Even-wave harmonic-oscillator theory of baryonic states. IV. Structure functions versus slope of neutron charge form factor

The structure of a mixed nucleon facilitated by the even-wave harmonic-oscillator model, which was shown to be quite successful in explaining certain important low-energy parameters such as $\frac{G_A}{G_V}$, $\Delta \to N\pi$ width, $G_{\mathrm{NN}\pi }$, and a few hitherto unresolved cases of baryon photocouplings, is employed, without extra parameters, to study the shape of the $n$,$p$ structure functions as well as the neutron charge radius squared ($〈r_n^{}{}_{}{}^2〉$). A mixing angle close to the ideal ($cot\theta =\sqrt{2}$) (determined from earlier investigations) is found to give a good account of the ratio $R^{\mathrm{np}} (=\frac{F_2^{\mathrm{en}}}{F_2^{\mathrm{ep}}}$) except for small values of the scaling variable ($z$) as well as of the difference ${\Delta }^{\mathrm{pn}} (=F_2^{\mathrm{ep}}-F_2^{\mathrm{en}}$) over the entire range of $z$. However, the same angle ($\theta >0\mathrm{}$) gives the wrong sign for $〈r_n^{}{}_{}{}^2〉$. The incompatibility of the sign of $〈r_n^{}{}_{}{}^2〉$ with the behavior of $R^{\mathrm{np}}$, as found by A. Le Yaouanc et al., thus remains unresolved in this simplest version of the even-wave model without further assumptions.