# Point-Kernel Code Development for Gamma-Ray Shielding Applications
## 1 Introduction  
The point-kernel technique (PK) applied to gamma radiation shielding is a very developed method, originating from the early days of nuclear reactors, nuclear power expansion and digital computers [1]. The Oak Ridge National Laboratory (ORNL) in USA was and still is one of the leading world facilities conducting pioneering research on computational and experimental aspects of radiation shielding, such as criteria and procedures for shield design, neutron-gamma attenuation, pool-type reactors, fast neutron removal, radiation streaming (albedos, ducts and voids), scattering from various structures, shield heating and weight optimization, shielding materials, analytical (ray tracing) andMonte Carlo (MC) methods, buildup \(B\)-factor concept, etc. The PK method for gamma radiation shielding is one of many successful methods developed over time, such as the Goldstein moments method, Spinney removal diffusion, corrective \(B\)-factor, etc. The basis of PK method is the linear superposition principle applied to distributed radiation sources, which are shielded with relatively simple shields, with point detector response being the objective of the calculation [2]. In a mathematical sense, the distributed source will produce a detector response equivalent to numerical integration of the radiation received from an equivalent number of point sources. In such a treatment, there is no interference between individual point sources, while inherent limitations of the PK method are inability to properly account for gamma scattering in shield and application of simple boundary conditions. Besides these restrictions, the PK method generally works for gamma-ray shielding problems (with inclusion of \(B\)-factor concept) and only specifically for fast neutron attenuation in hydrogenous medium (with definition of removal cross section) [1,2]. The common exposure \(B\)-factors used in most computer programs are for point gamma source in infinite medium and have a remarkable durability since they were introduced by [PERSON] in the late 1950s [3]. Tables of \(B\)-factors are readily available for gamma-ray energy and shield thickness (in mean free paths) for different materials and should be differentiated for point source and planar source. When performing the integration of distributed sources, it is often necessary to express \(B\)-factors in analytical form, and in this paper, we have used and compared several different forms. An excellent overview and historical evolution of analytical \(B\)-factor forms was carried out by [PERSON] [4], while supplementary data on \(B\)-factor parameters can be found in most appendices of typical radiation shielding handbooks [1]. Relatively recent publications and ongoing research in connection with \(B\)-factor concept in PK gamma-ray shielding can be seen in a variety of fields. The common intention of these trends is to achieve a better predictability of \(B\)-factors for complex composite shields, more flexible energy spectra, the integration of data-driven machine learning (ML) models trained on referent MC datasets, localized MC corrections for particle streaming, curvature corrections, multiphysics coupling, and so on. These efforts should well surpass traditional PK limitations of tabulated \(B\)-factors that have been used successfully for many decades in the radiation shielding community. [PERSON] et al. [5] developed a user-friendly PK program to estimate dose rates from 15 fixed geometry sources, 98 shield materials and compounds, several \(B\)-factor forms, 18 organ models from various exposure directions, internal decay library for 550 nuclides, and visualization options. [PERSON] et al. [6] showed how a support vector regression model, coming from a statistical learning theory, can be used for estimation of gamma-ray \(B\)-factors in multilayered shields.