Robust -spectra shape parameter extraction
Phys. Rev. C 113, 024321 – Published 17 February, 2026
DOI: https://doi.org/10.1103/5mk5-6grr
Abstract
Stable and consistent experimental extraction of -shape functions, , is challenging. Comparing different experimental shapes to each other and to those predicted by theory in a consistent manner is difficult. This difficulty is compounded when different parametrizations of the -shape function are used. Usually some form of a power polynomial of the total electron energy is chosen for this parametrization, but choosing a power polynomial results in extracted coefficients that are highly correlated, with their physical meaning and numerical value dependent on the order of polynomial chosen. This is true for both theoretical and experimental coefficients, and leads to challenges when comparing coefficients between polynomials of different orders. Accurately representing the highly correlated uncertainties is both difficult and subtle and limits the underlying physical interpretation of shape-function parameters. In this manuscript an alternative approach based on orthogonal polynomials is offered. Orthogonal polynomials offer more stable coefficient extraction with less dependence on the order of the polynomial, allow for easier comparison between theory and experimental coefficients from different order polynomials, can offer reduced correlations between coefficients, while also offering simple physical meaning and clarifying statistical limits of the extracted coefficients.
