The Relativistic Correction in the Meson Theory of Nuclear Force

In the present paper a systematic investigation is made on the relativistic corrections of the usual non-relativistic meson theories of nuclear force by expansion with respect to the dimensionless operator $\frac{\nabla }{M}$. The mixed theory initiated by Møller and Rosenfeld is considered since it is the only satisfactory theory in the non-relativistic region. It is found that the inadmissible singularity which has been removed in the mixed theory in the non-relativistic region reappears in the higher approximations. This means that the extension of the mixed theory to the relativistic region as done by Møller and Rosenfeld in explaining the quadrupole moment is not justified.