Study of the NaI(Tl) efficiency by Monte Carlo method

The Sodium Iodide detector NaI(Tl) presents a great efficiency for gamma-photon and the X-ray detection. The purpose of the present work is to study this efficiency versus different parameters that are related to the detection phenomenon. This has been achieved by using both analytical method and Monte Carlo simulation which give the same results. We have found that the intrinsic efficiency has a minimum at d/R approximately 0.7 (d is the source-NaI(Tl) distance and R is the NaI(Tl) radius). In order to explain this minima we have used the Dirac theory for the mean chord 1 of photons in the NaI(Tl) crystal and we have determined asymptotic limits of the efficiency corresponding to the following asymptotic limits of the mean chord: 1 = L (L: NaI(Tl) length) for large d/R and 1 = 4/3R for small d/R for point source. For distributed source (disk) the minimum is less pronounced and the asymptotic limit of the intrinsic efficiency is less than for the punctual source for small d/R while they are the same for large d/R. The total efficiency falls down at the d/R ratio corresponding to the minimum of the gamma-photons mean chord in the NaI(Tl) crystal so for a good photon detection we have shown that the source detector distance must respect the inequality: d/R < 0.01.

Convergence acceleration of neutronic Monte Carlo calculations

Often neutrons are produced in nuclear reactors with high energies, but they are needed at low energies for uses like activation analysis and neutron capture therapy. The evaluation of the slowed down neutron amount by using the Monte Carlo method is very expensive in computation time and the variance is large for natural simulation. In order to reduce the variance and the computation time, we used two biasing techniques to accelerate the calculation convergence. We have used the adjoint flux in the considered system as an importance function in the neutron slowing down equation. In this study, we have considered a homogeneous medium that contains a mixture of U238 (absorber) and hydrogen (scatterer). By handling the adjoint slowing down equation, we have used an analytical approximation of the fine structure of the adjoint flux, as a neutron importance function in the Monte Carlo simulation, for selecting the nuclide with which neutrons interact during their slowing down without absorption. For the second method, we modified the neutron slowing down equation by multiplying it by the adjoint flux. This allowed us to select neutron energies after collision and to avoid the energies corresponding to the absorption resonance. In fact, this was accomplished by assigning an appropriate statistical weight to the neutron, since its birth. For the two methods, a correction in the statistical weight was made after each neutron collision and a Fortran program was used to perform these calculations.

On the neutrons streaming in straight duct

The main aim of this study is to evaluate the thermal neutron streaming through a straight cylindrical duct by using the Monte Carlo method and evaluating the neutron reflection by the duct wall to the total flux at the exit of the duct. The duct walls are made separately of iron and aluminum. We have considered 10 groups of energy between 10(-5) and 10 eV. For a point source at the mouth of the duct, we have determined the direct and the reflected part of the total thermal neutron flux at the exit of the duct for different lengths and different radii of the duct. For a punctual source, we have found that the major contribution to the total flux of neutrons at the exit is due to the neutron reflection by walls, and the reflection contribution decreases when the neutron energy decreases. For a constant length of the duct, the reflected part decreases when the duct radius increases, while for the disk shaped source, we have found the opposite phenomenon. The transmitted neutron flux distribution at the exit of the duct is determined for a disk shaped source for different neutron energies and different distances from the exit center.

The vacuum geometry effect on neutron transmission and spatial resolution of neutron transmission.

