Sanford–Wang parameterisation

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.

${\frac {d^{2}\sigma (p+A\rightarrow \pi ^{+}+X)}{dpd\Omega }}(p,\theta )=$ $c_{1}p^{c_{2}}\left(1-{\frac {p}{p_{beam}}}\right)\exp \left[-c_{3}{\frac {p^{c_{4}}}{p_{beam}^{c_{5}}}}-c_{6}\theta (p-c_{7}p_{beam}(\cos \theta )^{c_{8}})\right]$

Where p and $\theta$ 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• J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished)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. (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:10.1103/physrevlett.25.1068. ISSN 0031-9007.
• Wang, C. L. (1970-11-23). "Errata: Pion, Kaon, and Antiproton Production between 10 and 70 BeV". Physical Review Letters. 25 (21). American Physical Society (APS): 1536. doi:10.1103/physrevlett.25.1536. ISSN 0031-9007.