Volume 79, Issue 1, January 2011
 PAPERS


Resource Letter NSM1: New insights into the nuclear shell model
View Description Hide DescriptionThis Resource Letter provides a guide to the literature on the spherical shell model as applied to nuclei. The nuclear shell model describes the structure of nuclei starting with a nuclear core developed by the classical neutron and proton magic numbers , where gaps occur in the singleparticle energies as a shell is filled, and the interactions of valence nucleons that reside beyond that core. Various modern extensions of this model for spherical nuclei are likewise described. Significant extensions of the nuclear shell model include new magic numbers for spherical nuclei and now for deformed nuclei as well. When both protons and neutrons have shell gaps at the same spherical or deformed shapes, they can reinforce each other to give added stability to that shape and lead to new magic numbers. The vanishings of the classical spherical shell model energy gaps and magic numbers in new neutronrich nuclei are described. Spherical and deformed shell gaps are seen to be critical for the existence of elements with .

What GayLussac didn’t tell us
View Description Hide DescriptionGayLussac’s 1801 experiments establishing the law of volumes for gases are brilliantly simple, and he described them with a level of detail that was new to physics writing. But he did not present his actual measurements or tell us how he analyzed them to conclude that between 0 to , a volume of any gas will expand by about 37.5%. We review his experiments and conclude that he measured initial and final volumes at slightly different pressures. By using the gas laws and his apparatus diagrams, we corrected his data so that they correspond to constant pressure. His corrected results give , the currently accepted value for nearly ideal gases. Aside from their intrinsic interest, our analyses can provide students intriguing applications of the gas laws and Pascal’s law and motivate them to consider Pascal’s paradox. We also note the influence of ballooning and of the French Revolution on GayLussac.

A question of mass
View Description Hide DescriptionWe present a pedagogical discussion of spontaneous symmetry breaking, the Goldstone theorem, and the Higgs mechanism. If the Higgs boson is found, it might provide an explanation of the origin of mass.

Experiments on buoyancy and surface tension following Galileo Galilei
View Description Hide DescriptionWe analyze passages of Galileo’s writings on aspects of floating. Galileo encountered peculiar effects such as the “floating” of light objects made of dense material and the creation of large drops of water that were difficult to explain because they are related to our current understanding of surface tension. Even though Galileo could not understand the phenomenon, his proposed explanations and experiments are interesting from an educational point of view. We replicate the experiment on water and wine that was described by Galileo in his Two New Sciences.

Ice rafts not sails: Floating the rocks at Racetrack Playa
View Description Hide DescriptionWe suggest that the existence of many of the rockcarved trails at Racetrack Playa in Death Valley National Park is predominantly due to the effect of arbitrarily weak winds on rocks that are floated off the soft bed by small rafts of ice, as also occurs in arctic tidal beaches to form boulder barricades. These ice cakes need not have a particularly large surface area if the ice is adequately thick—the ice cakes allow the rocks to move by buoyantly reducing the reaction and friction forces at the bed, not by increasing the wind drag. The parameter space of ice thickness and extent versus rock size for flotation is calculated and found to be reasonable. We demonstrate the effect with a simple experiment.

When action is not least for orbits in general relativity
View Description Hide DescriptionIn Newtonian mechanics, the action for a true trajectory between two spacetime events and is a minimum if the final event occurs before the kinetic focus of the initial event ; otherwise, the action is a saddle point. We give a simplified proof of an analogous theorem in differential geometry for worldlines in a curved spacetime. We locate the kinetic focus for orbits in a Schwarzschild field in the lowestorder postNewtonian approximation and show that the kinetic focus is shifted beyond its Newtonian value of one angular cycle by a fractional amount of order .

VaryingG cosmology with type Ia supernovae
View Description Hide DescriptionThe observation that type Ia supernovae (SNe Ia) are fainter than expected given their redshifts has led to the conclusion that the expansion of the universe is accelerating. The widely accepted hypothesis is that this acceleration is caused by a cosmological constant or some dark energy field that pervades the universe. We explore what the supernovae data tell us about this hypothesis by answering the question: Can these data be explained with a model in which the strength of gravity varies on a cosmic timescale? We conclude that they can and find that the supernovae data alone are insufficient to distinguish between a model with a cosmological constant and one in which varies. However, the varyingG models are not viable when other data are taken into account. The topic is an ideal one for undergraduate physics majors.

Visualizing circular motion around a Schwarzschild black hole
View Description Hide DescriptionAn observer who moves on a circular orbit around a Schwarzschild black hole with a constant but arbitrary velocity must compensate for the gravitational and centrifugal acceleration to stay on this orbit. The local reference frame of the observer undergoes a geodesic precession, which depends on the radius of the orbit and the velocity. We describe the details of this circular motion and an interactive program that shows what the observer would see.

Thermodynamics of heating a room
View Description Hide DescriptionA room is not heated by increasing its internal energy but by decreasing its entropy due to the fact that during heating, the volume and pressure remain constant and air is expelled. We first present a simple solution treating the air in the room as an ideal gas. We calculate the differential entropy change and heat transfer and give numbers for a typical room including estimates of heat loss through windows and walls. We also demonstrate the power of thermodynamics to derive the entropy and internal energy changes for any gas.

When does hot water freeze faster then cold water? A search for the Mpemba effect
View Description Hide DescriptionIt is possible to consistently observe hot water freezing faster than cold water under certain conditions. All conditions except the initial temperature of water specimens must be the same and remain so during cooling, and the cold water must supercool to a temperature significantly lower than the temperature to which the hot water supercools. For hot water at an initial temperature of and cold water at , the cold water must supercool to a temperature of at least , lower than the temperature to which hot water supercools. With these conditions satisfied, we observed initially hot water freezing before the initially cold water 28 times in 28 attempts. If the cold water does not supercool, it will freeze before the hot water because it always cools to first regardless of the initial temperatures.

