The GEANT 3.21 program package allows to calculate the bremsstrahlung photon yields in electron-nucleus interactions [1] but not secondary reactions induced by photons like (g,n). In order to calculate the activation of different dump materials (e.g. C, Al, Cu, Cr, Ni, Mn, Fe) by such processes a special procedure explained in the following has been performed. In these calculations the corresponding (g,n)-cross sections are required. Most of these data are available in [2,3], the cross section of iron was taken from [4]. The saturation activity of a given radioactive nucleus is calculated by

where I is the beam current and N_Z is the number of stable nuclei in the probe irradiated by the photon fluence F_g. In a first approximation, the fluence F_g was calculated as the number of photons per energy bin which transmit the surface of the considered probe. The known half-life of the isotope allows to calculate the activity N(t) at a given time.

Furthermore, activation by radiative capture of the complementary produced neutrons has also been taken into account by using the (n,g) cross section data from [9]. The calculation of the neutron production in the graphite core of the beam dump are based on simulations with the MCNP program package ([5]), which were found to be in agreement with estimates in [6]. The obtained neutron yield was transformed into an energy spectrum (Watt distribution)

The parameters a and b were obtained from fits to the photoneutron spectra of C, Cr and Au reported in [7].

Additionally, the production rate of radioactive nuclei induced by the radiative neutron capture was calculated in analogy to equation (1), where F_g(E_g), s_g,n(E_g) and dE_g were replaced by F_n(E_n), s_n,g(E_n) and dE_n, respectively.

We considered the activity of ⁶⁰Co which is assumed to be produced in the energy domain of the ELBE accelerator mainly via the reaction ⁶³Cu(n,a)⁶⁰Co by photoneutrons. In the calculations we used cross sections available in [8,9]. A saturation activity of about 2.1 · 10¹² Bq is expected for the 2 cm thick copper coating provided for cooling of the beam dump core as presented in [1]. The production of ²⁴Na in the reaction ²⁷Al(n,a)²⁴Na calculated by the same method yields a similar activity.
A complete representation of the results is given in [10].

References

[1] B. Naumann et al., A Possible Beam Dump Design for Intense Electron Beams, this Report p. 36

[2] S. S. Dietrich and B. L. Berman, Atomic and Nuclear Data Tables, 38 (1988) 199.

[3] EXFOR Data basis, http://www.nea.fr./html/dbdata/x4.

[4] S. Costa et al., Nuovo Cimento 51B (1967) 199.

[5] H. Kumpf, FZR Internal report, Institute of Safety Research, 17.6.1998.

[6] W. P. Swanson , IAEA Technical Reports Series No.188, Vienna 1979.

[7] M. Barbier, Induced Radiactivity, North Holland Publishing Company, Amsterdam 1969.

[8] P. Jessen et al., Nuclear Data A1 (1966) 103.

[9] ENDF (evaluated nuclear data files) of the NDS online Data Service,
http://www-nds.iaea.org/.

[10] B. Naumann, W. Neubert and D. Pröhl, FZR Report FZR-267, Juli 1999.  IKH 10/25/99 © B. Naumann