L. I. Schiff

First Page

The differential bremsstrahlung cross section of Bethe and Heitler is integrated over scattered electron angles to obtain an expression for the distribution in energy and angle of the radiation from fast electrons in very thing targets. Screening is taken into account through the assumption of an atomic potential $(\frac{\mathrm{Ze}}{r})\mathrm{exp}(\ensuremath{-}\frac{r}{a})$, and the calculation is restricted to high energies and to small to moderate angles. The result is the same as that of Sommerfeld for no screening, except that the argument of the logarithm now depends on angle as well as on energy. Integration of this expression over gamma-ray angle gives an analytic formula for the total intensity that is nowhere more than a few percent higher than the Bethe-Heither result calculated numerically on the basis of the Thomas-Fermi potential.

The possibility of measuring a very small nuclear electric dipole moment is explored by calculating the interaction of this moment with an external electric field. It is shown that for a quantum system of point, charged, electric dipoles in an external electrostatic potential of arbitrary form, there is complete shielding; i.e., there is no term in the interaction energy that is of first order in the electric dipole moments, regardless of the magnitude of the external potential. This is true even if the particles are of finite size, provided that the charge and dipole moment of each have the same spatial distribution. Relativistic and second-order effects are uninterestingly small. There is, however, a first-order interaction if the charge and moment distributions are different, and also for a point electric dipole if it also carries a magnetic dipole moment. Explicit calculations of both effects are given for hydrogen and helium atoms. It is found that the effective electric field at a ${\mathrm{He}}^{3}$ nucleus arising from the magnetic dipole effect is about a hundred times that arising from the finite size effect, and is roughly ${10}^{\ensuremath{-}7}$ times the external electric field.

Received 11 February 1960DOI:https://doi.org/10.1103/PhysRevLett.4.215©1960 American Physical Society