Teaching laser physics by experiments
View Description Hide DescriptionExperimental activities in the undergraduate physics curriculum often suffer from a lack of connection with the courses they are designed to support. This paper describes a set of experiments in laser physics based on a commercially available HeNe gain tube with one internal and one external mirror. The experiments take students through several important topics including the spatial and temporal properties of laser radiation, a rate equation based model for the laser, and elements of the underlying spectroscopy. The experiments can be integrated into existing courses or provide the backbone of a complete course with close integration of theory and experiment.

Less than perfect quantum wavefunctions in momentumspace: How senses disturbances in the force
View Description Hide DescriptionWe develop a systematic approach to determine the large behavior of the momentumspace wave function,, of a onedimensional quantum system for which the positionspace wave function,, has a discontinuous derivative at any order. We find that if the derivative of the potential energy function for the system has a discontinuity, there is a corresponding discontinuity in at the same point. This discontinuity leads directly to a powerlaw tail in the momentumspace wave function proportional to . A number of familiar pedagogical examples are examined in this context, leading to a general derivation of the result.

Relaxing gap capacitor models of electrified interfaces
View Description Hide DescriptionRelaxing gap capacitor models emphasize the chargeinduced variation of the effective gap of electric double layercapacitors. The first such model, the elasticcapacitor, resolved the theoretical puzzle of negative differential capacitance by linking its origin to the chargeinduced contraction of the effective gap. It also revealed the importance of treating the electrodecharge density as a selfadjustable equilibrium quantity rather than as an independently fixed variable. We show that negative differential capacitance for fixed electrodecharge density leads to a charging instability for fixed applied voltage. The “squishy capacitor” model, which allows for lateral variation of the effective gap, relates negative differential capacitance to instabilities in isolated systems, with a resultant lateral redistribution of surface charge. We review the origin of negative differential capacitance, discuss charging instabilities, and explore the analogy between the critical behavior of the squishy capacitor and firstorder phase transitions.

On the exact electric and magnetic fields of an electric dipole
View Description Hide DescriptionWe make a multipole expansion directly in Jefimenko’s equations to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. Some comments are made about the usual derivations in most undergraduate and graduate textbooks and in literature.

The significance of the Schott energy for energymomentum conservation of a radiating charge obeying the Lorentz–Abraham–Dirac equation
View Description Hide DescriptionIt is shown that energy and momentum are conserved during the runaway motion of a radiating charge and during free fall of a charge in a gravitational field. The runaway motion demonstrates the consistency of classical electrodynamics and the Lorentz–Abraham–Dirac equation. The important role of the Schott (acceleration) energy in this connection is made clear, and it is shown that the Schott energy is the part of the electromagnetic field energy that is proportional to (minus) the scalar product of the velocity and acceleration of a moving acceleratedcharged particle. The Schott energy is negative if the acceleration is in the same direction as the velocity and positive if it is opposite. During runaway motion, the Schott energy becomes more and more negative, and for a charged particle, it is localized at the particle. It is also shown that a proton and a neutron fall with the same acceleration in a uniform gravitational field, although the proton radiates and the neutron does not. The radiation energy comes from the Schott energy.

Listening to student conversations during clicker questions: What you have not heard might surprise you!
View Description Hide DescriptionWhen instructors provide time for students to discuss their ideas in Peer Instruction, instructors minimally expect that the conversation partners will discuss their opinions relating to the physical attributes posed in a question and submit clicker responses that coincide with individual opinions. We defined conversations that met these two criteria as “standard conversations.” In our study of 361 recorded Peer Instruction conversations from large introductory astronomy classrooms taught by experienced instructors, we found that 38% of student conversations were standard conversations. Of the remaining 62%, we identified three broad categories consisting of ten types of “nonstandard” conversations. The first category of conversations describes student ideas that were not reflected in any of the given multiple choice answers. The second category includes issues related to the interpretation of the statistical feedback provided by electronic classroom response systems. The third category describes common pitfalls experienced by students during conversations that led to unproductive interactions. Our analysis of nonstandard Peer Instruction conversations will be useful to practitioners and researchers seeking to improve the implementation of Peer Instruction.
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 PHYSICS EDUCATION RESEARCH


Connecting symbolic difficulties with failure in physics
View Description Hide DescriptionWe find that symbolic physics questions are significantly more difficult than their analogous numerical versions. Very few of the errors are due to manipulation errors of the symbolic equations. Instead, most errors are due to confusions of symbolic meaning. We also find that performance on symbolic questions is more highly correlated with the overall performance than performance on numeric questions. We devised a coding scheme that distinguishes questions based only on the mathematical structure of the solutions. The coding scheme can be used to identify both difficult and discriminating physics questions. The questions identified by this coding scheme require an algebraic representation and discourage problem solving strategies that do not require an understanding of symbolic equations. Our results suggest that an inability to interpret physicsequations may be a major contributor to student failure in introductory physics.
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 BOOK REVIEWS


Beyond Smoke and Mirrors: Climate Change and Energy in the 21st Century
View Description Hide DescriptionThis article reviews Beyond Smoke and Mirrors: Climate Change and Energy in the 21st Century by Burton Richter 
Selected Papers on the Periodic Table
View Description Hide DescriptionThis article reviews Selected Papers on the Periodic Table by Eric Scerri 
Quantum Physics: A Fundamental Approach to Modern Physics
View Description Hide DescriptionThis article reviews Quantum Physics: A Fundamental Approach to Modern Physics by John S. Townsend
