The Radiations Emitted from Artificially Produced Radioactive Substances. I. The Upper Limits and Shapes of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-Ray Spectra from Several Elements

TLDR

The Konopinski–Uhlenbeck theory predicts higher upper limits for β‑ray spectra than those inferred directly from data due to its high‑order contact with the momentum axis. β‑ray spectra of nine elements were measured by tracking curvature in a cloud chamber under a known magnetic field, with hydrogen tracks reducing scattering to reveal true momentum distributions above 1000 Hρ. The spectra of the nine elements agree with the Konopinski–Uhlenbeck modified Fermi theory, and the N13 upper limit was experimentally found to be 1.45 MV, closely matching the 1.5 MV theoretical value, supporting the theory’s validity.

Abstract

The $\ensuremath{\beta}$-ray spectra of ${\mathrm{N}}^{13}$, ${\mathrm{F}}^{17}$, ${\mathrm{Na}}^{24}$, ${\mathrm{Si}}^{31}$, ${\mathrm{P}}^{32}$, Cl, ${\mathrm{A}}^{41}$ and ${\mathrm{K}}^{42}$ have been investigated by measuring the curvatures of the tracks due to the $\ensuremath{\beta}$-rays in a cloud chamber traversed by a known magnetic field. By allowing the tracks to be formed in hydrogen the scattering of the tracks is so reduced that the distribution curves are felt completely to represent the true distributions for momenta greater than $1000H\ensuremath{\rho}$. It is found that the shapes of these curves are in very good accord with the Konopinski-Uhlenbeck modification of the Fermi theory for the first five elements mentioned above (two positron emitters and three electron emitters). The spectra of the last three elements above can be resolved into two components, each of which has a shape which fits the theory. In the case of ${\mathrm{N}}^{13}$ an upper limit has been found from fitting the data with a theoretical curve at 1.45 MV. The K-U theory always indicates a higher upper limit than is found by inspection of the data, because of the high order of contact with the momentum axis which it demands. The upper limit of ${\mathrm{N}}^{13}$ can be calculated from known reaction energies and should be 1.5 MV. The excellent agreement of these two values of the upper limits is regarded as suggesting that the high K-U limits represent the true energy changes in a $\ensuremath{\beta}$-disintegration.