The Sanford-Wang parameterisation is an empirical formula used to model the production of pions in nuclear interaction of the form p+A →
π
+
+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 (
Ω
) is as follows.
d
2
σ
(
p
+
A
→
π
+
+
X
)
d
p
d
Ω
(
p
,
θ
)
=
c
1
p
c
2
(
1
−
p
p
b
e
a
m
)
exp
[
−
c
3
p
c
4
p
b
e
a
m
c
5
−
c
6
θ
(
p
−
c
7
p
b
e
a
m
(
cos
θ
)
c
8
)
]
Where p and
θ
are the momentum of the outgoing pion and its angle from the direction of the incident proton. The numbers
c
1
…
c
8
are the Sanford-Wang parameters and are typically varied to give a good fit with experimental data.
