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The Sanford-Wang parameterisation is an empirical formula used to model the production of pions in nuclear interaction of the form p+A → π + {\displaystyle \pi ^{+}} +X where a beam of high-energy protons hit a material.
Its formula for the double-differential cross section with respect to momentum and solid angle is as follows.
d 2 σ d p d Ω = {\displaystyle {\frac {d^{2}\sigma }{dpd\Omega }}=} c 1 p c 2 exp c 8 ] ] {\displaystyle c_{1}p^{c_{2}}\left\exp \left^{c_{8}}]\right]}
Where p and θ {\displaystyle \theta } are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers c 1 … c 8 {\displaystyle c_{1}\ldots c_{8}} are the Sanford-Wang parameters and are typically varied to give a good fit with experimental data.