The summing of all pion bubble graphs in the computation of the $\sigma$-meson propagator leads to the appearance of ghost poles when $\sigma \pi \pi$ coupling strengths are equivalent to $\sigma$-meson decay widths greater than 625.2 MeV. A result satisfying dispersion relations is obtained by the direct subtraction of the ghost pole from the results published previously by this author. The effect is to decrease the sensitivity to the $\sigma$-meson width of both the central and spin-orbit nucleon-nucleon potentials. The potentials are small for separations greater than half a pion Compton wavelength and decrease in magnitude with increasing width. Larger widths are more compatible with phenomenological and dispersion-theory potentials.

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