Amongst various applications that experience a multi-directional particle source is the muon scattering tomography where a number of horizontal detectors of a limited angular acceptance conventionally track the cosmic-ray muons. In this study, we exhibit an elementary strategy that might be at disposal in diverse computational applications in the GEANT4 simulations with the purpose of hemispherical particle sources. To further detail, we initially generate random points on a spherical surface for a sphere of a practical radius by employing Gaussian distributions for the three components of the Cartesian coordinates, thereby obtaining a generating surface for the initial positions of the corresponding particles. Since we do not require the half bottom part of the produced spherical surface for our tomographic applications, we take the absolute value of the vertical component in the Cartesian coordinates by leading to a half-spherical shell, which is traditionally called a hemisphere. Last but not least, we direct the generated particles into the target material to be irradiated by favoring a selective momentum direction that is based on the vector construction between the random point on the hemispherical surface and the origin of the target material, hereby optimizing the particle loss through the source biasing. We also show a second scheme where the coordinate transformation is performed between the spherical coordinates and the Cartesian coordinates, and the above-mentioned procedure is applied to orient the generated muons towards the target material. In the end, a recipe hinged on the restrictive planes from our previous study is furthermore provided, and we incorporate our strategies by using G4ParticleGun in the GEANT4 code. While we plan to exert our strategy in the computational practices for muon scattering tomography, these source schemes might find its straightforward applications in different neighboring fields including but not limited to atmospheric sciences, space engineering, and astrophysics where a 3D particle source is a necessity for the modeling goals.

The structural characterization of the sealed or shielded nuclear materials constitutes an indispensable aspect that necessitates a careful transportation, a limited interaction, and under certain circumstances an on-site investigation for the nuclear fields including but not limited to nuclear waste management, nuclear forensics, and nuclear proliferation. To attain this purpose, among the promising non-destructive/non-hazardous techniques that are performed for the interrogation of the nuclear materials is the muon tomography where the target materials are discriminated by the interplay between the atomic number, the material density, and the material thickness on the basis of the scattering angle and the absorption in the course of the muon propagation within the target volume. In this study, we employ the Monte Carlo simulations by using the GEANT4 code to demonstrate the capability of muon tomography based on the dual-parameter analysis in the examination of the nuclear waste barrels. Our current hodoscope setup consists of three top and three bottom plastic scintillators made of polyvinyl toluene with the thickness of 0.4 cm, and the composite target material is a cylindrical nuclear waste drum with the height of 96 cm and the radius of 29.6 cm where the outermost layer is stainless steel with the lateral thickness of 3.2 cm and the filling material is ordinary concrete that encapsulates the nuclear materials of dimensions 20×20×20 cm3. By simulating with a narrow planar muon beam of 1×1 cm 2 over the uniform energy interval between 0.1 and 8 GeV, we determine the variation of the average scattering angle together with the standard deviation by utilizing a 0.5-GeV bin length, the counts of the scattering angle by using a 1-mrad step, and the number of the absorption events for the five prevalent nuclear materials starting from cobalt and ending in plutonium. Via the duo-parametric analysis that is founded on the scattering angle as well as the absorption in the present study, we show that the presence of the nuclear materials in the waste barrels is numerically visible in comparison with the concrete-filled waste drum without any nuclear material, and the muon tomography is capable of distinguishing these nuclear materials by coupling the information about the scattering angle and the number of absorption in the cases where one of these two parameters yields strong similarity for certain nuclear materials.