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 ($\mathrm{\Omega }$) is as follows.

$\frac{d^2\sigma (p+A\to {\pi }^{+}+X)}{dpd\mathrm{\Omega }}(p,\theta )=$ $c_1{p}^{c_2}(1-\frac{p}{p_{beam}})\exp [-c_3\frac{p^{c_4}}{p_{beam}^{c_5}}-c_6\theta (p-c_7{p}_{beam}(\cos \theta {)}^{c_8})]$

Where p and $\theta$ are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers $c_1\dots c_8$ 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• J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished)