2919.sagews

R=10*10^-9
NXe=50000
rho=54*NXe*3/(4*pi*R^3)
wavelength=1.5*10^-10
distance=1.0
Nph=10^12;
A=10^-12;

k,r=var('k,r')
assume(k>0)
k=real(k)
assume(r>0)
f=integral(4*pi*R^2*rho*sin(k*r)/(k*r), r,0, R)

"structure factor of the cluster: (integral evaluated outside the program)"

'structure factor of the cluster: (integral evaluated outside the program)'

f=8.1*10^6/R^3*(sin(R*k)-R*k*cos(R*k))/k^3

plot(f^2, 0, 5*2*pi/R)

"Thomson scattering cross section:"
    "sigma=re^2*((1+cos(2*theta))/2)*f^2"

'Thomson scattering cross section:'

epsilon0=8.85*10^-12;
q=1.6*10^-19;
m=9.91*10^-31;
c=3*10^8;
re=2.8*10^-15;
sigma=re^2*f^2

plot(sigma, 0, 5*2*pi/R)

ph_dens=Nph/A
px_A=(75*10^-6)^2
scattered_ph=sigma*ph_dens*solid_angle
k=var('k')
sc_angle=180/pi*2*asin(k*wavelength/(4*pi))
solid_angle=px_A/(4*pi*distance^2)*cos(sc_angle/180*pi)

import pylab
p=plot(scattered_ph,  0, 5*2*pi/R)

"photons per Pixel assuming constant solid angle for Pixel of px_A/L^2"

'photons per Pixel assuming constant solid angle for Pixel of px_A/L^2'

p

"detector_coverage"

'detector_coverage'

import numpy
detc_cov=numpy.arange(180/pi*atan((80*75*10^-6)/distance), 180/pi*atan(((80+512)*75*10^-6)/distance), 180/pi*atan((75*10^-6)/distance))

import numpy
pylab.clf()
pylab.plot([float(n(sc_angle(float(rr)))) for rr in numpy.arange(10^7,3*10^9, 10^7)], [float(n(scattered_ph(float(kk)))) for kk in numpy.arange(10^7,3*10^9, 10^7)])
pylab.plot([n(xx) for xx in detc_cov], 0.01*numpy.ones(len(detc_cov)))
pylab.gca().set_yscale('log')
pylab.savefig("voellig_egal")

[float(n(sc_angle(float(rr)))) for rr in numpy.arange(10^7,10^9, 10^7)]

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