import numpy as np

def P(r,rc,Z):
	return Z*np.exp(-r/rc)

P=np.vectorize(P)

def Pa(r,Za=4.8*10.**8.):
	#Za=4.8*10.**8.
	a=1.05*10.**-10.
	return P(r,a,Za)

Pa=np.vectorize(Pa)

def Pf(r,Zf=7.6*10.**10.):
	#Zf=7.6*10.**10.
	f=1.64*10.**-10.
	return P(r,f,Zf)
Pf=np.vectorize(Pf)