Lawrence Ruby

Applications of the Mathieu equation

The properties of the Mathieu equation are reviewed in order to discuss some of the applications that have appeared in recent years. Those mentioned are: vibrations in an elliptic drum, the inverted pendulum, the radio frequency quadrupole, frequency modulation, stability of a floating body, alternating gradient focusing, the Paul trap for charged particles, and the mirror trap for neutral particles.

Statistics of the detection process in radioactive decay

The equation for the probability p(n,c,t) of having n radioactive atoms and c accumulated counts at time t is solved under the assumption that the emission process is independent of the detection process. The solution is the product of two binomial distributions. The detailed properties of the joint distribution are shown to be important when only a few radioactive atoms are present. The solution is extended to the case of a radioactive source which decays by multiple emissions, and the result is shown to be related to the problem of measuring the probability distribution of the number of neutrons emitted in spontaneous fission.

Demonstration of the Buildup and Decay of Radioactivity

A simple apparatus is described which serves to demonstrate both the buildup and decay of radioactivity. The buildup is observed by, in effect, periodically sampling the radioactivity during activation. The sampling is effected by mounting Ag foil on a wheel which rotates it alternately between a neutron source and a beta detector.

Modern architects of the periodic system

Major discoveries, which have transformed The Periodic System of the Elements from the arrangement suggested by Mendeleev to the current configuration, are reviewed. In particular, the contributions of H. G. J. Moseley and G. T. Seaborg are described.

Binomial Aspects of Radioactivity.

On the basis of a probability equation approach, radioactivity is shown to be a binomially distributed process, for any value of the observation time. The approximations necessary to establish the validity of Poissonian statistics are discussed.

Applications of Nuclear Energy: A New Course for the Humanities

A course has been developed designed to acquaint the nontechnical student in the humanities with nuclear energy and its applications in many areas affecting human affairs. Course content includes atomic and nuclear structure, applications of radioisotopes, reactors, fusion research, nuclear explosives, and accelerators. Other than the relativistic transformations, the radioactive-decay law and the cyclotron equations are the only relations occurring of any complexity. Socio-economic considerations are treated briefly as they arise. Results are given of a questionnaire examining the extent of misinformation on nuclear energy matters.