R. R. Winters

On the calculation of Maxwellian-averaged capture cross sections

A recipe for the calculation of Maxwellian-averaged capture cross sections as a function of temperature kT from the existing excitation function is discussed. Detailed formulae are given to handle the various portions of this excitation function which in general contains both resolved resonance and an unresolved resonance parts. For the temperature region considered, the details of the thermal (0.0253 eV) capture cross section and a possible direct capture compoment are of importance. The treatment of resolved resonances depending on the characteristics of the resonance parameters is discussed

Continued fractions and the harmonic oscillator using Feynman’s path integrals

The simple harmonic oscillator plays a prominent role in most undergraduate quantum mechanics courses. The study of this system using path integrals can serve to introduce a formulation of quantum mechanics which is usually considered beyond the scope of most undergraduate courses. However, given the current interest in the interpretation and foundations of quantum mechanics, nonstandard approaches such as Feynman’s path integral formalism can be helpful in developing insights into the structure of quantum mechanics. In this paper we evaluate the path integration appearing in Feynman’s treatment in a natural and direct manner utilizing a symbolic computational program. This approach makes the use of the path integral formulation of quantum mechanics accessible to most undergraduate physics majors. As a by-product of our approach, we find a representation of the reciprocal of the sinc function, sinc (x)≡sin(x)/(x), in terms of an infinite product of partial approximates of a continued fraction. We have not...

The lunar capture hypothesis revisited

Recent work on planetary formation processes have suggested that ancient planetary bodies could have been warmer and, therefore, more easily deformable soon after formation than at present. By use of the estimates for the elastic parameters believed to be appropriate for a warm ancient Moon and Earth, it is shown that the energy of deformation of the planetary bodies during a close gravitational encounter was sufficient to effect capture.