On the Meson Theory of Nuclear Forces

Abstract

It has generally been believed that the vector, pseuclovcctor, and pseudoscalar meson theories of nuclear forces involve a 1'-3 difficulty. Mixtures of two fields were considered first by M~ller and Rosenfeld(1) .and later by SchwingerC2l in order to eliminate such a term. Further it was noticed by the present authorCa) that they involve also a divergence difficulty. and another mixture was suggested by him. This mixture could also eliminate a divergent part from the magnetic moment of nucleons. However, if we examine the procedure of deriving the nuclear force we can find that the above mentioned difficulties are due to the inadequacy of the method of the derivation, and that they have no direct connection with the general defect of the contemporary field theory. For example, the pseudoscalar mesons interact with nucleons by the pseudovector and pseudoscalar couplings. As we shall see later on, the pseudovector coupling is equivalent, except for a factor 2M/ p., to the pseudoscalar one in a nonrelativistic approximation. If we make use of this relation we can get a non-relativistic nuclear force which is free from the above mentioned difficultie.li. It was first suggested by Nelson(1) that the pseuc1ovector coupling includes a term of a pscudoscalar-coupling type. Later, using a unitary transformation, the latter was derived from the former by Dyson.(o) One may imagine that this relation can not be applied to the cases of vector and pseudovector meson theories because the couplings are different in these cases. But the term in question comes from the matrix elemcnt of the same type in all cases of these three theories. And we can find that the above mentioned result still holds in the vector and pseudovcctor theories.