X-ray peak shape description method and branch ratio constraint applied in spectrum unfolding

Background: Although counts under peaks in overlap region of multi-channel spectrum from X- and γ-rays can provide useful information, they are usually discarded because of much difficulty in being unfolded. The line-shape of X-ray peak could be asymmetric in left and right side caused by an energy-dependent detector efficiency. Purpose: To accurately fit out the shapes for the counts under the peaks, X- and γ-ray shapes should be described accurately, and all known information should be used as constraints for reliable results. Methods: With RooFit package, a method to describe the X-ray shape is proposed: take its intrinsic shape of X-ray described by a Lorentz function and multiplied by a detector efficiency function, then convoluted with a resolution function. Results: The results tested with the codes included in this paper show: the events number of input and output agrees within their statistical errors checked even with very heavily overlapped peaks unfolded with branch ratio constraint method. Conclusion: The method and the code introduced in this paper are feasible, and they can be used as an example to unfold overlap regions in X- and γ-ray multi-channel spectrum. (authors)