Structure of the Nucleon

Abstract

An attempt is made to determine what restrictions are imposed on the nucleon wave functional by the known values of the nucleon moments and by the neutron-electron interaction. The nucleon is assumed to consist of a core particle (nucleore) of spin \textonehalf{} surrounded by a pion field. No detailed reference is made to the interaction producing the field. Nucleore recoil is neglected. It is found that the neutron and proton moments satisfy a mirror condition ${\mathfrak{M}}_{n}+{\mathfrak{M}}_{p}=1\ensuremath{-}(\frac{4}{3}){P}_{1},$ where ${P}_{1}$ is the probability that pions (any number or charge) occur in the field with total orbital angular momentum $L=1$. Insertion of the measured values of the moments in the equation yields ${P}_{1}=9$ percent. A model of the nucleon in which one pion plays the predominant role is not consistent with this result. This is probably the underlying reason for the failure of the weak coupling theory to give the correct ratio of neutron to proton moments. The neutron and proton moments can be accounted for if the field contains at least two pions with appreciable probability. A successful model consists of 91 percent bare nucleore, and 9 percent a pair of mesons, each in $p$ states forming the state $L=1$.The neutron electron interaction is shown to depend on the mean square radius of the charge distribution, ${〈{r}^{2}〉}_{\mathrm{Av}}$, in the nucleon. If only one or two pions with $L=1$ are contained in the proper field with appreciable probability, the observed interaction combined with the above value of ${P}_{1}$ leads to the very reasonable value of the mean square displacement of a pion, $\ensuremath{\approx}0.5$ times the square of the Compton wavelength of the pion.The results suggest strongly that a weak nonlinear coupling would be capable of accounting for the data, but a linear coupling of intermediate strength cannot be excluded.An analysis of the pseudoscalar field in terms of spherical waves is given in the Appendix. Consideration is also given there to the space and time inversion properties of the field functionals.