Validation of new mathematical formulae for calculating well-type gamma-ray detector efficiencies

In this study, direct mathematical formulae are found for measuring the full-energy peak efficiency of an HPGe well-type detector, and the values of the measured efficiencies are compared with published studies on the old experimental and theoretical methods with good agreement. In this new approach, the path length d(θ, φ) is derived as a function of the polar angle θ and the azimuthal angle φ, which will reduce the mathematical formulae to a simple and compact shape.