Frequently, shields used against radiation contain some vacuum channels. We have therefore considered an infinite slab with a fixed thickness (thickness 20 lambda with lambda the mean free path of the neutron in the slab) and an infinite plane source of neutrons which arrived on the left side of the slab; transmitted neutrons through the slab to its right side are detected by finite detectors having windows equal to 2 lambda. This slab contains a vacuum channel. This channel has many legs with several horizontal parts. We used the Monte Carlo method for sampling the neutron history in the slab with a spatial biasing technique in order to accelerate the calculation convergence (Levitt, L. B. (1968) Nuclear Science and Engineering 31, 500-504; Jehouani, A., Ghassoun, J. and Aboubker, A. (1994) In Proceedings of 6th International Symposium on Radiation Physics, Rabat, Morocco). We studied the effects of the angle position and the number of horizontal parts of the channel on the neutron transmission. We have studied the effect of the vacuum channel opening (Artigas, R. and Hungerford, H. E. (1969) Nuclear Science and Engineering 36, 295-303) on the neutron transmission; for several values of this opening we have calculated the neutron transmission probability for each detector position. This study allowed us to determine the optimal conditions of vacuum geometries to improve protection against neutrons. In the second part we considered a shield which consists of a slab and a two-legged vacuum channel with two horizontal parts. The spatial distribution of neutrons transmitted through the protection screen was determined. This distribution shows two peaks. The study was made for different distances between the two horizontal parts. We have determined the smallest distance between the two horizontal parts for which the two peaks can be resolved.

The albedo effect on neutron transmission probability.

The aim of this study is to evaluate the albedo effect on the neutron transmission probability through slab shields. For this reason we have considered an infinite homogeneous slab having a fixed thickness equal to 20 lambda (lambda is the mean free path of the neutron in the slab). This slab is characterized by the factor Ps (scattering probability) and contains a vacuum channel which is formed by two horizontal parts and an inclined one (David, M. C. (1962) Duc and Voids in shields. In Reactor Handbook, Vol. III, Part B, p. 166). The thickness of the vacuum channel is taken equal to 2 lambda. An infinite plane source of neutrons is placed on the first of the slab (left face) and detectors, having windows equal to 2 lambda, are placed on the second face of the slab (right face). Neutron histories are sampled by the Monte Carlo method (Booth, T. E. and Hendricks, J. S. (1994) Nuclear Technology 5) using exponential biasing in order to increase the Monte Carlo calculation efficiency (Levitt, L. B. (1968) Nuclear Science and Engineering 31, 500-504; Jehouani, A., Ghassoun, J. and Abouker, A. (1994) In Proceedings of the 6th International Symposium on Radiation Physics, Rabat, Morocco) and we have applied the statistical weight method which supposes that the neutron is born at the source with a unit statistical weight and after each collision this weight is corrected. For different values of the scattering probability and for different slopes of the inclined part of the channel we have calculated the neutron transmission probability for different positions of the detectors versus the albedo at the vacuum channel-medium interface. Some analytical representations are also presented for these transmission probabilities.

The neutron channeling phenomenon.

Shields, used for protection against radiation, are often pierced with vacuum channels for passing cables and other instruments for measurements. The neutron transmission through these shields is an unavoidable phenomenon. In this work we study and discuss the effect of channels on neutron transmission through shields. We consider an infinite homogeneous slab, with a fixed thickness (20 lambda, with lambda the mean free path of the neutron in the slab), which contains a vacuum channel. This slab is irradiated with an infinite source of neutrons on the left side and on the other side (right side) many detectors with windows equal to 2 lambda are placed in order to evaluate the neutron transmission probabilities (Khanouchi, A., Aboubekr, A., Ghassoun, J. and Jehouani, A. (1994) Rencontre Nationale des Jeunes Chercheurs en Physique. Casa Blanca Maroc; Khanouchi, A., Sabir, A., Ghassoun, J. and Jehouani, A. (1995) Premier Congré International des Intéractions Rayonnements Matière. Eljadida Maroc). The neutron history within the slab is simulated by the Monte Carlo method (Booth, T. E. and Hendricks, J. S. (1994) Nuclear Technology 5) and using the exponential biasing technique in order to improve the Monte Carlo calculation (Levitt, L. B. (1968) Nuclear Science and Engineering 31, 500-504; Jehouani, A., Ghassoun, J. and Aboubker, A. (1994) In Proceedings of the 6th International Symposium on Radiation Physics, Rabat, Morocco). Then different geometries of the vacuum channel have been studied. For each geometry we have determined the detector response and calculated the neutron transmission probability for different detector positions. This neutron transmission probability presents a peak for the detectors placed in front of the vacuum channel. This study allowed us to clearly identify the neutron channeling phenomenon. One application of our study is to detect vacuum defects in materials.