The Meson as a Composite Particle

Calculations are carried out along the lines of the work of Fermi and Yang in which the $\pi$-meson is considered as a composite particle formed from a proton and an anti-neutron. On the assumption of a vector interaction it is found that the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state must be excluded because its energy goes to zero as the interaction goes to zero, while the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ state appears to give an acceptable solution. On the assumption of a tensor interaction it is found that ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ solutions both exist, but for opposite signs of the interaction. The tensor interaction must therefore be excluded since it would lead to the formation of a composite particle by a proton and a neutron. Using the vector interaction one finds that the ground state is a ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, but that there are other states with $j=0,1\mathrm{} \mathrm{and} 2$ lying near it, the proximity depending on the interaction range assumed.