William Rubinson

The Equations of Radioactive Transformation in a Neutron Flux

The standard equations of radioactive transformation are generalized to include the case where radioactive nuclei are subject to transformation by neutron absorption in addition to spontaneous decay. Opportunity is taken to derive the equations by a simple method which avoids recourse to the formal methods of solving differential equations. A method is pointed out whereby one may write simply by inspection the equation for the activity of a species which is descended from an ancestral species through a chain of any combination of decays and neutron absorptions. Some problems are solved as illustration.

The correction for atomic excitation energy in measurements of energies of e− capture decay

Abstract The theoretical basis for the measurement of the energy of an e − capture decay by way of the bremsstrahlung endpoint is outlined. It is pointed out that an experimental bremsstrahlung spectrum is a superposition of many spectra, one for each of the possible states of atomic excitation in which the daughter atom can be produced. Consequently it appears that the proper correction from the measured endpoint to the total decay energy should be the mean excitation energy of the daughter atom, rather than simply the binding energy corresponding to the hole left in the daughter by the capture act. The mean excitation energy of the daughter is worked out in detail and compared with the binding energy. The results show that the two are equally adequate as corrections from the endpoint to the total decay energy, even if measurements of the bremsstrahlung spectrum could be made with ideal accuracy. As a by-product of this work various experimental and theoretical values of atomic total binding energies are fitted by non-linear least squares to the form c Z k suggested by the Thomas- Fermi model.

Discrete state perturbation theory via Green’s functions

The exposition of stationary state perturbation theory via the Green’s function method in Goldberger and Watson’s Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on.