Sanford–Wang parameterisation explained

The Sanford–Wang parameterisation is an empirical formula used to model the production of pions in nuclear interaction of the form p+A →

\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 (

\Omega ) is as follows.(d ^{2\sigma(p+A →} \pi ^{+} + X))/(dpd\Omega) (p,\theta) = c _{1} p ^{c _{2}} \left( 1- (p)/(p _{beam}) \right)\exp\left[ - c _{3 (p ^{c _{4}})/(p ^{c _{5}} _{beam})} - c _{6\theta(p-c} _{7} p _{beam} (\cos\theta) ^{c _{8}} )\right]

Where p and

\theta are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers c _{1\ldots} c _{8} are the Sanford-Wang parameters and are typically varied to give a good fit with experimental data.

References

• J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished)
• Wang . C. L. . Pion, Kaon, and Antiproton Production Between 10 and 70 BeV . Physical Review Letters . American Physical Society (APS) . 25 . 15 . 1970-10-12 . 0031-9007 . 10.1103/physrevlett.25.1068 . 1068–1072.
• Wang . C. L. . Errata: Pion, Kaon, and Antiproton Production between 10 and 70 BeV . Physical Review Letters . American Physical Society (APS) . 25 . 21 . 1970-11-23 . 0031-9007 . 10.1103/physrevlett.25.1536 . 1536. free .