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 (p) and solid angle (Ω {\displaystyle \Omega }) is as follows.

d 2 σ ( p + A → π + + X ) d p d Ω ( p , θ ) = {\displaystyle {\frac {d^{2}\sigma (p+A\rightarrow \pi ^{+}+X)}{dpd\Omega }}(p,\theta )=} c 1 p c 2 ( 1 − p p b e a m ) exp ⁡ [ − c 3 p c 4 p b e a m c 5 − c 6 θ ( p − c 7 p b e a m ( cos ⁡ θ ) c 8 ) ] {\displaystyle c_{1}p^{c_{2}}\left(1-{\frac {p}{p_{beam}}}\right)\exp \left[-c_{3}{\frac {p^{c_{4}}}{p_{beam}^{c_{5}}}}-c_{6}\theta (p-c_{7}p_{beam}(\cos \theta )^{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.

  • J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished)
  • Wang, C. L. (1970-10-12). "Pion, Kaon, and Antiproton Production Between 10 and 70 BeV". Physical Review Letters. 25 (15). American Physical Society (APS): 1068–1072. doi:. ISSN .
  • Wang, C. L. (1970-11-23). . Physical Review Letters. 25 (21). American Physical Society (APS): 1536. doi:. ISSN .