Calculation of radiation yield

The number of photons per MeV per incident electron per [math]\displaystyle{ g/cm^2 }[/math] of radiator (Z,A) is given by [*]:

[math]\displaystyle{ \frac{d^2n}{d\kappa dt} = \frac{3.495 \times 10^{-4}}{A\kappa}[Z^2\Phi_n(Z,E_0,k)+Z\Phi_e(Z,E_0,k)](MeV^{-1}g^{-1}cm^2) }[/math],

where [math]\displaystyle{ \kappa }[/math] - photon kinetic energy in MeV;

[math]\displaystyle{ E_0 }[/math] - incident electron total energy (in units of the electron rest mass);

[math]\displaystyle{ k }[/math] - incident photon energy (in units of the electron rest mass);

[math]\displaystyle{ \Phi_e(Z,E_0,k) = C_B\{2[1-\frac{2E}{3E_0}+(\frac{E}{E})^2][L-\sqrt{\eta}]+\sqrt{\eta}[1-\frac{L^2}{2\rho}-\frac{1}{\rho^2}(\frac{1}{2}L-[\frac{\rho(\rho+2)(E_0+1)}{E_0-1}]^{\frac{1}{2}})^2]\} }[/math];

[math]\displaystyle{ E = E_0 - k }[/math];

[math]\displaystyle{ \rho = E_0 -k(1+E_0-\sqrt{E^2 - 1}) }[/math];

[math]\displaystyle{ \eta = \rho/(\rho+2) }[/math];

[math]\displaystyle{ L = 2 ln(\frac{(E_0-1)^{\frac{1}{2}}+[\eta(E_0+1)^{\frac{1}{2}}]}{(E_0-1)^{\frac{1}{2}}-[\eta(E_0+1)^{\frac{1}{2}}]}) }[/math];

[math]\displaystyle{ C_B = \frac{\frac{1}{4}\psi(\varepsilon)-1-lnZ^{\frac{2}{3}}}{3.798-ln\varepsilon-lnZ^{\frac{2}{3}}} }[/math], for \varepsilon \geq 0.88 the screening effect is negligible and hence C_B = 1.