Physics: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 → [math]\displaystyle{ \pi^+ }[/math]+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 ([math]\displaystyle{ \Omega }[/math]) is as follows.
[math]\displaystyle{ \frac{d^2\sigma(p+A\rightarrow \pi^+ + X)}{dpd\Omega}(p,\theta) = }[/math] [math]\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] }[/math]
Where p and [math]\displaystyle{ \theta }[/math] are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers [math]\displaystyle{ c_1\ldots c_8 }[/math] 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- J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished)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 (American Physical Society (APS)) 25 (15): 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 (American Physical Society (APS)) 25 (21): 1536. doi:10.1103/physrevlett.25.1536. ISSN 0031-9007.
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