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from numpy import *

def f(er):
      '''from 1707.01632 and the corresponding Ancillary files'''
      z=32.
      epsilon=11.5e0*er*z**(-7./3.)
      g=3.*epsilon**0.15+0.7*epsilon**0.6+epsilon
      k=0.157e0
      y=k*g/(1.e0+k*g)
      epsilon_gamma=3.e0 #average energy to create electron-hole pair
      ev=70.e0 #applied potential difference time elementary charge (in eV)
      return (1.+y*ev/epsilon_gamma)/(1.+ev/epsilon_gamma)