import matplotlib.pyplot as plt
import numpy as np
import math

# Rutherford cross section
def cross_section():
    thetas = np.linspace(0.1, math.pi, 100)
    sigmas = 1/(np.sin(thetas/2) ** 4)
    thetas = np.degrees(theta) for theta in thetas
    return (thetas, sigmas)

thetas, sigmas = cross_section()
fig, ax1 = plt.subplots()

color = 'tab:red'
ax1.set_xlabel('scattering angle (degrees)')
ax1.set_ylabel('cross section', color=color)
ax1.plot(thetas, sigmas, color=color)
ax1.tick_params(axis='y', labelcolor=color)

ax2 = ax1.twinx()  # instantiate a second Axes that shares the same x-axis

color = 'tab:blue'
ax2.set_ylabel('10000x', color=color)  # we already handled the x-label with ax1
# Drop large values at beginning and let auto-scaling redraw it larger.
ax2.plot(thetas-69:], sigmas-69:], color=color)
ax2.tick_params(axis='y', labelcolor=color)

fig.tight_layout()  # otherwise the right y-label is slightly clipped

plt.text(100, 10, "$1/\sin^4(\Theta/2)$", fontsize='x-large')
fig.savefig("RutherfordCrosssection2Scales.png")
plt.show()