The branching ratio R for the photoproduction of neutral soliton-antisoliton pairs (S°S-°) versus charged pairs (S+/-S-/+) is calculated for pristine trans polyacetylene. Within the SSH model, we find R vanishes in the adiabatic approximation as a consequence of inversion symmetry (parity) and the Pauli principle. If one includes nonadiabatic effects, we prove that R remains zero at least to second order in the electron-phonon interaction as a consequence of charge conjugation symmetry. Thus, neutral SS- photoproduction is strongly suppressed in (CH)x, in agreement with experiments by Flood, et al