mechanics. Using ideas which underlie Bethe's calculation of the Lamb shift and Luttinger's calculation of the electron magnetic moment, but without using second quantization of the electron field, we obtain the familiar g = 2[1 + (e2/hc)]. In addition, the calculation gives the correct form for the magnetic-field-dependent radiative corrections to g, namely a first term proportional to B and a second term proportional to B lnB. These B-dependent radiative terms differ only by numerical factors of the order of unity from the relativistic quantum electrodynamics corrections derived by Gupta. The self-energy integrals are fairly sensitive to the Bethe cutoff, but choosing the high-frequency cutoff at μc2/ħ yields, simultaneously, the correct Lamb shift and the Schwinger g value.
Single-Slit Diffraction Pattern of a Thermal Atomic Potassium Beam
Authors: Leavitt John A. , Bills Francis A.
Published: August 2005

The diffraction of a full thermal neutral atomic potassium beam by a single slit has been observed. Four experimental diffraction patterns of a 23.0(±0.4)μ diffracting slit were obtained with an atomic-beam apparatus which had a 2.5(±1)μ source slit, a 3.0(±0.1)μ detector wire, a source-to-slit distance of 96 cm, a slit-to-detector distance of 100 cm, and an oven temperature of 533° K. The experimental pattern was reproducible and is in good general agreement with the prediction of de Broglie's hypothesis and simple scalar Fresnel diffraction theory. The effect of diffraction is clearly evident; two prominent diffraction fringes are present on the top corners of the beam profiles. The theoretical prediction, calculated with the aid of a computer, included the effects of finite source and detector widths and the Maxwellian speed distribution of the K beam. Additional theoretical calculations showed that no major improvement in the clarity of the diffraction fringes could be obtained by using a velocity-selected beam, a Li7 beam, or a narrower diffracting slit.
An Inexpensive Fast-Light Detector for Student Laboratories
Authors: Sanders Steven G. , Porter Eshmal , LaBash Louis
Published: August 2005

A high-speed PIN diode and a transistor amplifier have been evaluated for use in student experiments with a pulsed-ruby laser. The electrical transient response of the amplifier and cabling was determined with a 1-nsec TDR pulse. The optical response of the entire system was checked with light pulses produced by reflecting a He-Ne laser beam onto the detector with a high speed rotating mirror. Pulses with 36-nsec risetimes were clearly resolved.
Optical Resource Letter on Radiometry
Authors: Nicodemus Fred E.
Published: August 2005

These Optical Resource Letters are patterned after the materials that have been developed by the AAPT Committee on Resource Letters and previously published in the American Journal of Physics. Since they contain information of direct interest to most teachers of physics, we are pleased to have the permission of the Journal of the Optical Society of America to reprint them in AJP. The purpose is to provide, in an important field of optics, briefly annotated references that should be of value to teachers, researchers, engineers, and technicians interested in the subject area. No claim is made for completeness or exhaustiveness of coverage; rather, it is hoped that the references quoted will be helpful in themselves and will be representative, or at least suggestive, of the broad literature on this subject. The letter E following an item number indicates that the reference is on a more-or-less elementary level; the letter A indicates an advanced level.

The present Optical Resource Letter, OR-2, was prepared under the direction of the OSA Ad Hoc Committee on Resource Letters: K. M. Baird, H. E. Breed, M. A. Jeppesen, J. M. Stone, and S. S. Ballard (Chairman).

Additional copies: Available from the Executive Office of the Optical Society of America, 2100 Pennsylvania Avenue, N. W., Washington, D. C. 20037. Request Optical Resource Letter OR-2 and please enclose a stamped return-addressed envelope.
Planetary Perihelion Precession with Velocity-Dependent Gravitational Mass
Authors: Engelke Ray , Chandler Colston
Published: August 2005

Planetary perihelion precession is theoretically examined within the framework of special relativity. The Eötvos experiment is used to motivate an assumption that the inertial and gravitational masses have the same velocity dependence. The resultant orbit equation is then approximated by one that is soluble in terms of trigonometric functions, and the accuracy of the approximation is examined. The perihelion advance predicted by the approximate equation is twice that predicted by special relativity without a velocity-dependent gravitational mass. Finally, the behavior of a photon in a gravitational field is investigated in a way consistent with the assumptions of this paper, and the usual values for the gravitational red-shift and light deflection as calculated with special relativity and the postulate of equivalence result.
Effective Interactions in Nuclear Structure
Authors: de Llano Manuel
Published: August 2005

The basic notions associated with the idea of an “effective interaction” in nuclear physics are sketched by first recalling isolated two-body scattering analyzed with integral equations and in which the transition operator appears naturally. Brueckner's reaction matrix operator is discussed in the context of both infinite nuclear matter and finite nuclei with doubly closed shells. Finally, open-shell nuclei are touched upon by way of a many-body effective interaction operator deduced in simple language and a possible connection between this and the reaction matrix operator is given. It is emphasized throughout that the basic merit of the vantage-point sketched here is its fundamental origin in the many-body Schrödinger equation.
Low-Frequency Bremsstrahlung in Coulomb Scatterings of Nonrelativistic Electrons
Authors: Gould Robert J.
Published: August 2005

A simplified derivation of the low-frequency bremsstrahlung cross section in the classical limit is presented. Also, by expanding Elwert's exact quantum-mechanical expression for the cross section in powers of (Ze2/ħv)2 and in powers of ħv/Ze2, corrections are obtained to the Born-limit and classical formulas, respectively. Averaging over a Maxwellian distribution of incident electrons gives the low-frequency thermal emission and absorption coefficients; corrections to the Born-limit and classical formulas are expressed as power series in Z2 Ry/kT and (kT/Z2 Ry)1/2, respectively. Significantly, the coefficient of the first-order correction term for the classical formulas for the cross section, and thermal coefficients turns out to be zero.
Energy Transients in Harmonic Oscillator Systems
Authors: Tobolsky A. V. , Hopkins I. L. , Samulski E. T.
Published: August 2005

The approach to energy equilibration is discussed for a system of N isolated classical oscillators, coupled or uncoupled. Exact solutions can be given for the kinetic and potential energies vs time, for a simple boundary condition which distributes the potential energy equally between all the normal modes at zero time and which gives zero kinetic energy to all the normal-mode oscillators at zero time. Most solutions are ergodic but a special class is nonergodic, i.e., the potential energy vs time shows exact recursions. The half-life for approaching the equilibrium value of potential or kinetic energy is of the order of the reciprocal maximum frequency of the oscillators. The fluctuations from equilibrium are treated by an extension of the method of Rayleigh's problem of random walks. The results are of interest in connection with the ergodic theorem of statistical mechanics.
Bose-Einstein Condensation of Noninteracting Particles
Authors: Zinke Otto Henry
Published: August 2005

The chemical potential is determined for a Bose-Einstein gas of noninteracting particles in a closed system. The calculation is done in a manner which shows dependence on an energy gap (ε1 − ε0), limits of application of the results, and behavior through the transition temperature.