Asymptotic form factors of hadrons and nuclei and the continuity of particle and nuclear dynamics. [Scale-invariant quark model, dimensional scaling predictions, democratic chain model]
The large-q/sup 2/ behavior of the elastic form factor of a hadron or nucleus is related by dimensional counting to the number of its elementary constituents. Dimensional-scaling predictions are derived for the B (q/sup 2/)/A (q/sup 2/) ratio in the Rosenbluth formula, multiple-photon-exchange 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 q/sup 2/, F (q/sup 2/) proportional (1 - q/sup 2//m/sub n/ /sup 2/)/sup 1 -//sup n/, where m/sub n/ /sup 2/ 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 f/sub A/(q/sup 2/) = F/sub A/(q/sup 2/)/Pi/sup A//sub i//sub 1/F/sub i/(q/sub i/ /sup 2/) in order to remove the minimal falloff of F/sub A/ due to the nucleon form factors at q/sub i/ /sup 2/ = (m/sub i/ /sup 2//M/sub A/ /sup 2/) q/sup 2/. Dimensional counting predicts (q/sup 2/)/sup A/sup -1//f/sub A/(q/sup 2/) ..-->.. const. A systematic comparison of the data for ..pi.., p, n, and deuteron form factors with the dimensional-scaling quark-model predictions is given. Predictions are made for the large-spacelike-q/sup 2/ /sup 3/He and ..cap alpha..-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 t/sup 5/F/sub d/(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 q/sup 2/f/sub d/(q/sup 2/) 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. (AIP)
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- OSTI ID:
- 7323483
- Journal Information:
- Phys. Rev., D; (United States), Vol. 14:11
- Country of Publication:
- United States
- Language:
- English
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ALPHA PARTICLES
FORM FACTORS
DEUTERONS
HELIUM 3
NEUTRONS
NUCLEI
STRUCTURE FUNCTIONS
PIONS
PROTONS
QUARK MODEL
ASYMPTOTIC SOLUTIONS
DIMENSIONS
ELASTIC SCATTERING
EXCHANGE INTERACTIONS
NUCLEAR POTENTIAL
NUCLEAR REACTIONS
PERTURBATION THEORY
RELATIVISTIC RANGE
SCALE INVARIANCE
SCATTERING
WAVE FUNCTIONS
BARYONS
BOSONS
CHARGED PARTICLES
COMPOSITE MODELS
ELEMENTARY PARTICLES
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EVEN-ODD NUCLEI
FERMIONS
FUNCTIONS
HADRONS
HELIUM ISOTOPES
INTERACTIONS
INVARIANCE PRINCIPLES
ISOTOPES
LIGHT NUCLEI
MATHEMATICAL MODELS
MESONS
NUCLEONS
PARTICLE MODELS
PARTICLE PROPERTIES
PSEUDOSCALAR MESONS
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