In [11]:

    

import matplotlib
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rc
rc('text', usetex=True)

def binomial(n, k):
    uvector = np.array(range(k+1, n+1))
    lvector = np.array(range(1, n-k+1))
    
    return np.e**(np.log(uvector).sum() - np.log(lvector).sum())


    

In [14]:

    

he4 = (2, 2)
c12 = (6,6)
o16 = (8,8)
ca40 = (20,20)
nuclei = [he4, c12, o16, ca40]
labels = [r"${}^4$He", r"${}^{12}$C", r"${}^{16}$O", r"${}^{40}$Ca"]

x = range(1, 201)


    

In [16]:

    

for label, nucleus in zip(labels, nuclei):
    p = np.array([binomial(n, nucleus[0]) for n in x])
    n = p = np.array([binomial(n, nucleus[1]) for n in x])
    y = p*n
    plt.plot(x, y, linewidth=2, label=label)
plt.xlabel('Number of single particle states', fontsize=18)
plt.ylabel('Number of Slater determinants', fontsize=18)
plt.legend(loc=2)
plt.tight_layout()
plt.yscale('log')
plt.savefig("slater_determinants.pdf")
plt.show()


    

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