Volume 37, Issue 5, May 1969
 PAPERS


The Development of Lead Salt Detectors
View Description Hide DescriptionIn 1930, a meeting to discuss photoelectric cells indicated that photoconductive cells were of marginal value. In 1954, interest in photoconductivity was sufficient to warrant a meeting to discuss that topic exclusively. The impetus for this change came largely from the military in its desire to develop a sensitive, reliable infrared detector. The varied investigations involve both German and U. S. A. wartime efforts and subsequent efforts in such diverse laboratories as university, military, and commercial. It is doubtless this diversification that has enabled so many successes to be achieved.

Contribution to Isotope Shifts by the Charge Distribution within a Neutron: A Naive, FirstOrder Perturbation Approach
View Description Hide DescriptionThe contribution of the charge distribution within a neutron to the isotope shift is estimated by means of a firstorder perturbation approach employing a simplistic model of the neutron. This “neutron shift,” of an isotope with neutron number relative to that with neutron number is shown to be given by , where is the electronic charge density at the nucleus, and is the effective radius of the negative charge cloud of the neutron as determined from electronscattering data. A specific case, the neutron shift of relative to , is worked out, and the neutron shift is seen to be small compared to the “volumeeffect” shift, but of comparable magnitude to the experimental error associated with the measurement of the latter.

A TimeofFlight Neutron Experiment for the Undergraduate Laboratory
View Description Hide DescriptionA neutrontimeofflightexperiment is described for use with neutrons from small accelerators. The neutrons were produced for this experiment by the reaction. This reaction is the one most commonly used for the production of 14.8 MeV neutrons. The method employed for the measurement is known as associated particle time of flight. For the reaction,neutrons that emerge in the forward direction are accompanied by associated alpha particles that are emitted with an angular separation of approximately 180° with respect to these neutrons. The alpha particles were used to start a timetopulseheight converter (TPHC), and the neutrons stopped this timing cycle. The output from the TPHC was a single isolated neutron group whose magnitude was proportional to the difference between the start and stop pulses. In the experiment, the velocity of the neutron is determined, and the total neutron cross section is measured for aluminum,copper, iron, and lead. All measured quantities give results that are in very good agreement with the accepted values. From the total crosssection measurements, a value of the nuclear radius was determined to be .

Origin of Counting Statistics in Simple Nucleonic Instruments
View Description Hide DescriptionThe variance of the (Poisson) counting statistics of a typical nucleonic instrument is shown to be expressible as the sum of contributions from a variety of distinct random processes. The utility of this decomposition is illustrated in an example where the effect of the random decay rate of the isotope is removed. Contradicting numerous articles and texts, it is also shown that the random decay rate of the isotope and the random detector counting statistics do not participate in a causeeffect relationship, but are nearly independent phenomena in most instruments.

Differential Form of the Elastic Collision Operator
View Description Hide DescriptionThe elastic collision integral in the Boltzmann equation can be converted into differential form when it describes the interactions between “light” and “heavy” particles. An elementary and straightforward demonstration of this conversion is effected by expanding the distribution function in powers of the collisional energy transfer.

The Lorentz Electron Theory of Relativity
View Description Hide DescriptionThis paper traces H. A. Lorentz's work on the electrodynamics of moving bodies from 1887 to 1909. His initial rejection of Michelson's 1881 interferometer experiment and the development of the “electron theory” as a modification and extension of Maxwell's ideas are discussed. The 1892 article in which Lorentz proposes the contraction hypothesis (LorentzFitzgerald contraction) is analyzed, and the manner in which the hypothesis is integrated into the electron theory then, and later in the 1895 Versuch, is presented. A discussion of the Versuch's introduction of “local time” and the “theorem of corresponding states” follows, and it is then shown that Lorentz introduced secondorder Lorentz transformations in an 1899 paper. The wellknown 1904 paper is analyzed, and is shown to be presenting the latest modifications in transformation equations designed to prove a theorem of corresponding states for many electromagnetic phenomena to all orders of . Using Lorentz's 1909 Theory of Electrons, it is argued that the Lorentz transformations as understood by Lorentz prior to Einstein's work possessed inverse transformations which entailed length dilations, time contractions, etc., and which were nonrelativistic and inconsistent with the Lorentz electron theory. Finally a brief discussion of a reason for Einstein's difference of approach is outlined.

Expanding Wavefronts in Special Relativity: A ComputerGenerated Film
View Description Hide DescriptionWe describe a computergenerated film which shows an expanding wavefront as seen from a coordinate frame relative to which the source moves with constant velocity. An expression for the wavefront as a function of time is derived, and features of it are discussed in terms of the relativistic laws for the addition of velocities. Sample stills from the film are presented and used in discussing the shape of the wavefront, the velocity of the center of the wavefront, and the headlight effect, all as functions of the signal velocity and the velocity of the source.

