Sanford-Wang parameterisation

The Sanford-Wang parameterisation is a 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^2sigma(p+A\; ightarrow\; pi^+\; +\; X)\}\{dpdOmega\}(p,\; heta)\; =$$c\_1\; p^\{c\_2\}\; left(1-frac\{p\}\{p\_\{beam\; ight)expleft\; [-c\_3frac\{p^\{c\_4\{p\_\{beam\}^\{c\_5-c\_6\; heta(p-c\_7\; p\_\{beam\}\; (cos\; heta)^\{c\_8\})\; ight]$

Where p and $heta$ are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers $c\_1ldots\; c\_8$ 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* J. R. Sanford and C. L. Wang, Brookhaven National Laboratory, AGS internal report, 1967 (unpublished); C. L. Wang, Phys. Rev. Letters 25, 1068 (1970); ibid. 25, 1536(E) (1970).