In 2012, D. K. Wehe and coauthors proposed a method of light yield amplification in scintillation detectors. A trivalent activator ion RE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> captures an electron produced by an incident particle in a scintillator and becomes a divalent rare earth ion RE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> . The scintillator is illuminated by laser photons that excite RE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ions, which quickly de-excite and generate light photons. By cyclically excitation RE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ions, one can obtain many light photons during any chosen accumulation time. Authors suggested that this method could remove the scintillation yield as a limiting factor of the energy resolution of scintillation detectors. This conclusion was based on the rather simplified theoretical examination of the pulse formation process in an amplified scintillator. In this work, the theory of branching cascade processes was applied to the description of the pulse formation process. The formulae for the energy resolution of an amplified scintillation detector and an ordinary scintillation detector were derived. From these formulae, it follows that the relative reduction in the energy resolution of the amplified scintillation detector with reference to the ordinary scintillation detector is less than a few percent.