#! /usr/bin/env python
#! /usr/bin/env python

# plot2.py
#
# Example python program introducing the use 
# of the matplotlib module.
#
# Paul Eugenio
# PHZ4151C
# Jan 28, 2019
#

import matplotlib.pyplot as plt 
plt.rc('text', usetex=True)     # needed for Latex formatting of figure lables

import numpy as np

def cross_section(t):
    """"  
    The transverse four-momentum scattering cross section:  t * exp(-t)
    """
    return t**2 * np.exp(-t)


# Generate an array of values to plot
#
x = np.linspace(0,10,101)
y = cross_section(x)



#
# Plotting Routines
#
plt.plot(x,y)

# figure dressing
plt.legend([r"$d\sigma/dt = t^2 e^{-t}$"])
plt.title("Scattering Probability")
plt.xlabel("t")
plt.ylabel(r"$d\sigma/dt$")

# Figure is saved as a png image and displayed in an X window.
plt.savefig("sigma-t.png")
plt.show()