A detailed analysis is made of the neutron-proton interaction yielded by the symmetrical pseudoscalar meson theory, with pseudoscalar coupling, using the Tamm-Dancoff nonadiabatic method which has been extended to include nucleon pair creation and higher order effects in the exchange of mesons. It is found that, in the nonrelativistic region, the second- and fourth-order terms provide the main contribution to the interaction, the remaining part of the potential giving only a small correction. In the relativistic region, little can be said about the convergence of the interaction, but there are indications that it becomes strongly repulsive at distances comparable with the nucleon Compton wavelength ($\frac{\hslash }{\mathrm{Mc}}$). The radiative corrections to the potential are calculated in the nonrelativistic limit, using the equation of Bethe and Salpeter, which has been transformed into a one-time equation by means of a method which has been given previously. It is shown that the corrections arising from vertex parts and closed loops in the Feynman diagrams are at most of the order of $\left(\frac{G^2}{4\pi }\right){\left(\frac{\mu }{2M}\right)}^2$ times the term which they correct. There exists, however, a class of finite self-energy terms which give a contribution to the interaction having the same analytical form as the fourth-order potential, times a numerical factor which can be expressed as a power series in $\frac{G^2}{4\pi }$.

The low energy properties of the neutron-proton system are discussed, using the nonrelativistic potential which is calculated in this paper, and replacing the interaction in the relativistic region by a boundary condition prescribing that the wave function tends to zero at a finite distance ${\mathrm{r}}_{\mathrm{c}}$. It is found that a good agreement with experiment can be achieved by choosing $\frac{G^2}{4\pi }=9.7\mathrm{}\pm 1.3$ and $r_c=(0.38\mathrm{}\pm 0.03)\left(\frac{\hslash }{\mu c}\right)$. Finally, an investigation of the neutron-proton scattering at 40 Mev shows that the same potential leads to a satisfactory description of the available experimental data.

• Received 7 August 1952

DOI:https://doi.org/10.1103/PhysRev.88.725