The interpretation of the proton-proton scattering experiments on the basis of Bethe's neutral meson theory leads to a range of nuclear forces $\approx \frac{\frac{1}{2}\hslash }{\mu c}$ ($\mu$ is meson mass). This implies a mass for the field particle equal to twice the mass of the cosmic-ray meson. It has also been found that a meson theory of nuclear forces, involving the emission and absorption of single charged mesons obeying Bose statistics, does not give the right sign of the quadrupole moment of the deuteron. In view of these difficulties and the fact that the single meson theory cannot correctly explain the $\beta$-decay anyway, we have investigated the consequences of a heavy electron pair theory of nuclear forces. The heavy electrons are assumed to be identical with electrons in every respect ("hole" theory, Fermi statistics, etc.) except that their rest mass is taken equal to the cosmic-ray meson mass. A tensor interaction between the nuclear particles and the heavy electron pair field can alone account for the spin dependence of the nuclear forces and the positive quadrupole moment of the deuteron. It is interesting that a pseudo-vector interaction gives both the wrong sign of the quadrupole moment and too much repulsion. The potential function between two nuclear particles behaves at large distances, $r$, as $\frac{e^{-2\mathrm{kr}}}{r^{2.5}}$, $k\approx \frac{\mu c}{\hslash }$ so that the range is effectively one-half the single meson range, and is directly connected with the rest mass of the heavy electron pair field (in contrast to the Gamow-Teller pair theory). At small $r$, the potential goes as $\frac{1}{r^5}$ so that one has to cut off in the same way as in the original electron-neutrino theory. The advantage of the heavy electron pair theory over a neutral meson theory is that it deals with particles which can be identified with the cosmic-ray mesons.

• Received 1 April 1940

DOI:https://doi.org/10.1103/PhysRev.57.1101