A. Kaşkaş

The HN method for solving linear transport equation: theory and applications

Abstract The system of singular integral equations which is obtained from the integro-differential form of the linear transport equation using the Placzek lemma is solved. The exit distributions at the boundaries of the various media and the infinite medium Greens function are used. The process is applied to the half-space and finite slab problems. The neutron angular density in terms of singular eigenfunctions of the method of elementary solutions is also used to derive the same analytical expressions.

Discrimination of gamma rays due to inelastic neutron scattering in AGATA

Possibilities of discriminating neutrons and γ rays in the AGATA γ -ray tracking spectrometer have been investigated with the aim of reducing the background due to inelastic scattering of neutrons ...

Solution of the CN equations using singular eigenfunctions and applications

Abstract The third form of Boltzmann equation involves only the angular flux at the boundary while the usual transport equation deals with the angular flux at any point. The kernel of this equation is the infinite medium Greens function and satisfies the lineer transport equation. The method of solution of this equation is known as the CN method and is based on the Placzek lemma and depends on the calculation of the infinite medium Greens function. Here, the well-known form of the Greens function in terms of elementary solutions is used to solve the third form of the transport equation and applications for the half-space albedo problems for both isotropic and extremely anisotropic scatterings are given. Uncollided neutrons are also taken into account.

The slab albedo problem using singular eigenfunctions and the third form of the transport equation

Abstract The albedo and the transmission factor for slabs are obtained using the infinite medium Greens function in terms of the singular eigenfunctions in the third form of the transport equation. Our analytical results are simple as in the F N method and the convergence of the numerical results is as fast as in the C N method. Calculations are also carried out by various incoming angular fluxes and uncollided neutrons are taken into account. Our numerical results are in very good agreement with the results of the C N method and, as shown in the tables, are obtained up to the eighth order of approximation.

The solution of the third form transport equation using singular eigenfunctions: the slab and the sphere criticality problems

Abstract A singular eigenfunction approach is used to solve the classical slab and the sphere criticality problems. This approach is based on the use of the infinite medium Greens function which is obtained by the method of elementary solutions in the C N equations, that is in the third form of the transport equation. It is shown that our numerical results, even in the approximations of the lowest order are very accurate.

The singular eigenfunction method: the Milne problem for isotropic and extremely anisotropic scattering

Abstract In the C N method of solving the third form of the transport equation, the medium as a result of Placzek lemma is extended to infinity. Infinite medium Green function which is obtained by the Fourier transform technique is used and the method is applied to one velocity problems in plane and cylindrical geometries. As the result of physical applications of the C N method in different geometries, it is seen that the only difficulty lies in writting the expression of the Green function in a form easy to handle. In the new method of solving the third form of the transport equation (that we have generated recently), three methods, namely, C N , F N and the method of elementary solutions are considered, compared and the Green function in terms of the singular eigenfunctions is used. This method yields simple analytical expressions that can be solved numerically more efficiently than the C N method because the expression of the Green function is in the form easy to handle. Here this new method is applied to calculate the extrapolation length for the Milne problem which is a classical problem in astrophysics concerned with the diffusion of radiation through a stellar atmosphere for both isotropic and anisotropic scatterings. It is shown that the numerical results which are tabulated for selected cases are accurate even in the approximations of the lowest order and are in good agreement with the numerical results obtained by the other methods.

The singular eigenfunction analysis of the third form transport equation using half-range orthogonality relations: the half-space problems

Abstract The third form transport equation is solved using the infinite medium Greens functions in terms of the singular eigenfunctions of the method of elementary solutions and their half-range orthogonality relations. For simplicity, we consider only the Fredholm equation of the first kind and obtain the solution of the two problems for isotropic scattering: (i) the albedo problem for a source free half-space and (ii) the extrapolation length for the Milne problem. The convergence of the numerical results is fast as in C N method and the analytical expressions are simple for solving numerically.

Isotropic spherical source analysis for ocean optics.

Plane-to-point transformations are used to develop a version of the Hydrolight computer program with which to compute the spatial dependence of the irradiance and the scalar irradiance of the light field away from an isotropic point source deep within a spatially uniform ocean. The transformations are also used to derive analytic approximations for determining the diffuse attenuation coefficient and the mean cosine of the radiance far from an isotropic point source. Approximations for determining the asymptotic diffuse attenuation coefficient from measurements at only two distances far from the source are derived and numerically tested with the modified version of the Hydrolight computer program. New spatial integrals of the outward irradiance are also derived that provide a different way for correlating the inherent optical properties of seawater.

An application of transport theory for optical oceanography: the isotropic point source

Transport theory methods can be applied to optical oceanography to compute the spatial dependence of irradiance and scalar irradiance of the light field from an isotropic point source deep within a spatially uniform ocean. The infinite medium Greens function for plane geometry is used to obtain scalar and plane irradiances. The isotropic point source expressions can be obtained from the isotropic plane source solutions using plane-to-point transformations. Then the analytical solutions for the diffuse attenuation coefficient and the mean cosine far from the isotropic point source are obtained. The problem is numerically solved for the Henyey–Greenstein phase function.

Identification and rejection of scattered neutrons in AGATA

gamma Rays and neutrons, emitted following spontaneous fission of Cf-252, were measured in an AGATA experiment performed at INFN Laboratori Nazionali di Legnaro in Italy. The setup consisted of four AGATA triple cluster detectors (12 36 fold segmented high purity germanium crystals), placed at a distance of 50 cm from the source, and 16 HELENA BaF2 detectors. The aim of the experiment was to study the interaction of neutrons in the segmented high purity germanium detectors of AGATA and to investigate the possibility to discriminate neutrons and gamma rays with the gamma-ray tracking technique. The BaF2 detectors were used for a time measurement, which gave an independent discrimination of neutrons and gamma rays and which was used to optimise the gamma-ray tracking based neutron rejection methods. It was found that standard gamma-ray tracking, without any additional neutron rejection features, eliminates effectively most of the interaction points clue to recoiling Ge nuclei after elastic scattering of neutrons. Standard Cracking rejects also a significant amount of the events due to inelastic scattering of neutrons in the germanium crystals. Further enhancements of the neutron rejection was obtained by setting conditions on the following quantities, which were evaluated for each event by the Cracking algorithm: energy of the first and second interaction point, difference in the calculated incoming direction of the gamma ray, and figure-of-merit value. The experimental results of Cracking with neutron rejection agree rather well with GEANT4 simulations.