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Chapter 10
Bounds on short-range correlations

The probability of finding two constituents at the same position enters into the calculation of many properties of composite systems. This is the case for the hyperfine splittings in atoms, molecules, mesons or baryons, when one uses spin–spin forces of Breit–Fermi type, which have zero range. One may also mention some production rates or decay widths. In this section, we review some properties [100, 101, 98] of the matrix elements

⟨ ⟩ δij ≡ Φ | δ(3)(rij) | Φ .
(10.1)

We already mentioned that, in the two–body case, the Schwinger rule (2.11), which can be rewritten as 4πδ12 = μ ′ ⟨V (r)⟩, is very useful for constraining δ 12 or for computing it in a reliable way. Its generalization to the three-body case will lead to upper limits on δ12 for symmetric baryons.

 10.1 Generalized Schwinger rule
 10.2 The case of linear confinement
 10.3 Correlations for more general potentials

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