#! /usr/bin/env python

# plot3.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)  

import numpy as np


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



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

# Plot data and set plot for multiple plot overlays
plt.plot(x,y)
#plt.hold(True) 

# Generate additional data and plot
b = 1
y = cross_section(x,b)
plt.plot(x,y)

# Dress up figure
plt.legend(["\sigma(t,0) = t^2 e^{-t}", "\sigma(t,1) = (t-1)^2 e^{-t}"])
plt.title("Scattering Probability")
plt.xlabel("t")
plt.ylabel("\sigma(t,b)")

plt.show()