Some Thermodynamic Relations for Superconducting Ellipsoids
View Description Hide DescriptionUnder the assumption that no latent heat is associated with the phase changes that occurwhen a superconducting ellipsoid of type I material (or type II material) enters or leaves theintermediate (or mixed) state in a constant uniform applied field, we expect finite jumps in thespecific heat at constant applied field, when these phase changes occur. The jumps are relatedto the magnetization curves at constant temperature.

Precision through Error Generation
View Description Hide DescriptionWhen the measurement values are discrete, relative to the intrinsic noise level of an experiment, it may be possible to increase accuracy by error generation. Several illustrations are given, and the use of normal law error generation is discussed in detail.

Forced Oscillations and Magnetic Resonance in the Introductory Laboratory
View Description Hide DescriptionA compass is placed in a uniform magnetic field produced by Helmholtz coils. An oscillator produces a perturbing field perpendicular to the uniform field causing a forced oscillation. A plot of the square of the resonant frequency versus the Helmholtz coil current yields a straight line. The slope gives the magneticdipole momentmoment of inertia ratio, and the intercept yields the damping constant.

Rotation Operators
View Description Hide DescriptionThe wide variety of conventions in use concerning rotation operators can be confusing to the student who is beginning a serious study of the quantum theory of angular momentum. These conventions are discussed and compared, and the relation between active and passive rotations is examined. Using these results, a useful formula is derived which connects the reduced matrix element of a tensor operator with quantities that are measured relative to a rotating reference frame.

Spatial Filtering Experiments for Undergraduate Laboratories
View Description Hide DescriptionExperiments in the spatial filtering of optical images, which are suitable for an upper division undergraduate laboratory, are presented. These experiments exploit the spatial coherence of laser radiation for their success. It is shown that the field distribution across the aperture of a lens, and the field distribution across the focal plane are a Fourier transform pair. Since a lens resolves an image into its Fourier components, filtering operations can be performed at the transform plane which enhance or eliminate selected components of the image. A second lens performs another transformation that recreates the original image, plus the effects of whatever filtering operation which has been performed. Three examples of experiments that use this principle are described. The irregularities across the wavefront of a laser output beam are eliminated. A twodimensional pattern is filtered so only the information in one dimension is transmitted. The squares which make up a selfportrait are subtracted, leaving a continuous rendition.

Quantum Fact and Fiction III
View Description Hide DescriptionPart III of this series [A. Landé, Amer. J. Phys. 33, 123 (1965), and 34, 160 (1966), quotedas Parts I and II] continues the critique of the customary interpretation of quantummechanics. It is directed against the idea that electrons, in opposition to the Born statisticalparticle interpretation of the wave function, are “wavicles.” Serious conceptual and elementarymathematical defects in Bohr's famous “Discussion with Einstein” are pointed out.The doctrine that position q and momentum p of a particle are blurred over an uncertaintyrange because both allegedly cannot be measured simultaneously, that q and p do not existsimultaneously, is due to a confusion of analogy with identity of qualities. In its secondpart, the paper offers a nonquantal derivation of the probability interference law as a necessityunder the postulate that the general interdependence between probabilities is to become theordinary probability addition law in the average. The wave picture of matter violates thepostulate of relativity.

Entropy Differences between Ideal and Nonideal Systems
View Description Hide DescriptionThe canonical entropy for an ideal (noninteracting) system is compared with the canonical entropy for a similar nonideal system at the same temperature. Using the GibbsBogoliubov inequality, upper and lower bounds are derived for . For classical fluids and for quantum or classical spin systems, the upper bound is found to be identically zero, yielding . The classical fluid result agrees with a recent finding of Baierlein and generalizes it to a class of momentumdependent potentials. The spin system result further extends the scope of Baierlein's inequality. For quantum fluids, a discussion of the bounds is given, but no conclusive results are obtained.

The Free Fall of Atoms
View Description Hide DescriptionThe gravitational deflection of beams of potassium atoms having welldefined speeds ranging from 186 m/sec to 551 m/sec has been observed over a horizontal flight path of 2.1 m. The experimental results are consistent with the assumption that individual atoms experience the usual gravitational force. If the experiment is regarded as one to determine , the result of a leastsquares fit of the data to the theoretical expectation yields .
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 NOTES AND DISCUSSIONS


Instructional Uses of the Computer: An Improved Computer Version of the Prism Spectrometer Experiment
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Remark on Integral Orbital Angular Momentum
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An Illustration from Classical Physics of Renormalization Mathematics
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How Often Do Beats Occur?
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Mechanical Demonstration of Inelastic Collisions and Excited States
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