Evaluation of Scattering Coefficient for Maze Calculation

The calculation of the leakage radiation though the maze requires the determination of the scattering coefficient for the bremsstrahlung incident on the first scattering surface. To evaluate the reflection coefficient we need the incident gamma-ray energy, which we take here to be the average photon energy at 90° in the Bremsstrahlung spectrum from incident E_o = 230 MeV electrons, which was obtained by Blumberg and Perlman [16] from integration of the Bremsstrahlung cross-section given by Bethe and Ashkin [17].

The photon energy spectrum is:

(1)

and the average photon energy in the spectrum is:

(2)

which is evaluated to give:

(3)

with y = E_min/E_o.

It is necessary to provide a low energy cut-off E_min in the integration The value of <E_g> is somewhat sensitive to the choice of E_min. For present purposes we look at the absorption coefficients m_x at low photon energy given by Bethe and Ashkin [17] and reproduced here as Figure 14. For Cu the coefficient is rising rapidly below E_g» 0.5 (mc²) and it seems reasonable to take E_min » 0.2 (mc²) » 0.1 MeV where the photons will be appreciably attenuated in the 0.11 cm steel vacuum pipe wall. Evaluating Eq. 8 for this choice of E_min [18] and, for an effective electron energy of 100 MeV as given in Figure 15 for 90° bremsstrahlung, results in an average photon energy of <Eg> » 12 MeV. This energy is beyond the range of Figure 6 and we make an extrapolation to obtain a₁ ~ 2.3x10^-3 for normal incidence on concrete.

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