A fun little man of rutherford scattering

So I coded up rutherford scattering in a real dumb way (you can significantly reduce your considerations by using symmetry and stuff).

I sort of monte carlo it with gaussian distributed initial conditions

import numpy as np
from scipy import integrate

z0 = -20.0
samples = 100
E=.5
t = np.linspace(0,50,100)


def F(x):
    return .1 * x / np.linalg.norm(x)**1.5

def D(x,t):
    return np.concatenate((x[3:],F(x[0:3])))



import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')



def update(E):
    ax.set_title('E='+str(E))
    for i in range(samples):
        initxy = 5*np.random.randn(2)
        init = np.append(initxy,[z0, 0., 0., np.sqrt(E)])
        sol = integrate.odeint(D, init, t)
        ax.plot(sol[:,0], sol[:,1],sol[:,2])
update(E)

plt.show()

The bundles that come off look pretty cool

rutherford

Lots that one could do with this. Compare the outgoing distribution to the formula, Try to discern shape of other potentials. Do a little statistics to see if charge or whatever can be determined from the data.

Show center of mass scattering. Try 4 particle scattering.

I guess I’m trying to play around in some high energy concepts.

 

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