Asymptotic form factors of hadrons and nuclei and the continuity of particle and nuclear dynamics

The large-q² behavior of the elastic form factor of a hadron or nucleus is related by dimensional counting to the number of its elementary constituents. Using the framework of a scale-invariant quark model, dimensional-scaling predictions are derived for the B(q²)A(q²) ratio in the Rosenbluth formula, multiple-photonexchange corrections, and the mass parameters which control the onset of the asymptotic power law in the meson, nucleon, and deuteron form factors. A simple "democratic chain" model predicts that for large q², F(q²)∝(1-q²mₙ²)^1-n, where mₙ² is proportional to the number of constituents n. In the case of nuclear targets (or systems with several scales of compositeness), we also define the "reduced" form factor fA(q²)=FA(q²)Πi=1A[Fᵢ(qᵢ²)] in order to remove the minimal falloff of FA due to the nucleon form factors at qᵢ²=(mᵢ²MA²)q². Dimensional counting predicts (q²)^A-1fA(q²)→const. A systematic comparison of the data for π, p, n, and deuteron form factors with the dimensional-scaling quark-model predictions is given. Predictions are made for the large-spacelike-q² ³He and α-particle form factors. We also relate the deuteron form factor to (off-shell) fixed-angle n-p scattering, and show that the experimental results for t⁵Fd(t) are consistent with the magnitude of the s-wave wave function u^'(0) obtained from soft-core potentials. The relation of the dynamics of an underlying six-quark state of the deuteron to the nucleon-potential and meson-exchange-current contributions is discussed. The scaling of q²fd(q²) implies that the nuclear potential (after removing the effects of nucleon structure) displays the scale-invariant behavior of a theory without a fundamental length scale. Predictions are also given for the structure functions, fragmentation, and large-angle scattering of a nucleus.