Radiation Damage Kinetics in Pwo Crystals

This note proposed a model to describe the kinetics of the irradiation damage in PWO crystal and apply it to two well-known measurement methods of the optical transmission damaged by irradiation. 1 . Introduction It is known that in some PWO crystals damage to their optical properties appears under ionizing radiation. A decrease of the optical transmission and then of light yield has been detected. We have determined that the level of damage strongly depends on the peculiarities of the crystal growth technology. However, the magnitude varies from crystal to crystal even for crystals grown from purified raw materials. This suggests the existence of several contributors to the damage process which are mainly structural defects. The amount of such defects is influenced by even small technological changes. Although the origin of these defects may differ, they can be characterized by some universal set of parameters which describes their kinetics under irradiation. Thus motivated, we have analysed within a phenomenological model the transmission radiation damage in the PWO crystals. The model does not include detailed background about peculiarities of free carriers capture under irradiation and recovery mechanisms of the damage centres. However, the model describes well the kinetics of the damage and gives the values of the parameters needed to estimate the level and the relative influence of different damage centres in the crystals. Using this model we describe and analyse here two well-known measurement methods of the transmission damage by irradiation. A similar approach has already been used by others [1] to analyse optical bleaching in BaF2 crystals, but in this case transmission and light output damage were not dependent on dose rate. 2 . The model Radiation damage in the crystals appears to be due to a charge-state change of the existing point structure defects. This means that creation of new defects due to inelastic scattering of damaging particles is negligible and that the concentration of impurities is considerably smaller than the amount of host defects. The radiation damage process is therefore driven by the change of the defects' electronic states which is at the origin of production of colour centres and the creation or suppression of their associated absorption bands. Let us suppose that the defects are randomly distributed in the crystal, that the interaction between them is negligible, and that the amount of each type of defect i is limited and considerably smaller than the amount of the lattice atoms. In this case the radiation damage will reach a saturation level after a certain time which is determined by the amount of pre-existing defects. Thus, the amount of damaged centres of type i is described by the following differential equation: dNi dt i Ni S di Ni Ni = − + − ω ( * ) , (1) where Ni is the amount of damaged centres of type i at the time t, ωi is the recovery rate of damaged centres of type i , S is the rate of irradiation, Ni * is the amount of pre-existing defects of type i , and di is the damage constant of the mentioned centres which depends on the capture cross-section of free carriers by the centres of type i. Summing all types of centres we get the following equation: dN dt i N i S 1 d i (N i * N i ) i = − + − ∑ ∑ i ω , (2) where N = N i i ∑ is the total amount of different types of damaged centres. Precise processing of the equation requires the values of the constants ωi, i * N , di but the simultaneous determination is rather difficult and a practical solution can only be reached through approximations.