7.3 Program Details and Applications
107
Fig. 7.4 Coulomb scattering
k = 2, η = 1. Visualization of
the absolute value of ψ(r, z),
Eq. (7.16), for r = 100
1
-1
-1
-0.5
0
0
0.5
1
0
z
1 -1
The syntax is [obj, result] = coulombwave(wsp,l,gamma,
rho,k). To evaluate the functions based on parameterization (a), Eq. (7.4), “wsp”
could have the values “Fl,” “Hl+,” “Hl-,” and “Gl” (the names speaks for itself) and
for parameterization (b), Eq. (7.5), “fl2” and “hl2” for the functions f l ((, ζ ) and
h l ((, ζ ). (The 2 in the variable name is added to avoid erroneous evaluations due
to a typos.) “l” is the angular momentum and has to be a scalar value, as well as
“gamma,” given by the charge of the point particles scaled with the wave number
for parameterization (a) and equals for parameterization (b). For parameterization
(a), “rho” is either the scaled radial coordinate (kr) or the radial coordinate r in case
the optional input parameter “k” (wave number) is added. For parameterization (b),
“rho” is the coordinate ζ . “rho” could be an arbitrary array.
Example
gamma = 1;
l = 2;
k = 1;
r = linspace(1,20);
[obj, result] = coulombwave(’Fl’,l,gamma,r,k);
The object “obj” has the properties:
– “value,” the value of the Coulomb wave function at position “r,”
– the input variables “l” and “gamma,”
– “rho” the scaled radial coordinate kr, respectively, ζ ,
– the input variable “k” if existent.
– “rhotp,” the turning point of rho or zeta. For parameterization (a),
rhotp = γ +
γ 2 + l(l + 1),
(7.19a)