Evaluation of gamma-ray transmission through rectangular collimator slits for application in nuclear fuel spectrometry

Gamma-ray spectrometry is widely applied in several science fields, and in particular in non-destructive gamma scanning and gamma emission tomography of irradiated nuclear fuel. Often, a collimator is used in the experimental setup, to selectively interrogate a region of interest in the fuel. For the optimization of instrument design, as well as for planning measurement campaigns, predictive models for the transmitted gamma-ray intensity through the collimator are needed. Commonly, Monte Carlo radiation transport tools are used for accurate prediction of gamma-ray transport, however, the long computation time requirements when used in low-efficiency experimental setups present challenges. In this work, the full-energy peak intensity transmitted through a rectangular collimator slit was examined. A uniform planar surface source emitting isotropically was considered, and the rate of photons reaching an ideal counter plane on the opposite side of the collimator was evaluated by analytical integration. To find a closed-form primitive function, some idealizations were required, and thereby parametric models were obtained for the optical field of view, dependent on slit dimensions (length, height and width) and source-to-collimator distance. It was shown that the count rate in the detector is independent of the collimator-to-source distance. For contributions from outside the optical field of view, where a closed-form expression cannot be found, instead fast numerical integration methods were proposed. The results were validated using the Monte Carlo code MCNP6.2. For the analytical method, deviations were larger, the shorter the collimator, with up to 25% of underestimation obtained for the shortest examined collimator of 10 cm length. However, the longer the collimator, the better the observed agreement. This accuracy is deemed to be sufficient for instrument design and measurement planning, where often the order of magnitude of the count rate is not a priori known. For the numerical method, the results showed an agreement within 3% for all evaluated collimator settings. The methods are planned for use in iterative optimization routines in the design of Gamma Emission Tomography devices, as well as for the prediction of gamma spectra obtained in the planning of fuel inspections. An application of the proposed method was demonstrated in spectrum prediction for a short cooling-time fuel rod test from the Halden reactor.