# Point-Kernel Code Development for Gamma-Ray Shielding Applications
## 1 Introduction
[PERSON] and [PERSON] [7] developed a stand-alone PK code similar to a well-known QADCGGP code, with geometry improvements in connection to fast reactors and radioactive plum release from a stack: multiple source shapes and energy distributions, hexagonal cylinder as a shield body, arbitrary source orientation, visualization of 3D objects, etc. [PERSON] and [PERSON] [8] developed an open-source program for estimating the thickness and height of depleted uranium shield for storing the gamma-ray point sources commonly used in nuclear industry and medicine, such as \({}^{60}\)Co, \({}^{137}\)Cs, \({}^{131}\)I and \({}^{99}\)Mo. [PERSON] et al. [9] implemented a voxelization algorithm using the PK method for modeling arbitrary shape 3D solids. The method is suitable for the radiological assessment of arbitrary shape components produced by cutting during decommissioning phase. [PERSON] et al. [10] developed a 3D model-based gamma-ray shielding package using a virtual reality platform for radiation dose assessment in nuclear safety and better usage of the PK method in interactive virtual simulations. [PERSON] and [PERSON] [11] developed 3D geometry and mesh modeling based on open-source finite element software with additional featuressuch as irregular source shapes, distributed gamma spectrum, modeling multilayered shields, and exporting results for advanced visualization. [PERSON] et al. [12] integrated deep neutral network for calculating the \(B\)-factor of multilayered shields. Important physical parameters of photon transport were trained using a neural network for \(B\)-factor prediction, resulting in a quick and accurate method for 3D radiation field calculation with broad application prospects. [PERSON] et al. [13] extended previous work to a GPU-based computing framework for advancing the computing power of virtual engine and proposed a novel voxelization algorithm of volumetric radioactive source. [PERSON] et al. [14] introduced NPTS-PK code supporting various \(B\)-factor calculations, acceleration of ray tracing, adaptive source geometry discretization and ability to handle a large-scale grid counting. [PERSON] et al. [15] developed a new 3D PK gamma shielding tool which proved to be proficient in calculating multi-layer buildup factors. The concept of buildup factors can be, at least in general, applied to both gamma rays and neutrons [16; 17], but for practical purposes it is mainly used for gamma-ray attenuation calculation as complex neutron interactions are more suitable for the MC method. The advance in machine learning and AI algorithms also gives an incentive to integrate such novelties inside the classical point-kernel paradigm [18]. It is evident how the \"historical\" PK method is used even today for integration with novel methods and technologies, boosting its potential for various applications. This paper presents one such effort, giving the theoretical and programming aspects of the analytical gamma flux solution on a point detector from several distributed sources of photons (line, disc, plane, sphere, volume slab, etc.) penetrating a slab shield. The used analytical \(B\)-factor forms are simple enough to allow the integration and derivation of closed-form solutions for gamma flux. These specific computational modules are currently being incorporated into a graphical user interface (GUI) with visualization options, developed for fast radiological characterization of simple shielding geometries. This will provide the user with a valuable supporting information in initial stage of shield design, often requiring many fast calculations for \"filtering\" out suitable composition of materials and/or geometry arrangement. After that, a more demanding particle transport simulation using production codes can provide the user with a detailed physical solution, capturing many microscopic phenomena which are out of the reach for the PK method. For that purpose, we have verified our selected PK shielding test cases with a referent MAVRIC MC solution [19].