Bag-model analyses of proton-antiproton scattering and atomic bound states

We study proton-antiproton ($p\overline{p}$) scattering using the static real potential of Bryan and Phillips outside a cutoff radius $r_0$ and two different shapes for the imaginary potential inside a radius $R^{*}$. These forms, motivated by bag models, are a one-gluon-annihilation potential and a simple geometric-overlap form. In both cases there are three adjustable parameters: the effective bag radius $R^{*}$, the effective strong coupling constant ${{\alpha }_s}^{*}$, and $r_0$. There is also a choice for the form of the real potential inside the cutoff radius $r_0$. Analysis of the $p\overline{p}$ scattering data in the laboratory-momentum region 0.4-0.7 GeV/c yields an effective nucleon bag radius $R^{*}$ in the range 0.6-1.1 fm, with the best fit obtained for $R^{*}=0.86\mathrm{}$ fm. Arguments are presented that the deduced value of $R^{*}$ is likely to be an upper bound on the isolated nucleon bag radius. The present results are consistent with the range of bag radii in current bag models. We have also used the resultant optical potential to calculate the shifts and widths of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ atomic bound states of the $p\overline{p}$ system. For both states we find upward (repulsive) shifts and widths of about 1 keV. We find no evidence for narrow, strongly bound $p\overline{p}$ states in our potential model.