The Electromagnetic Properties of Mesotrons

Abstract

A general theory describing particles of unit spin and arbitrary magnetic moment is developed and applied to the motion of such particles in a Coulomb field. In the particular case of magnetic moment unity (Proca theory), the exact equations for the radial components of the wave functions possess regular solutions only for those states ($j=l\ensuremath{\ne}0$ and $j=0$, $l=1$) in which the orbital angular momentum $l$ is a constant of the motion. For particles possessing a magnetic moment of two mesotron magnetons, the radial equations are free of singularities for all states but two: $j=1$, $l=0$ and $j=0$, $l=1$. The cross section for a fractional energy transfer to electrons by energetic mesotrons is calculated for the various simple possibilities of mesotron spin $\ensuremath{\sigma} (0,\frac{1}{2},1)$ and magnetic moment $\ensuremath{\mu}$ (arbitrary except for zero spin), and it is shown that only for $\ensuremath{\sigma}=\frac{1}{2}$, $\ensuremath{\mu}\ensuremath{\ne}1$ (in particular, $\ensuremath{\mu}=0$) and $\ensuremath{\sigma}=1$, $\ensuremath{\mu}=1$ is the cross section of the correct magnitude and form (i.e., essentially independent of the mesotron energy) to account for observed burst phenomena at energies greater than 2\ifmmode\times\else\texttimes\fi{}${10}^{10}$ ev. Criteria for the validity of these formulae indicate that the region of applicability for the theory $\ensuremath{\sigma}=1$, $\ensuremath{\mu}\ensuremath{\ne}1$ is more limited than that for $\ensuremath{\sigma}=1$, $\ensuremath{\mu}=1$ (Proca).